=2:\n return map(int,sys.stdin.readline().split()) \ndef makedict(var):\n return dict(Counter(var))\ntestcases=1\n# testcases=vary(1)\nfor _ in range(testcases):\n n,k=vary(2)\n temp=k\n num=[i for i in range(1,n+1)]\n j=0\n for i in range(k+1):\n if i%2==0:\n print(num[j],end=\" \")\n j+=1\n else:\n print(num[k],end=\" \")\n k-=1\n for i in range(temp+1,n):\n print(num[i],end=\" \")\n\n\n \n\n "}}},{"rowIdx":668,"cells":{"id":{"kind":"string","value":"507_C. Guess Your Way Out!_3149"},"description":{"kind":"string","value":"Amr bought a new video game \"Guess Your Way Out!\". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. \n\nLet's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≤ n ≤ 2h, the player doesn't know where the exit is so he has to guess his way out!\n\nAmr follows simple algorithm to choose the path. Let's consider infinite command string \"LRLRLRLRL...\" (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:\n\n * Character 'L' means \"go to the left child of the current node\"; \n * Character 'R' means \"go to the right child of the current node\"; \n * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; \n * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; \n * If he reached a leaf node that is not the exit, he returns to the parent of the current node; \n * If he reaches an exit, the game is finished. \n\n\n\nNow Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?\n\nInput\n\nInput consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2h).\n\nOutput\n\nOutput a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.\n\nExamples\n\nInput\n\n1 2\n\n\nOutput\n\n2\n\nInput\n\n2 3\n\n\nOutput\n\n5\n\nInput\n\n3 6\n\n\nOutput\n\n10\n\nInput\n\n10 1024\n\n\nOutput\n\n2046\n\nNote\n\nA perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. \n\nFollowing picture illustrates the sample test number 3. Nodes are labeled according to the order of visit.\n\n"},"code":{"kind":"string","value":"import sys\ndef main():\n rdl = list(map(int,input().split()))\n obx(rdl[0],rdl[1],0,1)\ndef obx(lvl, ind, kl, current):\n if lvl ==0:\n print(int(kl))\n sys.exit()\n all = 0\n for i in range(lvl+1):\n all += 2**i\n all -= 1\n\n if ind > (2**(lvl))/2:\n if current == 1:\n kl += all / 2 + 1\n else: \n kl += 1\n current *= -1\n obx(lvl-1,ind-(2**lvl)/2,kl,current)\n else: \n if current == -1:\n kl += all/2+1\n else: \n kl += 1\n current *= -1\n obx(lvl-1,ind,kl,current)\n \nmain()"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"1 2\\n\",\n \"10 1024\\n\",\n \"3 6\\n\",\n \"2 3\\n\",\n \"49 295606900104348\\n\",\n \"1 1\\n\",\n \"29 113463931\\n\",\n \"40 615535158153\\n\",\n \"50 905353992267944\\n\",\n \"22 3343393\\n\",\n \"20 589266\\n\",\n \"19 12783\\n\",\n \"30 414940886\\n\",\n \"32 3786259360\\n\",\n \"35 12080044014\\n\",\n \"13 4796\\n\",\n \"50 562949953421312\\n\",\n \"33 2599588275\\n\",\n \"16 21395\\n\",\n \"13 154\\n\",\n \"14 2334\\n\",\n \"24 14428281\\n\",\n \"7 31\\n\",\n \"21 1687606\\n\",\n \"35 31233562499\\n\",\n \"42 1042128038474\\n\",\n \"24 3543583\\n\",\n \"11 349\\n\",\n \"28 72803174\\n\",\n \"10 359\\n\",\n \"50 375299968947542\\n\",\n \"45 17519319833295\\n\",\n \"39 457181784666\\n\",\n \"4 14\\n\",\n \"17 80239\\n\",\n \"29 19827102\\n\",\n \"38 99361414961\\n\",\n \"20 742273\\n\",\n \"50 844424930131968\\n\",\n \"12 955\\n\",\n \"31 1819651953\\n\",\n \"18 153276\\n\",\n \"11 550\\n\",\n \"38 262402936512\\n\",\n \"8 19\\n\",\n \"12 2715\\n\",\n \"29 524109003\\n\",\n \"8 204\\n\",\n \"4 13\\n\",\n \"50 1125899906842624\\n\",\n \"10 577\\n\",\n \"40 874338951117\\n\",\n \"15 15512\\n\",\n \"3 5\\n\",\n \"9 43\\n\",\n \"25 678676\\n\",\n \"33 2696188969\\n\",\n \"3 8\\n\",\n \"46 34999315964173\\n\",\n \"6 40\\n\",\n \"50 1\\n\",\n \"27 109473899\\n\",\n \"22 3809417\\n\",\n \"19 13130\\n\",\n \"30 310686113\\n\",\n \"32 1974078185\\n\",\n \"13 1486\\n\",\n \"50 865276010242491\\n\",\n \"33 3120492793\\n\",\n \"28 21395\\n\",\n \"13 98\\n\",\n \"16 2334\\n\",\n \"24 720510\\n\",\n \"7 48\\n\",\n \"21 1890748\\n\",\n \"42 1454146769415\\n\",\n \"40 3543583\\n\",\n \"11 14\\n\",\n \"28 106984283\\n\",\n \"50 570076444813889\\n\",\n \"8 14\\n\",\n \"29 7131063\\n\",\n \"38 117354504358\\n\",\n \"13 955\\n\",\n \"31 1270150511\\n\",\n \"18 216017\\n\",\n \"11 19\\n\",\n \"38 90275483043\\n\",\n \"9 19\\n\",\n \"12 2442\\n\",\n \"5 13\\n\",\n \"10 50\\n\",\n \"15 26098\\n\",\n \"3 1\\n\",\n \"9 17\\n\",\n \"33 678676\\n\",\n \"3 3\\n\",\n \"46 46821697614159\\n\",\n \"6 45\\n\",\n \"9 1\\n\",\n \"27 27445737\\n\",\n \"3 4\\n\",\n \"13 147\\n\",\n \"33 3847539484\\n\",\n \"28 1168\\n\",\n \"8 98\\n\",\n \"13 2334\\n\",\n \"43 720510\\n\",\n \"7 53\\n\",\n \"21 588140\\n\",\n \"42 2844706328971\\n\",\n \"40 3307405\\n\",\n \"11 26\\n\",\n \"28 11483602\\n\",\n \"50 774178672041300\\n\",\n \"29 7444530\\n\",\n \"24 216017\\n\",\n \"38 162204501579\\n\",\n \"18 19\\n\",\n \"12 3307\\n\",\n \"5 17\\n\",\n \"16 50\\n\",\n \"15 15212\\n\",\n \"9 13\\n\",\n \"41 678676\\n\",\n \"5 3\\n\",\n \"6 58\\n\",\n \"14 1\\n\",\n \"27 48974904\\n\",\n \"6 4\\n\",\n \"13 207\\n\",\n \"33 7345333483\\n\",\n \"28 924\\n\",\n \"8 54\\n\",\n \"17 2334\\n\",\n \"43 9221\\n\",\n \"14 53\\n\",\n \"21 171538\\n\",\n \"40 2419461\\n\",\n \"28 7136641\\n\",\n \"29 6206402\\n\",\n \"24 401960\\n\",\n \"14 19\\n\",\n \"38 180588510466\\n\",\n \"17 19\\n\",\n \"12 1627\\n\",\n \"5 26\\n\",\n \"14 50\\n\",\n \"15 18949\\n\",\n \"2 2\\n\",\n \"9 6\\n\",\n \"49 678676\\n\",\n \"7 3\\n\",\n \"9 58\\n\",\n \"27 14496059\\n\",\n \"6 7\\n\",\n \"17 207\\n\",\n \"16 924\\n\",\n \"30 2334\\n\",\n \"43 7927\\n\",\n \"7 19\\n\",\n \"2 1\\n\"\n ],\n \"output\": [\n \"2\\n\",\n \"2046\\n\",\n \"10\\n\",\n \"5\\n\",\n \"820858833984106\\n\",\n \"1\\n\",\n \"347736449\\n\",\n \"1572205271927\\n\",\n \"1871650493613618\\n\",\n \"7009189\\n\",\n \"1505684\\n\",\n \"503251\\n\",\n \"372407442\\n\",\n \"8003335020\\n\",\n \"2415167450\\n\",\n \"10298\\n\",\n \"562949953421312\\n\",\n \"1357401405\\n\",\n \"2899\\n\",\n \"7770\\n\",\n \"9440\\n\",\n \"26969983\\n\",\n \"95\\n\",\n \"3522472\\n\",\n \"60951693197\\n\",\n \"3195908899134\\n\",\n \"10865127\\n\",\n \"1057\\n\",\n \"50649698\\n\",\n \"91\\n\",\n \"50\\n\",\n \"17381304930499\\n\",\n \"830699159852\\n\",\n \"26\\n\",\n \"177237\\n\",\n \"478963048\\n\",\n \"28342263489\\n\",\n \"1182599\\n\",\n \"1407374883553280\\n\",\n \"2871\\n\",\n \"3412135549\\n\",\n \"328766\\n\",\n \"408\\n\",\n \"519008349260\\n\",\n \"205\\n\",\n \"4185\\n\",\n \"1052258991\\n\",\n \"422\\n\",\n \"27\\n\",\n \"2251799813685246\\n\",\n \"1345\\n\",\n \"1800799608767\\n\",\n \"14926\\n\",\n \"11\\n\",\n \"391\\n\",\n \"31527640\\n\",\n \"505562011\\n\",\n \"14\\n\",\n \"34646522010881\\n\",\n \"88\\n\",\n \"1125899906842623\\n\",\n \"209022797\\n\",\n \"7446127\\n\",\n \"502318\\n\",\n \"141700399\\n\",\n \"1627513051\\n\",\n \"4528\\n\",\n \"1909734402989387\\n\",\n \"905768705\\n\",\n \"268372819\\n\",\n \"8032\\n\",\n \"58592\\n\",\n \"14744962\\n\",\n \"18\\n\",\n \"3839292\\n\",\n \"35665512973\\n\",\n \"1099505715687\\n\",\n \"2028\\n\",\n \"90139167\\n\",\n \"1677245864919377\\n\",\n \"236\\n\",\n \"524988209\\n\",\n \"77454057000\\n\",\n \"6967\\n\",\n \"2736971871\\n\",\n \"402327\\n\",\n \"1997\\n\",\n \"4068763953\\n\",\n \"461\\n\",\n \"5482\\n\",\n \"13\\n\",\n \"944\\n\",\n \"53746\\n\",\n \"7\\n\",\n \"465\\n\",\n \"8587907800\\n\",\n \"3\\n\",\n \"70649864678473\\n\",\n \"77\\n\",\n \"511\\n\",\n \"85501397\\n\",\n \"4\\n\",\n \"7759\\n\",\n \"3489833704\\n\",\n \"268431988\\n\",\n \"96\\n\",\n \"1248\\n\",\n \"8796090989954\\n\",\n \"39\\n\",\n \"455758\\n\",\n \"4694418230653\\n\",\n \"1099505952629\\n\",\n \"2008\\n\",\n \"235845018\\n\",\n \"1336844846897188\\n\",\n \"527259574\\n\",\n \"16393113\\n\",\n \"350905120053\\n\",\n \"262093\\n\",\n \"6855\\n\",\n \"47\\n\",\n \"65456\\n\",\n \"12876\\n\",\n \"493\\n\",\n \"2199021228760\\n\",\n \"27\\n\",\n \"118\\n\",\n \"16383\\n\",\n \"12725174\\n\",\n \"60\\n\",\n \"7857\\n\",\n \"13447910099\\n\",\n \"268434264\\n\",\n \"166\\n\",\n \"124128\\n\",\n \"8796092994553\\n\",\n \"16295\\n\",\n \"1596886\\n\",\n \"1099504468735\\n\",\n \"256561545\\n\",\n \"521939912\\n\",\n \"16095648\\n\",\n \"16333\\n\",\n \"282994276620\\n\",\n \"131021\\n\",\n \"1305\\n\",\n \"54\\n\",\n \"16304\\n\",\n \"41465\\n\",\n \"2\\n\",\n \"500\\n\",\n \"562949951394520\\n\",\n \"123\\n\",\n \"440\\n\",\n \"110668991\\n\",\n \"55\\n\",\n \"130737\\n\",\n \"64344\\n\",\n \"1073734880\\n\",\n \"8796093013227\\n\",\n \"77\\n\",\n \"3\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nAmr bought a new video game \"Guess Your Way Out!\". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. \n\nLet's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≤ n ≤ 2h, the player doesn't know where the exit is so he has to guess his way out!\n\nAmr follows simple algorithm to choose the path. Let's consider infinite command string \"LRLRLRLRL...\" (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:\n\n * Character 'L' means \"go to the left child of the current node\"; \n * Character 'R' means \"go to the right child of the current node\"; \n * If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node; \n * If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command; \n * If he reached a leaf node that is not the exit, he returns to the parent of the current node; \n * If he reaches an exit, the game is finished. \n\n\n\nNow Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?\n\nInput\n\nInput consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2h).\n\nOutput\n\nOutput a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.\n\nExamples\n\nInput\n\n1 2\n\n\nOutput\n\n2\n\nInput\n\n2 3\n\n\nOutput\n\n5\n\nInput\n\n3 6\n\n\nOutput\n\n10\n\nInput\n\n10 1024\n\n\nOutput\n\n2046\n\nNote\n\nA perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. \n\nFollowing picture illustrates the sample test number 3. Nodes are labeled according to the order of visit.\n\n\n\n### Input:\n1 2\n\n### Output:\n2\n\n\n### Input:\n10 1024\n\n### Output:\n2046\n\n\n### Code:\nimport sys\ndef main():\n rdl = list(map(int,input().split()))\n obx(rdl[0],rdl[1],0,1)\ndef obx(lvl, ind, kl, current):\n if lvl ==0:\n print(int(kl))\n sys.exit()\n all = 0\n for i in range(lvl+1):\n all += 2**i\n all -= 1\n\n if ind > (2**(lvl))/2:\n if current == 1:\n kl += all / 2 + 1\n else: \n kl += 1\n current *= -1\n obx(lvl-1,ind-(2**lvl)/2,kl,current)\n else: \n if current == -1:\n kl += all/2+1\n else: \n kl += 1\n current *= -1\n obx(lvl-1,ind,kl,current)\n \nmain()"}}},{"rowIdx":669,"cells":{"id":{"kind":"string","value":"556_D. Case of Fugitive_3152"},"description":{"kind":"string","value":"Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.\n\nThe only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≤ i ≤ n - 1.\n\nTo reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≤ x ≤ ri, li + 1 ≤ y ≤ ri + 1 and y - x = a. \n\nThe detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.\n\nInput\n\nThe first line contains integers n (2 ≤ n ≤ 2·105) and m (1 ≤ m ≤ 2·105) — the number of islands and bridges.\n\nNext n lines each contain two integers li and ri (1 ≤ li ≤ ri ≤ 1018) — the coordinates of the island endpoints.\n\nThe last line contains m integer numbers a1, a2, ..., am (1 ≤ ai ≤ 1018) — the lengths of the bridges that Andrewid got.\n\nOutput\n\nIf it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line \"No\" (without the quotes), otherwise print in the first line \"Yes\" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. \n\nIf there are multiple correct answers, print any of them. Note that in this problem it is necessary to print \"Yes\" and \"No\" in correct case.\n\nExamples\n\nInput\n\n4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8\n\n\nOutput\n\nYes\n2 3 1 \n\n\nInput\n\n2 2\n11 14\n17 18\n2 9\n\n\nOutput\n\nNo\n\n\nInput\n\n2 1\n1 1\n1000000000000000000 1000000000000000000\n999999999999999999\n\n\nOutput\n\nYes\n1 \n\nNote\n\nIn the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14.\n\nIn the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist."},"code":{"kind":"string","value":"#!/usr/bin/env python\n# 556D_fug.py - Codeforces.com 556D Fug quiz\n#\n# Copyright (C) 2015 Sergey\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n# http://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\n\"\"\"\nInput\n\nThe first line contains integers n and m - the number of islands and bridges.\n\nNext n lines each contain two integers li and ri - the coordinates of the\nisland endpoints.\n\nThe last line contains m integer numbers a1..am - the lengths of the bridges\nthat Andrewid got.\nOutput\n\nIf it is impossible to place a bridge between each pair of adjacent islands\nin the required manner, print on a single line \"No\" (without the quotes)\n, otherwise print in the first line \"Yes\" (without the quotes), and in the\nsecond line print n-1 numbers b1, bn-1, which mean that between islands\ni and i+1 there must be used a bridge number bi.\n\nIf there are multiple correct answers, print any of them. Note that in this\nproblem it is necessary to print \"Yes\" and \"No\" in correct case\n\"\"\"\n\n# Standard modules\nimport unittest\nimport sys\nimport re\n\n# Additional modules\nimport bisect\n\n###############################################################################\n# Fastlist Class\n###############################################################################\n\n\nclass Fastlist(object):\n \"\"\" Fastlist representation \"\"\"\n\n def __init__(self, l=[], load=5000, sorted=0):\n self._load = load\n self._sorted = sorted\n self._lists = []\n self._starts = []\n self._mins = []\n self._insert_list()\n self._irev = 0\n self.extend(l)\n\n def _index_location(self, index):\n if len(self._lists[0]) == 0:\n raise IndexError(\"List index out of range\")\n if index == 0:\n return (0, 0)\n if index == -1:\n return (len(self._lists) - 1, len(self._lists[-1]) - 1)\n if self._sorted:\n raise RuntimeError(\"No index access to the sorted list, exc 0, -1\")\n length = len(self)\n if index < 0:\n index = length + index\n if index >= length:\n raise IndexError(\"List index out of range\")\n il = bisect.bisect_right(self._starts, index) - 1\n return (il, index - self._starts[il])\n\n def _insert_list(self, il=None):\n if il is None:\n il = len(self._lists)\n self._lists.insert(il, [])\n if self._sorted:\n if il == 0:\n self._mins.insert(il, None)\n else:\n self._mins.insert(il, self._lists[il-1][-1])\n else:\n if il == 0:\n self._starts.insert(il, 0)\n else:\n start = self._starts[il-1] + len(self._lists[il-1])\n self._starts.insert(il, start)\n\n def _del_list(self, il):\n del self._lists[il]\n if self._sorted:\n del self._mins[il]\n else:\n del self._starts[il]\n\n def _rebalance(self, il):\n illen = len(self._lists[il])\n if illen >= self._load * 2:\n self._insert_list(il)\n self._even_lists(il)\n if illen <= self._load * 0.2:\n if il != 0:\n self._even_lists(il-1)\n elif len(self._lists) > 1:\n self._even_lists(il)\n\n def _even_lists(self, il):\n tot = len(self._lists[il]) + len(self._lists[il+1])\n if tot < self._load * 1:\n self._lists[il] += self._lists[il+1]\n self._del_list(il+1)\n if self._sorted:\n self._mins[il] = self._lists[il][0]\n else:\n half = tot//2\n ltot = self._lists[il] + self._lists[il+1]\n self._lists[il] = ltot[:half]\n self._lists[il+1] = ltot[half:]\n if self._sorted:\n self._mins[il] = self._lists[il][0]\n self._mins[il+1] = self._lists[il+1][0]\n else:\n self._starts[il+1] = self._starts[il] + len(self._lists[il])\n\n def _obj_location(self, obj, l=0):\n if not self._sorted:\n raise RuntimeError(\"No by value access to an unserted list\")\n il = 0\n if len(self._mins) > 1 and obj > self._mins[0]:\n if l:\n il = bisect.bisect_left(self._mins, obj) - 1\n else:\n il = bisect.bisect_right(self._mins, obj) - 1\n if l:\n ii = bisect.bisect_left(self._lists[il], obj)\n else:\n ii = bisect.bisect_right(self._lists[il], obj)\n if ii == len(self._lists[il]) and il != len(self._lists) - 1:\n ii = 0\n il += 1\n return (il, ii)\n\n def insert(self, index, obj):\n (il, ii) = self._index_location(index)\n self._lists[il].insert(ii, obj)\n for j in range(il + 1, len(self._starts)):\n self._starts[j] += 1\n self._rebalance(il)\n\n def append(self, obj):\n if len(self._lists[-1]) >= self._load:\n self._insert_list()\n self._lists[-1].append(obj)\n if self._sorted and self._mins[0] is None:\n self._mins[0] = self._lists[0][0]\n\n def extend(self, iter):\n for n in iter:\n self.append(n)\n\n def pop(self, index=None):\n if index is None:\n index = -1\n (il, ii) = self._index_location(index)\n item = self._lists[il].pop(ii)\n if self._sorted:\n if ii == 0 and len(self._lists[il]) > 0:\n self._mins[il] = self._lists[il][0]\n else:\n for j in range(il + 1, len(self._starts)):\n self._starts[j] -= 1\n self._rebalance(il)\n return item\n\n def clear(self):\n self._lists.clear()\n self._starts.clear()\n self._mins.clear()\n self._insert_list()\n\n def as_list(self):\n return sum(self._lists, [])\n\n def insort(self, obj, l=0):\n (il, ii) = self._obj_location(obj, l)\n self._lists[il].insert(ii, obj)\n if ii == 0:\n self._mins[il] = obj\n self._rebalance(il)\n\n def add(self, obj):\n if self._sorted:\n self.insort(obj)\n else:\n self.append(obj)\n\n def insort_left(self, obj):\n self.insort(obj, l=1)\n\n def lower_bound(self, obj):\n (self._il, self._ii) = self._obj_location(obj, l=1)\n return self\n\n def upper_bound(self, obj):\n (self._il, self._ii) = self._obj_location(obj)\n return self\n\n def __str__(self):\n return str(self.as_list())\n\n def __setitem__(self, index, obj):\n if isinstance(index, int):\n (il, ii) = self._index_location(index)\n self._lists[il][ii] = obj\n elif isinstance(index, slice):\n raise RuntimeError(\"Slice assignment is not supported\")\n\n def __getitem__(self, index):\n if isinstance(index, int):\n (il, ii) = self._index_location(index)\n return self._lists[il][ii]\n elif isinstance(index, slice):\n rg = index.indices(len(self))\n if rg[0] == 0 and rg[1] == len(self) and rg[2] == 1:\n return self.as_list()\n return [self.__getitem__(index) for index in range(*rg)]\n\n def __iadd__(self, obj):\n if self._sorted:\n [self.insort(n) for n in obj]\n else:\n [self.append(n) for n in obj]\n return self\n\n def __delitem__(self, index):\n if isinstance(index, int):\n self.pop(index)\n elif isinstance(index, slice):\n rg = index.indices(len(self))\n [self.__delitem__(rg[0]) for i in range(*rg)]\n\n def __len__(self):\n if self._sorted:\n return sum([len(l) for l in self._lists])\n return self._starts[-1] + len(self._lists[-1])\n\n def __contains__(self, obj):\n if self._sorted:\n it = self.lower_bound(obj)\n return not it.iter_end() and obj == it.iter_getitem()\n else:\n for n in self:\n if obj == n:\n return True\n return False\n\n def __bool__(self):\n return len(self._lists[0]) != 0\n\n def __iter__(self):\n self._il = self._ii = self._irev = 0\n return self\n\n def __reversed__(self):\n self._il = len(self._lists) - 1\n self._ii = len(self._lists[self._il]) - 1\n self._irev = 1\n return self\n\n def __next__(self):\n if self._il in (-1, len(self._lists)) or len(self._lists[0]) == 0:\n raise StopIteration(\"Iteration stopped\")\n item = self._lists[self._il][self._ii]\n if not self._irev:\n self._ii += 1\n if self._ii == len(self._lists[self._il]):\n self._il += 1\n self._ii = 0\n else:\n self._ii -= 1\n if self._ii == 0:\n self._il -= 1\n self._ii = len(self._lists[self._il])\n return item\n\n def iter_getitem(self):\n return self._lists[self._il][self._ii]\n\n def iter_end(self):\n return (self._il == len(self._lists) - 1 and\n self._ii == len(self._lists[self._il]))\n\n def iter_del(self):\n self.iter_pop()\n\n def iter_pop(self):\n item = self._lists[self._il].pop(self._ii)\n if self._sorted:\n if self._ii == 0 and len(self._lists[self._il]) > 0:\n self._mins[self._il] = self._lists[self._il][0]\n else:\n for j in range(self._il + 1, len(self._starts)):\n self._starts[j] -= 1\n self._rebalance(self._il)\n return item\n\n\n###############################################################################\n# Fug Class\n###############################################################################\n\n\nclass Fug:\n \"\"\" Fug representation \"\"\"\n\n def __init__(self, args):\n \"\"\" Default constructor \"\"\"\n self.gsrt = args[0]\n self.asrt = args[1]\n self.gn = args[2]\n self.result = [0]*self.gn\n self.a = Fastlist(self.asrt, load=500, sorted=1)\n\n def calculate(self):\n \"\"\" Main calcualtion function of the class \"\"\"\n\n for i in range(self.gn):\n g = self.gsrt[i]\n it = self.a.lower_bound((g[1], 0))\n if not it.iter_end():\n alb = it.iter_getitem()\n if alb[0] > g[0]:\n return \"No\"\n self.result[g[2]] = alb[1]+1\n it.iter_del()\n else:\n return \"No\"\n\n answer = \"Yes\\n\" + \" \".join(str(n) for n in self.result)\n\n return answer\n\n\n###############################################################################\n# Executable code\n###############################################################################\n\n\ndef get_inputs(test_inputs=None):\n\n it = iter(test_inputs.split(\"\\n\")) if test_inputs else None\n\n def uinput():\n \"\"\" Unit-testable input function wrapper \"\"\"\n if it:\n return next(it)\n else:\n return sys.stdin.readline()\n\n # Getting string inputs. Place all uinput() calls here\n num = [int(s) for s in uinput().split()]\n gaps = []\n prevli = [int(s) for s in uinput().split()]\n for i in range(num[0] - 1):\n li = [int(s) for s in uinput().split()]\n min = li[0] - prevli[1]\n max = li[1] - prevli[0]\n gaps.append((max, min, i))\n prevli = li\n alist = [(int(s), i) for i, s in enumerate(uinput().split())]\n\n # Decoding inputs into a list\n\n inputs = [sorted(gaps), sorted(alist), num[0]-1]\n\n return inputs\n\n\ndef calculate(test_inputs=None):\n \"\"\" Base class calculate method wrapper \"\"\"\n return Fug(get_inputs(test_inputs)).calculate()\n\n\n###############################################################################\n# Unit Tests\n###############################################################################\n\n\nclass unitTests(unittest.TestCase):\n\n def test_sample_tests(self):\n \"\"\" Quiz sample tests. Add \\n to separate lines \"\"\"\n\n # Sample test 1\n test = \"4 4\\n1 4\\n7 8\\n9 10\\n12 14\\n4 5 3 8\"\n self.assertEqual(calculate(test), \"Yes\\n2 3 1\")\n self.assertEqual(\n get_inputs(test),\n [[(3, 1, 1), (5, 2, 2), (7, 3, 0)],\n [(3, 2), (4, 0), (5, 1), (8, 3)], 3])\n\n # My tests\n test = \"5 5\\n1 1\\n2 7\\n8 8\\n10 10\\n16 16\\n1 1 5 6 2\"\n self.assertEqual(calculate(test), \"Yes\\n1 2 5 4\")\n\n # Other tests\n test = \"2 2\\n11 14\\n17 18\\n2 9\"\n self.assertEqual(calculate(test), \"No\")\n\n # Other tests\n test = (\n \"2 1\\n1 1\\n1000000000000000000 1000000000000000000\" +\n \"\\n999999999999999999\")\n self.assertEqual(calculate(test), \"Yes\\n1\")\n\n test = (\"5 9\\n1 2\\n3 3\\n5 7\\n11 13\\n14 20\\n2 3 4 10 6 2 6 9 5\")\n self.assertEqual(calculate(test), \"Yes\\n1 6 3 2\")\n\n size = 200000\n test = str(size) + \" \" + str(size) + \"\\n\"\n x = size*1000\n for i in range(size):\n test += str(x) + \" \" + str(x + i + 1) + \"\\n\"\n x += 2 * (i + 1)\n for i in reversed(range(size)):\n test += str(i) + \" \"\n self.assertEqual(calculate(test)[0], \"Y\")\n\n def test_Fug_class__basic_functions(self):\n \"\"\" Fug class basic functions testing \"\"\"\n\n # Constructor test\n d = Fug([[(1, 3, 1), (2, 5, 2), (3, 7, 0)],\n [(3, 2), (4, 0), (5, 1), (8, 3)], 3])\n\n # Sort bridges\n self.assertEqual(d.asrt[0], (3, 2))\n\n # Sort Gaps\n self.assertEqual(d.gsrt[0], (1, 3, 1))\n\nif __name__ == \"__main__\":\n\n # Avoiding recursion limitaions\n sys.setrecursionlimit(100000)\n\n if sys.argv[-1] == \"-ut\":\n unittest.main(argv=[\" \"])\n\n # Print the result string\n sys.stdout.write(calculate())\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4 4\\n1 4\\n7 8\\n9 10\\n12 14\\n4 5 3 8\\n\",\n \"2 2\\n11 14\\n17 18\\n2 9\\n\",\n \"2 1\\n1 1\\n1000000000000000000 1000000000000000000\\n999999999999999999\\n\",\n \"2 1\\n1 1\\n100 100\\n5\\n\",\n \"3 2\\n1000000000000000 1000000000000000\\n3000000000000000 4000000000000000\\n6000000000000000 7000000000000000\\n2000000000000000 4000000000000000\\n\",\n \"6 9\\n1 2\\n8 16\\n21 27\\n31 46\\n49 57\\n59 78\\n26 27 28 13 2 4 2 2 24\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 36\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 100\\n4 7 6 1 5 4 3 1 5 2\\n\",\n \"6 9\\n1 4\\n10 18\\n23 29\\n33 43\\n46 57\\n59 77\\n11 32 32 19 20 17 32 24 32\\n\",\n \"3 2\\n1 5\\n6 12\\n14 100000000000\\n10000000000 4\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 20\\n9 10 2 9 10 4 9 9 9 10\\n\",\n \"2 1\\n1 2\\n5 6\\n1\\n\",\n \"5 9\\n1 2\\n3 3\\n5 7\\n11 13\\n14 20\\n2 3 4 10 6 2 6 9 5\\n\",\n \"3 2\\n1000000000000000 1000000000000000\\n3000000000000000 4000000000000000\\n6000000000000000 7000000000000000\\n3052752506693368 4000000000000000\\n\",\n \"6 9\\n1 4\\n10 18\\n23 29\\n33 43\\n46 57\\n59 77\\n14 32 32 19 20 17 32 24 32\\n\",\n \"3 2\\n1000000000000000 1000000000000001\\n3000000000000000 4000000000000000\\n6000000000000000 7000000000000000\\n2000000000000000 4000000000000000\\n\",\n \"5 9\\n1 2\\n3 3\\n5 7\\n11 13\\n14 20\\n2 3 4 20 6 2 6 9 5\\n\",\n \"2 2\\n11 14\\n15 18\\n2 9\\n\",\n \"6 9\\n1 2\\n8 16\\n21 27\\n31 46\\n49 57\\n59 78\\n26 27 28 26 2 4 2 2 24\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 36\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 5 2\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 29\\n9 10 2 9 10 4 9 9 9 10\\n\",\n \"5 9\\n1 2\\n3 2\\n5 7\\n11 13\\n14 20\\n2 3 4 10 6 2 6 9 5\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 5 2\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 29\\n9 10 2 9 10 4 9 9 13 10\\n\",\n \"5 9\\n1 2\\n3 2\\n5 7\\n16 13\\n14 20\\n2 3 4 10 6 2 6 9 5\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 29\\n9 11 2 9 10 4 9 9 13 10\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"5 10\\n1 2\\n3 1\\n5 7\\n11 13\\n14 29\\n9 11 2 9 10 4 9 9 13 10\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"5 10\\n1 2\\n3 1\\n5 7\\n11 13\\n14 29\\n9 14 2 9 10 4 9 9 13 10\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 001\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 50\\n79 80\\n81 82\\n84 87\\n88 91\\n98 001\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 50\\n79 80\\n89 82\\n84 87\\n88 91\\n98 001\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n11 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 50\\n79 80\\n89 82\\n84 87\\n88 91\\n98 001\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n11 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 111\\n130 68\\n69 70\\n74 50\\n79 80\\n89 82\\n84 87\\n88 91\\n98 001\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"6 9\\n1 2\\n8 16\\n21 27\\n31 46\\n49 57\\n59 151\\n26 27 28 13 2 4 2 2 24\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 36\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 100\\n4 7 6 1 5 4 3 2 5 2\\n\",\n \"2 1\\n1 1\\n1000000000000000000 1000000000100000000\\n999999999999999999\\n\",\n \"3 2\\n1000000000000000 1000000000000000\\n3000000000000000 4000000000000000\\n6000000000000000 7000000000000000\\n3052752506693368 973599012707272\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 36\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n118 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 5 2\\n\",\n \"6 9\\n1 4\\n10 18\\n23 29\\n33 43\\n46 57\\n67 77\\n14 32 32 19 20 17 32 24 32\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 22\\n9 10 2 9 10 4 9 9 9 10\\n\",\n \"5 9\\n1 2\\n3 2\\n5 7\\n16 19\\n14 20\\n2 3 4 10 6 2 6 9 5\\n\",\n \"20 10\\n4 9\\n10 15\\n21 18\\n20 21\\n25 27\\n29 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 5 2\\n\",\n \"5 10\\n1 2\\n3 3\\n5 7\\n11 13\\n14 29\\n9 10 2 9 10 7 9 9 13 10\\n\",\n \"20 10\\n4 9\\n10 15\\n17 18\\n20 21\\n25 27\\n29 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 25\\n65 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"20 10\\n4 9\\n10 15\\n17 29\\n20 21\\n25 27\\n13 32\\n35 40\\n46 48\\n49 51\\n53 56\\n59 60\\n63 64\\n130 68\\n69 70\\n74 75\\n79 80\\n81 82\\n84 87\\n88 91\\n98 000\\n4 7 6 1 5 4 3 1 8 2\\n\",\n \"5 10\\n1 2\\n3 1\\n5 7\\n11 13\\n14 29\\n9 14 2 9 2 4 9 9 13 10\\n\"\n ],\n \"output\": [\n \"Yes\\n2 3 1 \",\n \"No\",\n \"Yes\\n1 \",\n \"No\",\n \"Yes\\n1 2 \",\n \"No\",\n \"No\",\n \"Yes\\n1 6 4 5 8 \",\n \"Yes\\n2 1 \",\n \"No\",\n \"No\",\n \"Yes\\n1 6 3 2 \",\n \"No\\n\",\n \"Yes\\n1 6 4 5 8\\n\",\n \"Yes\\n1 2\\n\",\n \"Yes\\n1 6 3 2\\n\",\n \"Yes\\n1\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\n1\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\n1 6 4 5 8\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nAndrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.\n\nThe only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≤ i ≤ n - 1.\n\nTo reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≤ x ≤ ri, li + 1 ≤ y ≤ ri + 1 and y - x = a. \n\nThe detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.\n\nInput\n\nThe first line contains integers n (2 ≤ n ≤ 2·105) and m (1 ≤ m ≤ 2·105) — the number of islands and bridges.\n\nNext n lines each contain two integers li and ri (1 ≤ li ≤ ri ≤ 1018) — the coordinates of the island endpoints.\n\nThe last line contains m integer numbers a1, a2, ..., am (1 ≤ ai ≤ 1018) — the lengths of the bridges that Andrewid got.\n\nOutput\n\nIf it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line \"No\" (without the quotes), otherwise print in the first line \"Yes\" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi. \n\nIf there are multiple correct answers, print any of them. Note that in this problem it is necessary to print \"Yes\" and \"No\" in correct case.\n\nExamples\n\nInput\n\n4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8\n\n\nOutput\n\nYes\n2 3 1 \n\n\nInput\n\n2 2\n11 14\n17 18\n2 9\n\n\nOutput\n\nNo\n\n\nInput\n\n2 1\n1 1\n1000000000000000000 1000000000000000000\n999999999999999999\n\n\nOutput\n\nYes\n1 \n\nNote\n\nIn the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14.\n\nIn the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.\n\n### Input:\n4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8\n\n### Output:\nYes\n2 3 1 \n\n### Input:\n2 2\n11 14\n17 18\n2 9\n\n### Output:\nNo\n\n### Code:\n#!/usr/bin/env python\n# 556D_fug.py - Codeforces.com 556D Fug quiz\n#\n# Copyright (C) 2015 Sergey\n# Licensed under the Apache License, Version 2.0 (the \"License\");\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n# http://www.apache.org/licenses/LICENSE-2.0\n#\n# Unless required by applicable law or agreed to in writing, software\n# distributed under the License is distributed on an \"AS IS\" BASIS,\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n# limitations under the License.\n\n\"\"\"\nInput\n\nThe first line contains integers n and m - the number of islands and bridges.\n\nNext n lines each contain two integers li and ri - the coordinates of the\nisland endpoints.\n\nThe last line contains m integer numbers a1..am - the lengths of the bridges\nthat Andrewid got.\nOutput\n\nIf it is impossible to place a bridge between each pair of adjacent islands\nin the required manner, print on a single line \"No\" (without the quotes)\n, otherwise print in the first line \"Yes\" (without the quotes), and in the\nsecond line print n-1 numbers b1, bn-1, which mean that between islands\ni and i+1 there must be used a bridge number bi.\n\nIf there are multiple correct answers, print any of them. Note that in this\nproblem it is necessary to print \"Yes\" and \"No\" in correct case\n\"\"\"\n\n# Standard modules\nimport unittest\nimport sys\nimport re\n\n# Additional modules\nimport bisect\n\n###############################################################################\n# Fastlist Class\n###############################################################################\n\n\nclass Fastlist(object):\n \"\"\" Fastlist representation \"\"\"\n\n def __init__(self, l=[], load=5000, sorted=0):\n self._load = load\n self._sorted = sorted\n self._lists = []\n self._starts = []\n self._mins = []\n self._insert_list()\n self._irev = 0\n self.extend(l)\n\n def _index_location(self, index):\n if len(self._lists[0]) == 0:\n raise IndexError(\"List index out of range\")\n if index == 0:\n return (0, 0)\n if index == -1:\n return (len(self._lists) - 1, len(self._lists[-1]) - 1)\n if self._sorted:\n raise RuntimeError(\"No index access to the sorted list, exc 0, -1\")\n length = len(self)\n if index < 0:\n index = length + index\n if index >= length:\n raise IndexError(\"List index out of range\")\n il = bisect.bisect_right(self._starts, index) - 1\n return (il, index - self._starts[il])\n\n def _insert_list(self, il=None):\n if il is None:\n il = len(self._lists)\n self._lists.insert(il, [])\n if self._sorted:\n if il == 0:\n self._mins.insert(il, None)\n else:\n self._mins.insert(il, self._lists[il-1][-1])\n else:\n if il == 0:\n self._starts.insert(il, 0)\n else:\n start = self._starts[il-1] + len(self._lists[il-1])\n self._starts.insert(il, start)\n\n def _del_list(self, il):\n del self._lists[il]\n if self._sorted:\n del self._mins[il]\n else:\n del self._starts[il]\n\n def _rebalance(self, il):\n illen = len(self._lists[il])\n if illen >= self._load * 2:\n self._insert_list(il)\n self._even_lists(il)\n if illen <= self._load * 0.2:\n if il != 0:\n self._even_lists(il-1)\n elif len(self._lists) > 1:\n self._even_lists(il)\n\n def _even_lists(self, il):\n tot = len(self._lists[il]) + len(self._lists[il+1])\n if tot < self._load * 1:\n self._lists[il] += self._lists[il+1]\n self._del_list(il+1)\n if self._sorted:\n self._mins[il] = self._lists[il][0]\n else:\n half = tot//2\n ltot = self._lists[il] + self._lists[il+1]\n self._lists[il] = ltot[:half]\n self._lists[il+1] = ltot[half:]\n if self._sorted:\n self._mins[il] = self._lists[il][0]\n self._mins[il+1] = self._lists[il+1][0]\n else:\n self._starts[il+1] = self._starts[il] + len(self._lists[il])\n\n def _obj_location(self, obj, l=0):\n if not self._sorted:\n raise RuntimeError(\"No by value access to an unserted list\")\n il = 0\n if len(self._mins) > 1 and obj > self._mins[0]:\n if l:\n il = bisect.bisect_left(self._mins, obj) - 1\n else:\n il = bisect.bisect_right(self._mins, obj) - 1\n if l:\n ii = bisect.bisect_left(self._lists[il], obj)\n else:\n ii = bisect.bisect_right(self._lists[il], obj)\n if ii == len(self._lists[il]) and il != len(self._lists) - 1:\n ii = 0\n il += 1\n return (il, ii)\n\n def insert(self, index, obj):\n (il, ii) = self._index_location(index)\n self._lists[il].insert(ii, obj)\n for j in range(il + 1, len(self._starts)):\n self._starts[j] += 1\n self._rebalance(il)\n\n def append(self, obj):\n if len(self._lists[-1]) >= self._load:\n self._insert_list()\n self._lists[-1].append(obj)\n if self._sorted and self._mins[0] is None:\n self._mins[0] = self._lists[0][0]\n\n def extend(self, iter):\n for n in iter:\n self.append(n)\n\n def pop(self, index=None):\n if index is None:\n index = -1\n (il, ii) = self._index_location(index)\n item = self._lists[il].pop(ii)\n if self._sorted:\n if ii == 0 and len(self._lists[il]) > 0:\n self._mins[il] = self._lists[il][0]\n else:\n for j in range(il + 1, len(self._starts)):\n self._starts[j] -= 1\n self._rebalance(il)\n return item\n\n def clear(self):\n self._lists.clear()\n self._starts.clear()\n self._mins.clear()\n self._insert_list()\n\n def as_list(self):\n return sum(self._lists, [])\n\n def insort(self, obj, l=0):\n (il, ii) = self._obj_location(obj, l)\n self._lists[il].insert(ii, obj)\n if ii == 0:\n self._mins[il] = obj\n self._rebalance(il)\n\n def add(self, obj):\n if self._sorted:\n self.insort(obj)\n else:\n self.append(obj)\n\n def insort_left(self, obj):\n self.insort(obj, l=1)\n\n def lower_bound(self, obj):\n (self._il, self._ii) = self._obj_location(obj, l=1)\n return self\n\n def upper_bound(self, obj):\n (self._il, self._ii) = self._obj_location(obj)\n return self\n\n def __str__(self):\n return str(self.as_list())\n\n def __setitem__(self, index, obj):\n if isinstance(index, int):\n (il, ii) = self._index_location(index)\n self._lists[il][ii] = obj\n elif isinstance(index, slice):\n raise RuntimeError(\"Slice assignment is not supported\")\n\n def __getitem__(self, index):\n if isinstance(index, int):\n (il, ii) = self._index_location(index)\n return self._lists[il][ii]\n elif isinstance(index, slice):\n rg = index.indices(len(self))\n if rg[0] == 0 and rg[1] == len(self) and rg[2] == 1:\n return self.as_list()\n return [self.__getitem__(index) for index in range(*rg)]\n\n def __iadd__(self, obj):\n if self._sorted:\n [self.insort(n) for n in obj]\n else:\n [self.append(n) for n in obj]\n return self\n\n def __delitem__(self, index):\n if isinstance(index, int):\n self.pop(index)\n elif isinstance(index, slice):\n rg = index.indices(len(self))\n [self.__delitem__(rg[0]) for i in range(*rg)]\n\n def __len__(self):\n if self._sorted:\n return sum([len(l) for l in self._lists])\n return self._starts[-1] + len(self._lists[-1])\n\n def __contains__(self, obj):\n if self._sorted:\n it = self.lower_bound(obj)\n return not it.iter_end() and obj == it.iter_getitem()\n else:\n for n in self:\n if obj == n:\n return True\n return False\n\n def __bool__(self):\n return len(self._lists[0]) != 0\n\n def __iter__(self):\n self._il = self._ii = self._irev = 0\n return self\n\n def __reversed__(self):\n self._il = len(self._lists) - 1\n self._ii = len(self._lists[self._il]) - 1\n self._irev = 1\n return self\n\n def __next__(self):\n if self._il in (-1, len(self._lists)) or len(self._lists[0]) == 0:\n raise StopIteration(\"Iteration stopped\")\n item = self._lists[self._il][self._ii]\n if not self._irev:\n self._ii += 1\n if self._ii == len(self._lists[self._il]):\n self._il += 1\n self._ii = 0\n else:\n self._ii -= 1\n if self._ii == 0:\n self._il -= 1\n self._ii = len(self._lists[self._il])\n return item\n\n def iter_getitem(self):\n return self._lists[self._il][self._ii]\n\n def iter_end(self):\n return (self._il == len(self._lists) - 1 and\n self._ii == len(self._lists[self._il]))\n\n def iter_del(self):\n self.iter_pop()\n\n def iter_pop(self):\n item = self._lists[self._il].pop(self._ii)\n if self._sorted:\n if self._ii == 0 and len(self._lists[self._il]) > 0:\n self._mins[self._il] = self._lists[self._il][0]\n else:\n for j in range(self._il + 1, len(self._starts)):\n self._starts[j] -= 1\n self._rebalance(self._il)\n return item\n\n\n###############################################################################\n# Fug Class\n###############################################################################\n\n\nclass Fug:\n \"\"\" Fug representation \"\"\"\n\n def __init__(self, args):\n \"\"\" Default constructor \"\"\"\n self.gsrt = args[0]\n self.asrt = args[1]\n self.gn = args[2]\n self.result = [0]*self.gn\n self.a = Fastlist(self.asrt, load=500, sorted=1)\n\n def calculate(self):\n \"\"\" Main calcualtion function of the class \"\"\"\n\n for i in range(self.gn):\n g = self.gsrt[i]\n it = self.a.lower_bound((g[1], 0))\n if not it.iter_end():\n alb = it.iter_getitem()\n if alb[0] > g[0]:\n return \"No\"\n self.result[g[2]] = alb[1]+1\n it.iter_del()\n else:\n return \"No\"\n\n answer = \"Yes\\n\" + \" \".join(str(n) for n in self.result)\n\n return answer\n\n\n###############################################################################\n# Executable code\n###############################################################################\n\n\ndef get_inputs(test_inputs=None):\n\n it = iter(test_inputs.split(\"\\n\")) if test_inputs else None\n\n def uinput():\n \"\"\" Unit-testable input function wrapper \"\"\"\n if it:\n return next(it)\n else:\n return sys.stdin.readline()\n\n # Getting string inputs. Place all uinput() calls here\n num = [int(s) for s in uinput().split()]\n gaps = []\n prevli = [int(s) for s in uinput().split()]\n for i in range(num[0] - 1):\n li = [int(s) for s in uinput().split()]\n min = li[0] - prevli[1]\n max = li[1] - prevli[0]\n gaps.append((max, min, i))\n prevli = li\n alist = [(int(s), i) for i, s in enumerate(uinput().split())]\n\n # Decoding inputs into a list\n\n inputs = [sorted(gaps), sorted(alist), num[0]-1]\n\n return inputs\n\n\ndef calculate(test_inputs=None):\n \"\"\" Base class calculate method wrapper \"\"\"\n return Fug(get_inputs(test_inputs)).calculate()\n\n\n###############################################################################\n# Unit Tests\n###############################################################################\n\n\nclass unitTests(unittest.TestCase):\n\n def test_sample_tests(self):\n \"\"\" Quiz sample tests. Add \\n to separate lines \"\"\"\n\n # Sample test 1\n test = \"4 4\\n1 4\\n7 8\\n9 10\\n12 14\\n4 5 3 8\"\n self.assertEqual(calculate(test), \"Yes\\n2 3 1\")\n self.assertEqual(\n get_inputs(test),\n [[(3, 1, 1), (5, 2, 2), (7, 3, 0)],\n [(3, 2), (4, 0), (5, 1), (8, 3)], 3])\n\n # My tests\n test = \"5 5\\n1 1\\n2 7\\n8 8\\n10 10\\n16 16\\n1 1 5 6 2\"\n self.assertEqual(calculate(test), \"Yes\\n1 2 5 4\")\n\n # Other tests\n test = \"2 2\\n11 14\\n17 18\\n2 9\"\n self.assertEqual(calculate(test), \"No\")\n\n # Other tests\n test = (\n \"2 1\\n1 1\\n1000000000000000000 1000000000000000000\" +\n \"\\n999999999999999999\")\n self.assertEqual(calculate(test), \"Yes\\n1\")\n\n test = (\"5 9\\n1 2\\n3 3\\n5 7\\n11 13\\n14 20\\n2 3 4 10 6 2 6 9 5\")\n self.assertEqual(calculate(test), \"Yes\\n1 6 3 2\")\n\n size = 200000\n test = str(size) + \" \" + str(size) + \"\\n\"\n x = size*1000\n for i in range(size):\n test += str(x) + \" \" + str(x + i + 1) + \"\\n\"\n x += 2 * (i + 1)\n for i in reversed(range(size)):\n test += str(i) + \" \"\n self.assertEqual(calculate(test)[0], \"Y\")\n\n def test_Fug_class__basic_functions(self):\n \"\"\" Fug class basic functions testing \"\"\"\n\n # Constructor test\n d = Fug([[(1, 3, 1), (2, 5, 2), (3, 7, 0)],\n [(3, 2), (4, 0), (5, 1), (8, 3)], 3])\n\n # Sort bridges\n self.assertEqual(d.asrt[0], (3, 2))\n\n # Sort Gaps\n self.assertEqual(d.gsrt[0], (1, 3, 1))\n\nif __name__ == \"__main__\":\n\n # Avoiding recursion limitaions\n sys.setrecursionlimit(100000)\n\n if sys.argv[-1] == \"-ut\":\n unittest.main(argv=[\" \"])\n\n # Print the result string\n sys.stdout.write(calculate())\n"}}},{"rowIdx":670,"cells":{"id":{"kind":"string","value":"582_B. Once Again..._3156"},"description":{"kind":"string","value":"You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.\n\nInput\n\nThe first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).\n\nOutput\n\nPrint a single number — the length of a sought sequence.\n\nExamples\n\nInput\n\n4 3\n3 1 4 2\n\n\nOutput\n\n5\n\nNote\n\nThe array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. "},"code":{"kind":"string","value":"f = lambda: map(int, input().split())\nn, m = f()\nt = list(f())\ns = [0] * 301\nd = s[:]\nfor i in t: d[i] += 1\nfor i in t * min(m, 2 * n): s[i] = max(s[:i + 1]) + 1\nprint(max(s) + max((m - n * 2) * max(d), 0))"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4 3\\n3 1 4 2\\n\",\n \"100 10000000\\n1 2 2 1 2 2 1 1 2 2 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1\\n\",\n \"99 10000000\\n96 97 98 93 94 95 90 91 92 87 88 89 84 85 86 81 82 83 78 79 80 75 76 77 72 73 74 69 70 71 66 67 68 63 64 65 60 61 62 57 58 59 54 55 56 51 52 53 48 49 50 45 46 47 42 43 44 39 40 41 36 37 38 33 34 35 30 31 32 27 28 29 24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 11 6 7 8 3 4 5 2 1 99\\n\",\n \"98 10000000\\n1 2 95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\\n\",\n \"99 10000000\\n1 2 3 95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\\n\",\n \"31 3767\\n16 192 152 78 224 202 186 52 118 19 13 38 199 196 35 295 100 64 205 37 166 124 169 214 66 243 134 192 253 270 92\\n\",\n \"2 8698\\n71 225\\n\",\n \"100 10000000\\n285 219 288 277 266 249 297 286 290 266 210 201 275 280 200 272 297 253 246 292 272 285 226 250 297 270 214 251 263 285 237 292 245 225 247 221 263 250 253 280 235 288 278 297 283 294 208 279 227 290 246 208 274 238 282 240 214 277 239 282 255 278 214 292 277 267 290 257 239 234 252 246 217 274 254 249 229 275 210 297 254 215 222 228 262 287 290 292 277 227 292 282 248 278 207 249 236 240 252 216\\n\",\n \"1 10000000\\n1\\n\",\n \"99 84\\n62 4 145 285 106 132 30 96 211 28 144 190 95 184 227 177 128 60 143 19 19 81 38 83 108 172 241 228 48 39 171 282 233 294 74 271 178 87 24 180 212 190 223 153 230 198 261 232 150 18 190 91 265 61 280 13 207 70 182 117 270 77 242 163 138 212 165 273 247 23 52 88 243 85 293 12 135 284 162 91 174 109 42 19 218 289 9 59 9 117 61 122 78 287 144 176 281 123 243\\n\",\n \"2 766\\n147 282\\n\",\n \"39 1057\\n1 120 247 206 260 117 152 24 162 266 202 152 278 199 63 188 271 62 62 177 213 77 229 197 263 178 211 102 255 257 163 134 14 66 11 113 216 288 225\\n\",\n \"98 10000000\\n1 2 195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104\\n\",\n \"99 9\\n218 254 64 32 130 52 242 40 29 188 196 300 258 165 110 151 265 142 295 166 141 260 158 218 184 251 180 16 177 125 192 279 201 189 170 37 7 150 117 79 97 13 69 156 254 287 17 214 95 300 150 197 133 161 46 26 82 119 174 6 252 42 264 136 273 127 42 274 113 278 165 173 231 209 159 56 248 39 46 41 222 278 114 84 150 13 63 106 179 279 44 15 13 74 50 168 38 181 127\\n\",\n \"46 13793\\n1 239 20 83 33 183 122 208 46 141 11 264 196 266 104 130 116 117 31 213 235 207 219 206 206 46 89 112 260 191 245 234 87 255 186 4 251 177 130 59 81 54 227 116 105 284\\n\",\n \"81 10683\\n3 52 265 294 213 242 185 151 27 165 128 237 124 14 43 147 104 162 124 103 233 156 288 57 289 195 129 77 97 138 153 289 203 126 34 5 97 35 224 120 200 203 222 94 171 294 293 108 145 193 227 206 34 295 1 233 258 7 246 34 60 232 58 169 77 150 272 279 171 228 168 84 114 229 149 97 66 246 212 236 151\\n\",\n \"1 1\\n5\\n\",\n \"100 100\\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\\n\",\n \"100 199\\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\\n\",\n \"100 10000000\\n31 150 132 17 273 18 292 260 226 217 165 68 36 176 89 75 227 246 137 151 87 215 267 242 21 156 27 27 202 73 218 290 57 2 85 159 96 39 191 268 67 64 55 266 29 209 215 85 149 267 161 153 118 293 104 197 91 252 275 56 288 76 82 239 215 105 283 88 76 294 138 166 9 273 14 119 67 101 250 13 63 215 80 5 221 234 258 195 129 67 152 56 277 129 111 98 213 22 209 299\\n\",\n \"2 2\\n1 2\\n\",\n \"68 2450\\n107 297 185 215 224 128 8 65 101 202 19 145 255 233 138 223 144 132 32 122 153 85 31 160 219 125 167 220 138 255 219 119 165 249 47 124 20 37 160 24 156 154 163 226 270 88 74 192 204 300 194 184 235 93 267 160 12 216 91 191 267 241 152 9 111 76 201 295\\n\",\n \"99 10000000\\n97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2 99\\n\",\n \"1 1000\\n42\\n\",\n \"98 10000000\\n95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 97 98\\n\",\n \"99 105\\n16 118 246 3 44 149 156 290 44 267 221 123 57 175 233 24 23 120 298 228 119 62 23 183 169 294 195 115 131 157 223 298 77 106 283 117 255 41 17 298 22 176 164 187 214 101 10 181 117 70 271 291 59 156 44 204 140 205 253 176 270 43 188 287 40 250 271 100 244 297 133 228 98 218 290 69 171 66 195 283 63 154 191 66 238 104 32 122 79 190 55 110 276 2 188 26 44 276 230\\n\",\n \"98 10000000\\n1 1 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\\n\",\n \"99 10000000\\n300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300\\n\",\n \"100 10000000\\n300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300\\n\",\n \"2 1\\n1 2\\n\",\n \"2 13101\\n180 199\\n\",\n \"98 10000000\\n195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\\n\",\n \"95 10000000\\n192 193 194 189 190 191 186 187 188 183 184 185 180 181 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95 94 93 98 97 96\\n\",\n \"95 10000000\\n192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 15 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 256 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\\n\",\n \"100 10000000\\n98 99 96 97 94 95 92 93 90 91 88 89 86 87 84 85 82 164 80 81 78 79 76 77 74 75 72 73 70 71 68 69 66 67 64 65 62 63 60 61 58 59 56 57 54 55 52 53 34 51 48 49 46 47 44 45 42 43 40 41 38 39 36 37 34 35 32 33 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 14 15 12 13 10 11 8 9 6 7 4 5 2 3 1 100\\n\",\n \"98 10000000\\n1 2 5 4 3 8 7 6 11 10 9 14 13 12 17 16 19 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 89 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\\n\"\n ],\n \"output\": [\n \"5\\n\",\n \"560000000\\n\",\n \"10000065\\n\",\n \"20000034\\n\",\n \"20000034\\n\",\n \"7546\\n\",\n \"8699\\n\",\n \"50000016\\n\",\n \"10000000\\n\",\n \"280\\n\",\n \"767\\n\",\n \"2128\\n\",\n \"10000066\\n\",\n \"51\\n\",\n \"27600\\n\",\n \"32070\\n\",\n \"1\\n\",\n \"150\\n\",\n \"249\\n\",\n \"40000023\\n\",\n \"3\\n\",\n \"7366\\n\",\n \"10000050\\n\",\n \"1000\\n\",\n \"20000034\\n\",\n \"435\\n\",\n \"20000032\\n\",\n \"990000000\\n\",\n \"1000000000\\n\",\n \"2\\n\",\n \"13102\\n\",\n \"10000065\\n\",\n \"10000063\\n\",\n \"260000004\\n\",\n \"1001\\n\",\n \"10000050\\n\",\n \"10000033\\n\",\n \"268\\n\",\n \"12234\\n\",\n \"274\\n\",\n \"580000001\\n\",\n \"20000033\\n\",\n \"3845\\n\",\n \"250\\n\",\n \"404\\n\",\n \"15919\\n\",\n \"10000067\\n\",\n \"251\\n\",\n \"550000000\\n\",\n \"20000033\\n\",\n \"20000034\\n\",\n \"15294\\n\",\n \"280\\n\",\n \"1128\\n\",\n \"2129\\n\",\n \"50\\n\",\n \"32069\\n\",\n \"1\\n\",\n \"201\\n\",\n \"399\\n\",\n \"40000023\\n\",\n \"7366\\n\",\n \"20000002\\n\",\n \"1100\\n\",\n \"436\\n\",\n \"20000032\\n\",\n \"20927\\n\",\n \"10000065\\n\",\n \"10000063\\n\",\n \"270000002\\n\",\n \"12234\\n\",\n \"274\\n\",\n \"570000002\\n\",\n \"3845\\n\",\n \"401\\n\",\n \"404\\n\",\n \"403\\n\",\n \"5\\n\",\n \"1223\\n\",\n \"281\\n\",\n \"202\\n\",\n \"400\\n\",\n \"3937\\n\",\n \"10000064\\n\",\n \"270000003\\n\",\n \"20000033\\n\",\n \"20000034\\n\",\n \"20000033\\n\",\n \"20000002\\n\",\n \"20000033\\n\",\n \"20000033\\n\",\n \"20000034\\n\",\n \"20000033\\n\",\n \"20000032\\n\",\n \"20000034\\n\",\n \"1128\\n\",\n \"2129\\n\",\n \"20000034\\n\",\n \"50\\n\",\n \"32069\\n\",\n \"1\\n\",\n \"40000023\\n\",\n \"20000002\\n\",\n \"20000033\\n\",\n \"436\\n\",\n \"20000032\\n\",\n \"10000063\\n\",\n \"20000002\\n\",\n \"20000033\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nYou are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.\n\nInput\n\nThe first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).\n\nOutput\n\nPrint a single number — the length of a sought sequence.\n\nExamples\n\nInput\n\n4 3\n3 1 4 2\n\n\nOutput\n\n5\n\nNote\n\nThe array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. \n\n### Input:\n4 3\n3 1 4 2\n\n### Output:\n5\n\n\n### Input:\n100 10000000\n1 2 2 1 2 2 1 1 2 2 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1\n\n### Output:\n560000000\n\n\n### Code:\nf = lambda: map(int, input().split())\nn, m = f()\nt = list(f())\ns = [0] * 301\nd = s[:]\nfor i in t: d[i] += 1\nfor i in t * min(m, 2 * n): s[i] = max(s[:i + 1]) + 1\nprint(max(s) + max((m - n * 2) * max(d), 0))"}}},{"rowIdx":671,"cells":{"id":{"kind":"string","value":"604_B. More Cowbell_3160"},"description":{"kind":"string","value":"Kevin Sun wants to move his precious collection of n cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into k boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection. \n\nKevin is a meticulous cowbell collector and knows that the size of his i-th (1 ≤ i ≤ n) cowbell is an integer si. In fact, he keeps his cowbells sorted by size, so si - 1 ≤ si for any i > 1. Also an expert packer, Kevin can fit one or two cowbells into a box of size s if and only if the sum of their sizes does not exceed s. Given this information, help Kevin determine the smallest s for which it is possible to put all of his cowbells into k boxes of size s.\n\nInput\n\nThe first line of the input contains two space-separated integers n and k (1 ≤ n ≤ 2·k ≤ 100 000), denoting the number of cowbells and the number of boxes, respectively.\n\nThe next line contains n space-separated integers s1, s2, ..., sn (1 ≤ s1 ≤ s2 ≤ ... ≤ sn ≤ 1 000 000), the sizes of Kevin's cowbells. It is guaranteed that the sizes si are given in non-decreasing order.\n\nOutput\n\nPrint a single integer, the smallest s for which it is possible for Kevin to put all of his cowbells into k boxes of size s.\n\nExamples\n\nInput\n\n2 1\n2 5\n\n\nOutput\n\n7\n\n\nInput\n\n4 3\n2 3 5 9\n\n\nOutput\n\n9\n\n\nInput\n\n3 2\n3 5 7\n\n\nOutput\n\n8\n\nNote\n\nIn the first sample, Kevin must pack his two cowbells into the same box. \n\nIn the second sample, Kevin can pack together the following sets of cowbells: {2, 3}, {5} and {9}.\n\nIn the third sample, the optimal solution is {3, 5} and {7}."},"code":{"kind":"string","value":"n, k = map(int, input().split())\na = [int(s) for s in input().split()]\n\n\np = n - k\nq = 2*k - n\n\nif n < k:\n q = n\n p = 0\n\n\nma = 0\nfor i in range ((n - q) // 2):\n ma = max((a[i] + a[n - q - i - 1]), ma)\n\nma2 = 0\nfor i in range(n - q, n):\n ma2 = max(a[i], ma2)\n\n\nprint(max(ma,ma2))\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4 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589 792 870 1041 1055 1122 1141 1166 1310 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 3295 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 1903 9323 9477 9489 9518 9621 9699 9804\\n\",\n \"100 84\\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 892 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 4095 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\\n\",\n \"20 11\\n1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1\\n\",\n \"100 61\\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 4653 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\\n\",\n \"1 31139\\n4\\n\",\n \"10 9\\n12 10 10 32 36 38 69 80 48 93\\n\",\n \"100 49990\\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2093 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 7786 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\\n\",\n \"3 2\\n5 5 6\\n\"\n ],\n \"output\": [\n \"9\\n\",\n \"7\\n\",\n \"8\\n\",\n \"109\\n\",\n \"9946\\n\",\n \"74\\n\",\n \"10676\\n\",\n \"23456\\n\",\n \"9986\\n\",\n \"1\\n\",\n \"10\\n\",\n \"88\\n\",\n \"10011\\n\",\n \"10009\\n\",\n \"9983\\n\",\n \"9970\\n\",\n \"10\\n\",\n \"2\\n\",\n \"9927\\n\",\n \"12345\\n\",\n \"2\\n\",\n \"11103\\n\",\n \"93\\n\",\n \"3\\n\",\n \"9934\\n\",\n \"100\\n\",\n \"9946\\n\",\n \"675\\n\",\n \"9986\\n\",\n \"10\\n\",\n \"176\\n\",\n \"10011\\n\",\n \"10009\\n\",\n \"9983\\n\",\n \"9970\\n\",\n \"2\\n\",\n \"9927\\n\",\n \"4\\n\",\n \"93\\n\",\n \"9934\\n\",\n \"100\\n\",\n \"5\\n\",\n \"8\\n\",\n \"258\\n\",\n \"334\\n\",\n \"277\\n\",\n \"12792\\n\",\n \"6\\n\",\n \"453\\n\",\n \"333\\n\",\n \"137\\n\",\n \"88\\n\",\n \"22263\\n\",\n \"3\\n\",\n \"7\\n\",\n \"780\\n\",\n \"11\\n\",\n \"95\\n\",\n \"675\\n\",\n \"9986\\n\",\n \"176\\n\",\n \"10011\\n\",\n \"10009\\n\",\n \"9983\\n\",\n \"9970\\n\",\n \"9927\\n\",\n \"93\\n\",\n \"9934\\n\",\n \"5\\n\",\n \"675\\n\",\n \"176\\n\",\n \"9983\\n\",\n \"9970\\n\",\n \"9927\\n\",\n \"93\\n\",\n \"9934\\n\",\n \"5\\n\",\n \"9983\\n\",\n \"9970\\n\",\n \"9927\\n\",\n \"93\\n\",\n \"4\\n\",\n \"334\\n\",\n \"9983\\n\",\n \"9927\\n\",\n \"277\\n\",\n \"334\\n\",\n \"9983\\n\",\n \"12792\\n\",\n \"9927\\n\",\n \"277\\n\",\n \"334\\n\",\n \"9983\\n\",\n \"9927\\n\",\n \"334\\n\",\n \"9983\\n\",\n \"453\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9983\\n\",\n \"9946\\n\",\n \"9986\\n\",\n \"9983\\n\",\n \"10\\n\",\n \"2\\n\",\n \"9927\\n\",\n \"9934\\n\",\n \"6\\n\",\n \"6\\n\",\n \"9946\\n\",\n \"9986\\n\",\n \"176\\n\",\n \"10011\\n\",\n \"10009\\n\",\n \"9970\\n\",\n \"2\\n\",\n \"9927\\n\",\n \"4\\n\",\n \"93\\n\",\n \"9934\\n\",\n \"10\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nKevin Sun wants to move his precious collection of n cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into k boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection. \n\nKevin is a meticulous cowbell collector and knows that the size of his i-th (1 ≤ i ≤ n) cowbell is an integer si. In fact, he keeps his cowbells sorted by size, so si - 1 ≤ si for any i > 1. Also an expert packer, Kevin can fit one or two cowbells into a box of size s if and only if the sum of their sizes does not exceed s. Given this information, help Kevin determine the smallest s for which it is possible to put all of his cowbells into k boxes of size s.\n\nInput\n\nThe first line of the input contains two space-separated integers n and k (1 ≤ n ≤ 2·k ≤ 100 000), denoting the number of cowbells and the number of boxes, respectively.\n\nThe next line contains n space-separated integers s1, s2, ..., sn (1 ≤ s1 ≤ s2 ≤ ... ≤ sn ≤ 1 000 000), the sizes of Kevin's cowbells. It is guaranteed that the sizes si are given in non-decreasing order.\n\nOutput\n\nPrint a single integer, the smallest s for which it is possible for Kevin to put all of his cowbells into k boxes of size s.\n\nExamples\n\nInput\n\n2 1\n2 5\n\n\nOutput\n\n7\n\n\nInput\n\n4 3\n2 3 5 9\n\n\nOutput\n\n9\n\n\nInput\n\n3 2\n3 5 7\n\n\nOutput\n\n8\n\nNote\n\nIn the first sample, Kevin must pack his two cowbells into the same box. \n\nIn the second sample, Kevin can pack together the following sets of cowbells: {2, 3}, {5} and {9}.\n\nIn the third sample, the optimal solution is {3, 5} and {7}.\n\n### Input:\n4 3\n2 3 5 9\n\n### Output:\n9\n\n\n### Input:\n2 1\n2 5\n\n### Output:\n7\n\n\n### Code:\nn, k = map(int, input().split())\na = [int(s) for s in input().split()]\n\n\np = n - k\nq = 2*k - n\n\nif n < k:\n q = n\n p = 0\n\n\nma = 0\nfor i in range ((n - q) // 2):\n ma = max((a[i] + a[n - q - i - 1]), ma)\n\nma2 = 0\nfor i in range(n - q, n):\n ma2 = max(a[i], ma2)\n\n\nprint(max(ma,ma2))\n"}}},{"rowIdx":672,"cells":{"id":{"kind":"string","value":"626_E. Simple Skewness_3163"},"description":{"kind":"string","value":"Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of n (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.\n\nThe mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.\n\nInput\n\nThe first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of elements in the list.\n\nThe second line contains n integers xi (0 ≤ xi ≤ 1 000 000) — the ith element of the list.\n\nOutput\n\nIn the first line, print a single integer k — the size of the subset.\n\nIn the second line, print k integers — the elements of the subset in any order.\n\nIf there are multiple optimal subsets, print any.\n\nExamples\n\nInput\n\n4\n1 2 3 12\n\n\nOutput\n\n3\n1 2 12 \n\n\nInput\n\n4\n1 1 2 2\n\n\nOutput\n\n3\n1 1 2 \n\n\nInput\n\n2\n1 2\n\n\nOutput\n\n2\n1 2\n\nNote\n\nIn the first case, the optimal subset is , which has mean 5, median 2, and simple skewness of 5 - 2 = 3.\n\nIn the second case, the optimal subset is . Note that repetition is allowed.\n\nIn the last case, any subset has the same median and mean, so all have simple skewness of 0."},"code":{"kind":"string","value":"from itertools import accumulate\nfrom fractions import Fraction\n\nn = int(input())\nA = [int(x) for x in input().split()]\nA.sort()\nB = list(accumulate([0] + A))\ndef condition(i, z):\n return (2*z - 1)*(A[i-z] + A[-z]) > 2*(B[i+1] - B[i-z+1] + B[-1] - B[-z])\ndef average(i, z):\n return Fraction((B[i+1] - B[i-z] + B[-1] - B[-z-1]) , 2*z + 1)\nmaxans = 0\nargmax = (0, 0)\nfor i in range(1, n-1):\n x, y = 0, min(i, n-1-i)\n while y - x > 1:\n z = (x + y)//2\n if condition(i, z):\n x = z\n else:\n y = z\n if condition(i, y): x = y\n if maxans < average(i, x) - A[i]:\n maxans = average(i, x) - A[i]\n argmax = (i, x)\nprint(argmax[1]*2 + 1)\nfor i in range(argmax[0] - argmax[1], argmax[0] + 1):\n print(A[i], end = ' ')\nfor i in range(-argmax[1], 0):\n print(A[i], end = ' ')\n\n \n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"2\\n1 2\\n\",\n \"4\\n1 1 2 2\\n\",\n \"4\\n1 2 3 12\\n\",\n \"21\\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 1000000\\n\",\n \"1\\n412237\\n\",\n \"3\\n76427 184396 963319\\n\",\n \"5\\n741304 281944 258539 54430 284591\\n\",\n \"2\\n725491 635622\\n\",\n \"40\\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 999872 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 934464 868928 868928 737856 737856 475712 0\\n\",\n \"1\\n935454\\n\",\n \"2\\n847420 569122\\n\",\n \"4\\n950582 784676 190241 964614\\n\",\n \"4\\n109509 792173 120296 495368\\n\",\n \"1\\n1000000\\n\",\n \"1\\n534166\\n\",\n \"4\\n231438 762672 125033 26806\\n\",\n \"3\\n599645 198217 986791\\n\",\n \"2\\n566563 590441\\n\",\n \"2\\n248707 649443\\n\",\n \"5\\n460447 303948 286063 992238 738282\\n\",\n \"20\\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712\\n\",\n \"5\\n301519 370449 319010 460799 983970\\n\",\n \"5\\n900232 289442 225592 622868 113587\\n\",\n \"3\\n758573 206400 991528\\n\",\n \"1\\n253309\\n\",\n \"3\\n198356 154895 894059\\n\",\n \"5\\n582376 311446 253801 560676 530279\\n\",\n \"4\\n549294 703669 96824 126683\\n\",\n \"3\\n880502 176898 958582\\n\",\n \"2\\n407635 619942\\n\",\n \"1\\n94381\\n\",\n \"21\\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 999998\\n\",\n \"4\\n390366 733171 92086 595244\\n\",\n \"1\\n486777\\n\",\n \"3\\n76427 184396 1437965\\n\",\n \"5\\n741304 281944 258539 54430 419816\\n\",\n \"2\\n51907 635622\\n\",\n \"40\\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 999872 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 1364934 868928 868928 737856 737856 475712 0\\n\",\n \"1\\n1696575\\n\",\n \"2\\n847420 966923\\n\",\n \"4\\n950582 649987 190241 964614\\n\",\n \"4\\n109509 792173 88452 495368\\n\",\n \"1\\n1000001\\n\",\n \"1\\n410450\\n\",\n \"4\\n231438 1402360 125033 26806\\n\",\n \"3\\n88771 198217 986791\\n\",\n \"2\\n566563 792523\\n\",\n \"2\\n248707 1199711\\n\",\n \"5\\n460447 167993 286063 992238 738282\\n\",\n \"20\\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 758345 934464 868928 737856 475712\\n\",\n \"5\\n301519 370449 36656 460799 983970\\n\",\n \"5\\n900232 570744 225592 622868 113587\\n\",\n \"3\\n688616 206400 991528\\n\",\n \"1\\n208702\\n\",\n \"3\\n198356 154895 1445756\\n\",\n \"5\\n582376 311446 46457 560676 530279\\n\",\n \"4\\n549294 703669 185327 126683\\n\",\n \"3\\n880502 120259 958582\\n\",\n \"2\\n407635 880302\\n\",\n \"1\\n173299\\n\",\n \"21\\n999999 999998 999996 999992 999984 174767 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 999998\\n\",\n \"4\\n390366 1291931 92086 595244\\n\",\n \"2\\n1 3\\n\",\n \"4\\n1 0 2 2\\n\",\n \"4\\n1 2 1 12\\n\",\n \"1\\n449273\\n\",\n \"3\\n76427 184396 1187133\\n\",\n \"5\\n741304 281944 258539 54430 15172\\n\",\n \"2\\n16179 635622\\n\",\n \"40\\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 470707 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 1364934 868928 868928 737856 737856 475712 0\\n\",\n \"1\\n2267645\\n\",\n \"2\\n847420 448499\\n\",\n \"4\\n950582 649987 214953 964614\\n\",\n \"4\\n109509 409442 88452 495368\\n\",\n \"1\\n1010001\\n\",\n \"1\\n701708\\n\",\n \"4\\n231438 1402360 125033 14616\\n\",\n \"3\\n88771 158611 986791\\n\",\n \"2\\n1127897 792523\\n\",\n \"2\\n255532 1199711\\n\",\n \"5\\n460447 167993 286063 347037 738282\\n\",\n \"20\\n999999 999998 999996 999992 999984 999968 999936 1444212 999744 999488 998976 997952 995904 991808 983616 758345 934464 868928 737856 475712\\n\",\n \"5\\n301519 370449 36656 174158 983970\\n\",\n \"5\\n1532321 570744 225592 622868 113587\\n\",\n \"3\\n688616 310389 991528\\n\",\n \"1\\n52345\\n\",\n \"3\\n198356 156571 1445756\\n\",\n \"5\\n582376 311446 52784 560676 530279\\n\",\n \"4\\n549294 703669 311387 126683\\n\"\n ],\n \"output\": [\n \"1\\n 1 \\n\",\n \"3\\n 1 1 2 \\n\",\n \"3\\n 1 2 12 \\n\",\n \"1\\n 475712 \\n\",\n \"1\\n 412237 \\n\",\n \"3\\n 76427 184396 963319 \\n\",\n \"3\\n 281944 284591 741304 \\n\",\n \"1\\n 635622 \\n\",\n \"3\\n 737856 737856 999999 \\n\",\n \"1\\n 935454 \\n\",\n \"1\\n 569122 \\n\",\n \"1\\n 190241 \\n\",\n \"3\\n 109509 120296 792173 \\n\",\n \"1\\n 1000000 \\n\",\n \"1\\n 534166 \\n\",\n \"3\\n 26806 125033 762672 \\n\",\n \"1\\n 198217 \\n\",\n \"1\\n 566563 \\n\",\n \"1\\n 248707 \\n\",\n \"3\\n 286063 303948 992238 \\n\",\n \"1\\n 475712 \\n\",\n \"3\\n 301519 319010 983970 \\n\",\n \"3\\n 113587 225592 900232 \\n\",\n \"1\\n 206400 \\n\",\n \"1\\n 253309 \\n\",\n \"3\\n 154895 198356 894059 \\n\",\n \"3\\n 253801 311446 582376 \\n\",\n \"3\\n 96824 126683 703669 \\n\",\n \"1\\n 176898 \\n\",\n \"1\\n 407635 \\n\",\n \"1\\n 94381 \\n\",\n \"3\\n 999998 999998 999999 \\n\",\n \"3\\n 92086 390366 733171 \\n\",\n \"1\\n486777 \",\n \"3\\n76427 184396 1437965 \",\n \"3\\n258539 281944 741304 \",\n \"1\\n51907 \",\n \"3\\n737856 737856 1364934 \",\n \"1\\n1696575 \",\n \"1\\n847420 \",\n \"1\\n190241 \",\n \"3\\n88452 109509 792173 \",\n \"1\\n1000001 \",\n \"1\\n410450 \",\n \"3\\n26806 125033 1402360 \",\n \"3\\n88771 198217 986791 \",\n \"1\\n566563 \",\n \"1\\n248707 \",\n \"3\\n167993 286063 992238 \",\n \"3\\n737856 758345 999999 \",\n \"3\\n301519 370449 983970 \",\n \"3\\n113587 225592 900232 \",\n \"1\\n206400 \",\n \"1\\n208702 \",\n \"3\\n154895 198356 1445756 \",\n \"3\\n46457 311446 582376 \",\n \"3\\n126683 185327 703669 \",\n \"1\\n120259 \",\n \"1\\n407635 \",\n \"1\\n173299 \",\n \"3\\n174767 475712 999999 \",\n \"3\\n92086 390366 1291931 \",\n \"1\\n1 \",\n \"1\\n0 \",\n \"3\\n1 1 12 \",\n \"1\\n449273 \",\n \"3\\n76427 184396 1187133 \",\n \"3\\n15172 54430 741304 \",\n \"1\\n16179 \",\n \"3\\n470707 475712 1364934 \",\n \"1\\n2267645 \",\n \"1\\n448499 \",\n \"1\\n214953 \",\n \"3\\n88452 109509 495368 \",\n \"1\\n1010001 \",\n \"1\\n701708 \",\n \"3\\n14616 125033 1402360 \",\n \"3\\n88771 158611 986791 \",\n \"1\\n792523 \",\n \"1\\n255532 \",\n \"3\\n167993 286063 738282 \",\n \"3\\n737856 758345 1444212 \",\n \"3\\n36656 174158 983970 \",\n \"3\\n113587 225592 1532321 \",\n \"1\\n310389 \",\n \"1\\n52345 \",\n \"3\\n156571 198356 1445756 \",\n \"3\\n52784 311446 582376 \",\n \"3\\n126683 311387 703669 \"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nDefine the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of n (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.\n\nThe mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.\n\nInput\n\nThe first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of elements in the list.\n\nThe second line contains n integers xi (0 ≤ xi ≤ 1 000 000) — the ith element of the list.\n\nOutput\n\nIn the first line, print a single integer k — the size of the subset.\n\nIn the second line, print k integers — the elements of the subset in any order.\n\nIf there are multiple optimal subsets, print any.\n\nExamples\n\nInput\n\n4\n1 2 3 12\n\n\nOutput\n\n3\n1 2 12 \n\n\nInput\n\n4\n1 1 2 2\n\n\nOutput\n\n3\n1 1 2 \n\n\nInput\n\n2\n1 2\n\n\nOutput\n\n2\n1 2\n\nNote\n\nIn the first case, the optimal subset is , which has mean 5, median 2, and simple skewness of 5 - 2 = 3.\n\nIn the second case, the optimal subset is . Note that repetition is allowed.\n\nIn the last case, any subset has the same median and mean, so all have simple skewness of 0.\n\n### Input:\n2\n1 2\n\n### Output:\n1\n 1 \n\n\n### Input:\n4\n1 1 2 2\n\n### Output:\n3\n 1 1 2 \n\n\n### Code:\nfrom itertools import accumulate\nfrom fractions import Fraction\n\nn = int(input())\nA = [int(x) for x in input().split()]\nA.sort()\nB = list(accumulate([0] + A))\ndef condition(i, z):\n return (2*z - 1)*(A[i-z] + A[-z]) > 2*(B[i+1] - B[i-z+1] + B[-1] - B[-z])\ndef average(i, z):\n return Fraction((B[i+1] - B[i-z] + B[-1] - B[-z-1]) , 2*z + 1)\nmaxans = 0\nargmax = (0, 0)\nfor i in range(1, n-1):\n x, y = 0, min(i, n-1-i)\n while y - x > 1:\n z = (x + y)//2\n if condition(i, z):\n x = z\n else:\n y = z\n if condition(i, y): x = y\n if maxans < average(i, x) - A[i]:\n maxans = average(i, x) - A[i]\n argmax = (i, x)\nprint(argmax[1]*2 + 1)\nfor i in range(argmax[0] - argmax[1], argmax[0] + 1):\n print(A[i], end = ' ')\nfor i in range(-argmax[1], 0):\n print(A[i], end = ' ')\n\n \n"}}},{"rowIdx":673,"cells":{"id":{"kind":"string","value":"676_A. Nicholas and Permutation_3169"},"description":{"kind":"string","value":"Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.\n\nNicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.\n\nInput\n\nThe first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation.\n\nThe second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.\n\nOutput\n\nPrint a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.\n\nExamples\n\nInput\n\n5\n4 5 1 3 2\n\n\nOutput\n\n3\n\n\nInput\n\n7\n1 6 5 3 4 7 2\n\n\nOutput\n\n6\n\n\nInput\n\n6\n6 5 4 3 2 1\n\n\nOutput\n\n5\n\nNote\n\nIn the first sample, one may obtain the optimal answer by swapping elements 1 and 2.\n\nIn the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.\n\nIn the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2."},"code":{"kind":"string","value":"n = int(input())\na = list(map(int, input().split()))\n\nmaxLocate = a.index(n)\nminLocate = a.index(1)\n\ndistanceMax = len(a) - 1 - a.index(n)\ndistanceMin = len(a) - 1 - a.index(1)\n\nprint(max(maxLocate, minLocate, distanceMax, distanceMin))\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"6\\n6 5 4 3 2 1\\n\",\n \"7\\n1 6 5 3 4 7 2\\n\",\n \"5\\n4 5 1 3 2\\n\",\n \"76\\n1 47 54 17 38 37 12 32 14 48 43 71 60 56 4 13 64 41 52 57 62 24 23 49 20 10 63 3 25 66 59 40 58 33 53 46 70 7 35 61 72 74 73 19 30 5 29 6 15 28 21 27 51 55 50 9 65 8 67 39 76 42 31 34 16 2 36 11 26 44 22 45 75 18 69 68\\n\",\n \"12\\n3 6 7 8 9 10 12 5 4 2 11 1\\n\",\n \"81\\n63 22 4 41 43 74 64 39 10 35 20 81 11 28 70 67 53 79 16 61 68 52 27 37 58 9 50 49 18 30 72 47 7 60 78 51 23 48 73 66 44 13 15 57 56 38 1 76 25 45 36 34 42 8 75 26 59 14 71 21 6 77 5 17 2 32 40 54 46 24 29 3 31 19 65 62 33 69 12 80 55\\n\",\n \"98\\n85 94 69 86 22 52 27 79 53 91 35 55 33 88 8 75 76 95 64 54 67 30 70 49 6 16 2 48 80 32 25 90 98 46 9 96 36 81 10 92 28 11 37 97 15 41 38 40 83 44 29 47 23 3 31 61 87 39 78 20 68 12 17 73 59 18 77 72 43 51 84 24 89 65 26 7 74 93 21 19 5 14 50 42 82 71 60 56 34 62 58 57 45 66 13 63 4 1\\n\",\n \"22\\n8 3 17 4 16 21 14 11 10 15 6 18 13 12 22 20 5 2 9 7 19 1\\n\",\n \"14\\n6 10 13 9 7 1 12 14 3 2 5 4 11 8\\n\",\n \"100\\n76 70 67 54 40 1 48 63 64 36 42 90 99 27 47 17 93 7 13 84 16 57 74 5 83 61 19 56 52 92 38 91 82 79 34 66 71 28 37 98 35 94 77 53 73 10 26 80 15 32 8 81 3 95 44 46 72 6 33 11 21 85 4 30 24 51 49 96 87 55 14 31 12 60 45 9 29 22 58 18 88 2 50 59 20 86 23 41 100 39 62 68 69 97 78 43 25 89 65 75\\n\",\n \"4\\n1 2 4 3\\n\",\n \"70\\n19 12 15 18 36 16 61 69 24 7 11 13 3 48 55 21 37 17 43 31 41 22 28 32 27 63 38 49 59 56 30 25 67 51 52 45 50 44 66 57 26 60 5 46 33 6 23 34 8 40 2 68 14 39 65 64 62 42 47 54 10 53 9 1 70 58 20 4 29 35\\n\",\n \"11\\n5 4 6 9 10 11 7 3 1 2 8\\n\",\n \"6\\n5 4 2 6 1 3\\n\",\n \"82\\n50 24 17 41 49 18 80 11 79 72 57 31 21 35 2 51 36 66 20 65 38 3 45 32 59 81 28 30 70 55 29 76 73 6 33 39 8 7 19 48 63 1 77 43 4 13 78 54 69 9 40 46 74 82 60 71 16 64 12 14 47 26 44 5 10 75 53 25 27 15 56 42 58 34 23 61 67 62 68 22 37 52\\n\",\n \"6\\n2 1 3 4 5 6\\n\",\n \"99\\n33 48 19 41 59 64 16 12 17 13 7 1 9 6 4 92 61 49 60 25 74 65 22 97 30 32 10 62 14 55 80 66 82 78 31 23 87 93 27 98 20 29 88 84 77 34 83 96 79 90 56 89 58 72 52 47 21 76 24 70 44 94 5 39 8 18 57 36 40 68 43 75 3 2 35 99 63 26 67 73 15 11 53 28 42 46 69 50 51 95 38 37 54 85 81 91 45 86 71\\n\",\n \"67\\n66 16 2 53 35 38 49 28 18 6 36 58 21 47 27 5 50 62 44 12 52 37 11 56 15 31 25 65 17 29 59 41 7 42 4 43 39 10 1 40 24 13 20 54 19 67 46 60 51 45 64 30 8 33 26 9 3 22 34 23 57 48 55 14 63 61 32\\n\",\n \"19\\n12 19 3 11 15 6 18 14 5 10 2 13 9 7 4 8 17 16 1\\n\",\n \"13\\n8 4 3 7 5 11 9 1 10 2 13 12 6\\n\",\n \"32\\n15 32 11 3 18 23 19 14 5 8 6 21 13 24 25 4 16 9 27 20 17 31 2 22 7 12 30 1 26 10 29 28\\n\",\n \"31\\n29 13 26 27 9 28 2 16 30 21 12 11 3 31 23 6 22 20 1 5 14 24 19 18 8 4 10 17 15 25 7\\n\",\n \"7\\n1 5 3 6 2 4 7\\n\",\n \"4\\n3 1 4 2\\n\",\n \"84\\n75 8 66 21 61 63 72 51 52 13 59 25 28 58 64 53 79 41 34 7 67 11 39 56 44 24 50 9 49 55 1 80 26 6 73 74 27 69 65 37 18 43 36 17 30 3 47 29 76 78 32 22 12 68 46 5 42 81 57 31 33 83 54 48 14 62 10 16 4 20 71 70 35 15 45 19 60 77 2 23 84 40 82 38\\n\",\n \"100\\n22 47 34 65 69 5 68 78 53 54 41 23 80 51 11 8 2 85 81 75 25 58 29 73 30 49 10 71 17 96 76 89 79 20 12 15 55 7 46 32 19 3 82 35 74 44 38 40 92 14 6 50 97 63 45 93 37 18 62 77 87 36 83 9 90 61 57 28 39 43 52 42 24 56 21 84 26 99 88 59 33 70 4 60 98 95 94 100 13 48 66 72 16 31 64 91 1 86 27 67\\n\",\n \"9\\n6 8 5 3 4 7 9 2 1\\n\",\n \"44\\n4 38 6 40 29 3 44 2 30 35 25 36 34 10 11 31 21 7 14 23 37 19 27 18 5 22 1 16 17 9 39 13 15 32 43 8 41 26 42 12 24 33 20 28\\n\",\n \"6\\n5 2 3 1 6 4\\n\",\n \"52\\n16 45 23 7 15 19 43 20 4 32 35 36 9 50 5 26 38 46 13 33 12 2 48 37 41 31 10 28 8 42 3 21 11 1 17 27 34 30 44 40 6 51 49 47 25 22 18 24 52 29 14 39\\n\",\n \"100\\n100 97 92 12 62 17 19 58 37 26 30 95 31 35 87 10 13 43 98 61 28 89 76 1 23 21 11 22 50 56 91 74 3 24 96 55 64 67 14 4 71 16 18 9 77 68 51 81 32 82 46 88 86 60 29 66 72 85 70 7 53 63 33 45 83 2 25 94 52 93 5 69 20 47 49 54 57 39 34 27 90 80 78 59 40 42 79 6 38 8 48 15 65 73 99 44 41 84 36 75\\n\",\n \"2\\n1 2\\n\",\n \"4\\n2 4 1 3\\n\",\n \"50\\n31 45 3 34 13 43 32 4 42 9 7 8 24 14 35 6 19 46 44 17 18 1 25 20 27 41 2 16 12 10 11 47 38 21 28 49 30 15 50 36 29 26 22 39 48 5 23 37 33 40\\n\",\n \"6\\n3 2 1 4 6 5\\n\",\n \"51\\n47 29 2 11 43 44 27 1 39 14 25 30 33 21 38 45 34 51 16 50 42 31 41 46 15 48 13 19 6 37 35 7 22 28 20 4 17 10 5 8 24 40 9 36 18 49 12 26 23 3 32\\n\",\n \"5\\n2 3 1 5 4\\n\",\n \"94\\n29 85 82 78 61 83 80 63 11 38 50 43 9 24 4 87 79 45 3 17 90 7 34 27 1 76 26 39 84 47 22 41 81 19 44 23 56 92 35 31 72 62 70 53 40 88 13 14 73 2 59 86 46 94 15 12 77 57 89 42 75 48 18 51 32 55 71 30 49 91 20 60 5 93 33 64 21 36 10 28 8 65 66 69 74 58 6 52 25 67 16 37 54 68\\n\",\n \"3\\n1 3 2\\n\",\n \"34\\n34 30 7 16 6 1 10 23 29 13 15 25 32 26 18 11 28 3 14 21 19 5 31 33 4 17 8 9 24 20 27 22 2 12\\n\",\n \"42\\n42 15 24 26 4 34 19 29 38 32 31 33 14 41 21 3 11 39 25 6 5 20 23 10 16 36 18 28 27 1 7 40 22 30 9 2 37 17 8 12 13 35\\n\",\n \"4\\n1 4 2 3\\n\",\n \"37\\n24 1 12 23 11 6 30 15 4 21 13 20 25 17 5 8 36 19 32 26 14 9 7 18 10 29 37 35 16 2 22 34 3 27 31 33 28\\n\",\n \"97\\n40 63 44 64 84 92 38 41 28 91 3 70 76 67 94 96 35 79 29 22 78 88 85 8 21 1 93 54 71 80 37 17 13 26 62 59 75 87 69 33 89 49 77 61 12 39 6 36 58 18 73 50 82 45 74 52 11 34 95 7 23 30 15 32 31 16 55 19 20 83 60 72 10 53 51 14 27 9 68 47 5 2 81 46 57 86 56 43 48 66 24 25 4 42 65 97 90\\n\",\n \"10\\n2 9 3 4 1 10 5 6 7 8\\n\",\n \"89\\n68 40 14 58 56 25 8 44 49 55 9 76 66 54 33 81 42 15 59 17 21 30 75 60 4 48 64 6 52 63 61 27 12 57 72 67 23 86 77 80 22 13 43 73 26 78 50 51 18 62 1 29 82 16 74 2 87 24 3 41 11 46 47 69 10 84 65 39 35 79 70 32 34 31 20 19 53 71 36 28 83 88 38 85 7 5 37 45 89\\n\",\n \"4\\n4 2 1 3\\n\",\n \"48\\n29 26 14 18 34 33 13 39 32 1 37 20 35 19 28 48 30 23 46 27 5 22 24 38 12 15 8 36 43 45 16 47 6 9 31 40 44 17 2 41 11 42 25 4 21 3 10 7\\n\",\n \"8\\n2 3 4 5 1 6 8 7\\n\",\n \"10\\n8 7 10 1 2 3 4 6 5 9\\n\",\n \"4\\n1 4 3 2\\n\",\n \"15\\n3 14 13 12 7 2 4 11 15 1 8 6 5 10 9\\n\",\n \"29\\n21 11 10 25 2 5 9 16 29 8 17 4 15 13 6 22 7 24 19 12 18 20 1 3 23 28 27 14 26\\n\",\n \"25\\n12 13 22 17 1 18 14 5 21 2 10 4 3 23 11 6 20 8 24 16 15 19 9 7 25\\n\",\n \"88\\n1 83 73 46 61 31 39 86 57 43 16 29 26 80 82 7 36 42 13 20 6 64 19 40 24 12 47 87 8 34 75 9 69 3 11 52 14 25 84 59 27 10 54 51 81 74 65 77 70 17 60 35 23 44 49 2 4 88 5 21 41 32 68 66 15 55 48 58 78 53 22 38 45 33 30 50 85 76 37 79 63 18 28 62 72 56 71 67\\n\",\n \"100\\n66 100 53 88 7 73 54 41 31 42 8 46 65 90 78 14 94 30 79 39 89 5 83 50 38 61 37 86 22 95 60 98 34 57 91 10 75 25 15 43 23 17 96 35 93 48 87 47 56 13 19 9 82 62 67 80 11 55 99 70 18 26 58 85 12 44 16 45 4 49 20 71 92 24 81 2 76 32 6 21 84 36 52 97 59 63 40 51 27 64 68 3 77 72 28 33 29 1 74 69\\n\",\n \"18\\n8 6 14 17 9 11 15 13 5 3 18 1 2 7 12 16 4 10\\n\",\n \"6\\n5 4 2 1 6 3\\n\",\n \"8\\n2 5 6 4 8 3 1 7\\n\",\n \"3\\n2 3 1\\n\",\n \"6\\n4 6 3 5 2 1\\n\",\n \"4\\n4 3 1 2\\n\",\n \"61\\n61 11 26 29 31 40 32 30 35 3 18 52 9 53 42 4 50 54 20 58 28 49 22 12 2 19 16 15 57 34 51 43 7 17 25 41 56 47 55 60 46 14 44 45 24 27 33 1 48 13 59 23 38 39 6 5 36 10 8 37 21\\n\",\n \"4\\n4 3 2 1\\n\",\n \"65\\n10 11 55 43 53 25 35 26 16 37 41 38 59 21 48 2 65 49 17 23 18 30 62 36 3 4 47 15 28 63 57 54 31 46 44 12 51 7 29 13 56 52 14 22 39 19 8 27 45 5 6 34 32 61 20 50 9 24 33 58 60 40 1 42 64\\n\",\n \"3\\n1 2 3\\n\",\n \"92\\n67 57 76 78 25 89 6 82 11 16 26 17 59 48 73 10 21 31 27 80 4 5 22 13 92 55 45 85 63 28 75 60 54 88 91 47 29 35 7 87 1 39 43 51 71 84 83 81 46 9 38 56 90 24 37 41 19 86 50 61 79 20 18 14 69 23 62 65 49 52 58 53 36 2 68 64 15 42 30 34 66 32 44 40 8 33 3 77 74 12 70 72\\n\",\n \"23\\n1 23 11 20 9 3 12 4 7 17 5 15 2 10 18 16 8 22 14 13 19 21 6\\n\",\n \"4\\n3 1 2 4\\n\",\n \"54\\n6 39 17 3 45 52 16 21 23 48 42 36 13 37 46 10 43 27 49 7 38 32 31 30 15 25 2 29 8 51 54 19 41 44 24 34 22 5 20 14 12 1 33 40 4 26 9 35 18 28 47 50 11 53\\n\",\n \"69\\n29 49 25 51 21 35 11 61 39 54 40 37 60 42 27 33 59 53 34 10 46 2 23 69 8 47 58 36 1 38 19 12 7 48 13 3 6 22 18 5 65 24 50 41 66 44 67 57 4 56 62 43 9 30 14 15 28 31 64 26 16 55 68 17 32 20 45 52 63\\n\",\n \"60\\n60 27 34 32 54 55 33 12 40 3 47 44 50 39 38 59 11 25 17 15 16 30 21 31 10 52 5 23 4 48 6 26 36 57 14 22 8 56 58 9 24 7 37 53 42 43 20 49 51 19 2 46 28 18 35 13 29 45 41 1\\n\",\n \"4\\n2 1 4 3\\n\",\n \"57\\n39 28 53 36 3 6 12 56 55 20 50 19 43 42 18 40 24 52 38 17 33 23 22 41 14 7 26 44 45 16 35 1 8 47 31 5 30 51 32 4 37 25 13 34 54 21 46 10 15 11 2 27 29 48 49 9 57\\n\",\n \"4\\n3 4 1 2\\n\",\n \"3\\n2 1 3\\n\",\n \"4\\n1 2 3 4\\n\",\n \"86\\n64 56 41 10 31 69 47 39 37 36 27 19 9 42 15 6 78 59 52 17 71 45 72 14 2 54 38 79 4 18 16 8 46 75 50 82 44 24 20 55 58 86 61 43 35 32 33 40 63 30 28 60 13 53 12 57 77 81 76 66 73 84 85 62 68 22 51 5 49 7 1 70 80 65 34 48 23 21 83 11 74 26 29 67 25 3\\n\",\n \"100\\n22 59 25 77 68 79 32 45 20 28 61 60 38 86 33 10 100 15 53 75 78 39 67 13 66 34 96 4 63 23 73 29 31 35 71 55 16 14 72 56 94 97 17 93 47 84 57 8 21 51 54 85 26 76 49 81 2 92 62 44 91 87 11 24 95 69 5 7 99 6 65 48 70 12 41 18 74 27 42 3 80 30 50 98 58 37 82 89 83 36 40 52 19 9 88 46 43 1 90 64\\n\",\n \"83\\n64 8 58 17 67 46 3 82 23 70 72 16 53 45 13 20 12 48 40 4 6 47 76 60 19 44 30 78 28 22 75 15 25 29 63 74 55 32 14 51 35 31 62 77 27 42 65 71 56 61 66 41 68 49 7 34 2 83 36 5 33 26 37 80 59 50 1 9 54 21 18 24 38 73 81 52 10 39 43 79 57 11 69\\n\",\n \"53\\n53 30 50 22 51 31 32 38 12 7 39 43 1 23 6 8 24 52 2 21 34 13 3 35 5 15 19 11 47 18 9 20 29 4 36 45 27 41 25 48 16 46 44 17 10 14 42 26 40 28 33 37 49\\n\",\n \"87\\n14 20 82 47 39 75 71 45 3 37 63 19 32 68 7 41 48 76 27 46 84 49 4 44 26 69 17 64 1 18 58 33 11 23 21 86 67 52 70 16 77 78 6 74 15 87 10 59 13 34 22 2 65 38 66 61 51 57 35 60 81 40 36 80 31 43 83 56 79 55 29 5 12 8 50 30 53 72 54 9 24 25 42 62 73 28 85\\n\",\n \"55\\n26 15 31 21 32 43 34 51 7 12 5 44 17 54 18 25 48 47 20 3 41 24 45 2 11 22 29 39 37 53 35 28 36 9 50 10 30 38 19 13 4 8 27 1 42 6 49 23 55 40 33 16 46 14 52\\n\",\n \"75\\n75 28 60 19 59 17 65 26 32 23 18 64 8 62 4 11 42 16 47 5 72 46 9 1 25 21 2 50 33 6 36 68 30 12 20 40 53 45 34 7 37 39 38 44 63 61 67 3 66 51 29 73 24 57 70 27 10 56 22 55 13 49 35 15 54 41 14 74 69 48 52 31 71 43 58\\n\",\n \"56\\n6 20 38 46 10 11 40 19 5 1 47 33 4 18 32 36 37 45 56 49 48 52 12 26 31 14 2 9 24 3 16 51 41 43 23 17 34 7 29 50 55 25 39 44 22 27 54 8 28 35 30 42 13 53 21 15\\n\",\n \"77\\n10 20 57 65 53 69 59 45 58 32 28 72 4 14 1 33 40 47 7 5 51 76 37 16 41 61 42 2 21 26 38 74 35 64 43 77 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20\\n\",\n \"4\\n4 1 2 3\\n\",\n \"96\\n64 3 47 83 19 10 72 61 73 95 16 40 54 84 8 86 28 4 37 42 92 48 63 76 67 1 59 66 20 35 93 2 43 7 45 70 34 33 26 91 85 89 13 29 58 68 44 25 87 75 49 71 41 17 55 36 32 31 74 22 52 79 30 88 50 78 38 39 65 27 69 77 81 94 82 53 21 80 57 60 24 46 51 9 18 15 96 62 6 23 11 12 90 5 14 56\\n\",\n \"100\\n28 30 77 4 81 67 31 25 66 56 88 73 83 51 57 34 21 90 38 76 22 99 53 70 91 3 64 54 6 94 8 5 97 80 50 45 61 40 16 95 36 98 9 2 17 44 72 55 18 58 47 12 87 24 7 32 14 23 65 41 63 48 62 39 92 27 43 19 46 13 42 52 96 84 26 69 100 79 93 49 35 60 71 59 68 15 10 29 20 1 78 33 75 86 11 85 74 82 89 37\\n\",\n \"4\\n4 1 3 2\\n\",\n \"6\\n2 3 4 1 6 5\\n\",\n \"10\\n5 2 3 4 1 6 7 8 10 9\\n\",\n \"85\\n1 18 58 8 22 76 3 61 12 33 54 41 6 24 82 15 10 17 38 64 26 4 62 28 47 14 66 9 84 75 2 71 67 43 37 32 85 21 69 52 55 63 81 51 74 59 65 34 29 36 30 45 27 53 13 79 39 57 5 70 19 40 7 42 68 48 16 80 83 23 46 35 72 31 11 44 73 77 50 56 49 25 60 20 78\\n\",\n \"4\\n3 4 2 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\"58\\n\",\n \"4\\n\",\n \"8\\n\",\n \"99\\n\",\n \"34\\n\",\n \"70\\n\",\n \"52\\n\",\n \"26\\n\",\n \"5\\n\",\n \"60\\n\",\n \"98\\n\",\n \"65\\n\",\n \"3\\n\",\n \"38\\n\",\n \"21\\n\",\n \"4\\n\",\n \"99\\n\",\n \"45\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nNicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.\n\nNicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.\n\nInput\n\nThe first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation.\n\nThe second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.\n\nOutput\n\nPrint a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.\n\nExamples\n\nInput\n\n5\n4 5 1 3 2\n\n\nOutput\n\n3\n\n\nInput\n\n7\n1 6 5 3 4 7 2\n\n\nOutput\n\n6\n\n\nInput\n\n6\n6 5 4 3 2 1\n\n\nOutput\n\n5\n\nNote\n\nIn the first sample, one may obtain the optimal answer by swapping elements 1 and 2.\n\nIn the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.\n\nIn the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2.\n\n### Input:\n6\n6 5 4 3 2 1\n\n### Output:\n5\n\n\n### Input:\n7\n1 6 5 3 4 7 2\n\n### Output:\n6\n\n\n### Code:\nn = int(input())\na = list(map(int, input().split()))\n\nmaxLocate = a.index(n)\nminLocate = a.index(1)\n\ndistanceMax = len(a) - 1 - a.index(n)\ndistanceMin = len(a) - 1 - a.index(1)\n\nprint(max(maxLocate, minLocate, distanceMax, distanceMin))\n"}}},{"rowIdx":674,"cells":{"id":{"kind":"string","value":"69_A. Young Physicist_3173"},"description":{"kind":"string","value":"A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. \"Piece of cake\" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.\n\nInput\n\nThe first line contains a positive integer n (1 ≤ n ≤ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≤ xi, yi, zi ≤ 100).\n\nOutput\n\nPrint the word \"YES\" if the body is in equilibrium, or the word \"NO\" if it is not.\n\nExamples\n\nInput\n\n3\n4 1 7\n-2 4 -1\n1 -5 -3\n\n\nOutput\n\nNO\n\nInput\n\n3\n3 -1 7\n-5 2 -4\n2 -1 -3\n\n\nOutput\n\nYES"},"code":{"kind":"string","value":"sum1,sum2,sum3 = 0,0,0\nn = int(input())\nwhile n:\n n-=1\n l = list(map(int, input().split()))\n sum1 += l[0]\n sum2 += l[1]\n sum3 += l[2]\nif sum1==0 and sum2 ==0 and sum3 ==0:\n print(\"YES\")\nelse:\n print(\"NO\")"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3\\n3 -1 7\\n-5 2 -4\\n2 -1 -3\\n\",\n \"3\\n4 1 7\\n-2 4 -1\\n1 -5 -3\\n\",\n \"14\\n43 23 17\\n4 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19\\n41 -42 -1\\n49 -50 -6\\n-59 -22 1\\n-7 27 59\\n8 -27 -43\\n8 34 3\\n-11 -3 33\\n\",\n \"10\\n-6 21 18\\n20 -11 -3\\n37 -18 41\\n-10 8 33\\n34 23 32\\n30 -6 -8\\n39 -49 -36\\n56 47 -49\\n22 29 -2\\n-18 -6 3\\n\",\n \"12\\n3 28 -35\\n-56 -44 -5\\n9 -47 -6\\n-40 -22 20\\n-15 15 38\\n-21 71 48\\n-1 -37 -45\\n-10 -13 -50\\n-5 21 22\\n34 28 50\\n50 11 -35\\n37 0 0\\n\",\n \"3\\n-3 -1 0\\n1 -1 9\\n0 1 0\\n\"\n ],\n \"output\": [\n \"YES\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"YES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nA guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. \"Piece of cake\" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.\n\nInput\n\nThe first line contains a positive integer n (1 ≤ n ≤ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≤ xi, yi, zi ≤ 100).\n\nOutput\n\nPrint the word \"YES\" if the body is in equilibrium, or the word \"NO\" if it is not.\n\nExamples\n\nInput\n\n3\n4 1 7\n-2 4 -1\n1 -5 -3\n\n\nOutput\n\nNO\n\nInput\n\n3\n3 -1 7\n-5 2 -4\n2 -1 -3\n\n\nOutput\n\nYES\n\n### Input:\n3\n3 -1 7\n-5 2 -4\n2 -1 -3\n\n### Output:\nYES\n\n\n### Input:\n3\n4 1 7\n-2 4 -1\n1 -5 -3\n\n### Output:\nNO\n\n\n### Code:\nsum1,sum2,sum3 = 0,0,0\nn = int(input())\nwhile n:\n n-=1\n l = list(map(int, input().split()))\n sum1 += l[0]\n sum2 += l[1]\n sum3 += l[2]\nif sum1==0 and sum2 ==0 and sum3 ==0:\n print(\"YES\")\nelse:\n print(\"NO\")"}}},{"rowIdx":675,"cells":{"id":{"kind":"string","value":"742_A. Arpa’s hard exam and Mehrdad’s naive cheat_3179"},"description":{"kind":"string","value":"There exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.\n\nMehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n. \n\n\n\nMehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.\n\nInput\n\nThe single line of input contains one integer n (0 ≤ n ≤ 109).\n\nOutput\n\nPrint single integer — the last digit of 1378n.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n8\n\nInput\n\n2\n\n\nOutput\n\n4\n\nNote\n\nIn the first example, last digit of 13781 = 1378 is 8.\n\nIn the second example, last digit of 13782 = 1378·1378 = 1898884 is 4."},"code":{"kind":"string","value":"n = int(input())\nif n == 0:\n print(1)\nif n % 4 == 0 and n!= 0 :\n print(6)\nif n % 4 == 1:\n print(8)\nif n % 4 == 2:\n print(4)\nif n % 4 == 3:\n print(2)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"2\\n\",\n \"1\\n\",\n \"12\\n\",\n \"1378\\n\",\n \"51202278\\n\",\n \"989898989\\n\",\n \"4\\n\",\n \"7\\n\",\n \"9\\n\",\n \"6\\n\",\n \"8\\n\",\n \"12193721\\n\",\n \"999999995\\n\",\n \"999999999\\n\",\n \"11\\n\",\n \"999999996\\n\",\n \"999999998\\n\",\n \"3\\n\",\n \"14\\n\",\n \"15\\n\",\n \"10\\n\",\n \"999999994\\n\",\n \"1000\\n\",\n \"13781378\\n\",\n \"5\\n\",\n \"999999997\\n\",\n \"1000000000\\n\",\n \"13\\n\",\n \"16\\n\",\n \"0\\n\",\n \"24\\n\",\n \"1983990\\n\",\n \"937715\\n\",\n \"1902349577\\n\",\n \"0000000000\\n\",\n \"2584\\n\",\n \"394254778\\n\",\n \"341779918\\n\",\n \"21\\n\",\n \"215963833\\n\",\n \"1065810635\\n\",\n \"28\\n\",\n \"17\\n\",\n \"1760197508\\n\",\n \"1001\\n\",\n \"5602440\\n\",\n \"17877370\\n\",\n \"22\\n\",\n \"19\\n\",\n \"44\\n\",\n \"49\\n\",\n \"3952697\\n\",\n \"74399095\\n\",\n \"185380\\n\",\n \"212134273\\n\",\n \"45271055\\n\",\n \"1603265602\\n\",\n \"50\\n\",\n \"403279506\\n\",\n \"1011\\n\",\n \"212217\\n\",\n \"6373463\\n\",\n \"0001000000\\n\",\n \"26\\n\",\n \"23\\n\",\n \"43\\n\",\n \"53\\n\",\n \"252331\\n\",\n \"59773239\\n\",\n \"348367\\n\",\n \"274204102\\n\",\n \"88997880\\n\",\n \"37\\n\",\n \"333212833\\n\",\n \"1111\\n\",\n \"117086\\n\",\n \"3544279\\n\",\n \"0001000010\\n\",\n \"30\\n\",\n \"74\\n\",\n \"32\\n\",\n \"87\\n\",\n \"425517\\n\",\n \"39722903\\n\",\n \"129454\\n\",\n \"502575216\\n\",\n \"151917914\\n\",\n \"39\\n\",\n \"284885416\\n\",\n \"1010\\n\",\n \"184257\\n\",\n \"5976311\\n\",\n \"0101000010\\n\",\n \"48\\n\",\n \"18\\n\",\n \"38\\n\",\n \"160\\n\",\n \"769275\\n\",\n \"60872248\\n\",\n \"54684\\n\",\n \"787055094\\n\",\n \"251769870\\n\",\n \"31\\n\",\n \"1395680\\n\",\n \"0010\\n\",\n \"334614\\n\",\n \"2269906\\n\",\n \"0101000011\\n\",\n \"65\\n\",\n \"33\\n\",\n \"34\\n\",\n \"262\\n\",\n \"1263861\\n\",\n \"85907381\\n\",\n \"59967\\n\",\n \"646944545\\n\",\n \"213990998\\n\",\n \"72\\n\",\n \"787056\\n\",\n \"0011\\n\",\n \"245481\\n\",\n \"1079259\\n\",\n \"0101000111\\n\",\n \"27\\n\",\n \"42\\n\",\n \"25\\n\",\n \"400\\n\",\n \"1699298\\n\",\n \"127860079\\n\",\n \"34050\\n\"\n ],\n \"output\": [\n \"4\\n\",\n \"8\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"8\\n\",\n \"6\\n\",\n \"2\\n\",\n \"8\\n\",\n \"4\\n\",\n \"6\\n\",\n \"8\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"6\\n\",\n \"4\\n\",\n \"2\\n\",\n \"4\\n\",\n \"2\\n\",\n \"4\\n\",\n \"4\\n\",\n \"6\\n\",\n \"4\\n\",\n \"8\\n\",\n \"8\\n\",\n \"6\\n\",\n \"8\\n\",\n \"6\\n\",\n \"1\\n\",\n \"6\\n\",\n \"4\\n\",\n \"2\\n\",\n \"8\\n\",\n \"1\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"8\\n\",\n \"8\\n\",\n \"2\\n\",\n \"6\\n\",\n \"8\\n\",\n \"6\\n\",\n \"8\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"2\\n\",\n \"6\\n\",\n \"8\\n\",\n \"8\\n\",\n \"2\\n\",\n \"6\\n\",\n \"8\\n\",\n \"2\\n\",\n \"4\\n\",\n \"4\\n\",\n \"4\\n\",\n \"2\\n\",\n \"8\\n\",\n \"2\\n\",\n \"6\\n\",\n \"4\\n\",\n \"2\\n\",\n \"2\\n\",\n \"8\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"4\\n\",\n \"6\\n\",\n \"8\\n\",\n \"8\\n\",\n \"2\\n\",\n \"4\\n\",\n \"2\\n\",\n \"4\\n\",\n \"4\\n\",\n \"4\\n\",\n \"6\\n\",\n \"2\\n\",\n \"8\\n\",\n \"2\\n\",\n \"4\\n\",\n \"6\\n\",\n \"4\\n\",\n \"2\\n\",\n \"6\\n\",\n \"4\\n\",\n \"8\\n\",\n \"2\\n\",\n \"4\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"6\\n\",\n \"2\\n\",\n \"6\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"2\\n\",\n \"6\\n\",\n \"4\\n\",\n \"4\\n\",\n \"4\\n\",\n \"2\\n\",\n \"8\\n\",\n \"8\\n\",\n \"4\\n\",\n \"4\\n\",\n \"8\\n\",\n \"8\\n\",\n \"2\\n\",\n \"8\\n\",\n \"4\\n\",\n \"6\\n\",\n \"6\\n\",\n \"2\\n\",\n \"8\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"4\\n\",\n \"8\\n\",\n \"6\\n\",\n \"4\\n\",\n \"2\\n\",\n \"4\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nThere exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.\n\nMehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n. \n\n\n\nMehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.\n\nInput\n\nThe single line of input contains one integer n (0 ≤ n ≤ 109).\n\nOutput\n\nPrint single integer — the last digit of 1378n.\n\nExamples\n\nInput\n\n1\n\n\nOutput\n\n8\n\nInput\n\n2\n\n\nOutput\n\n4\n\nNote\n\nIn the first example, last digit of 13781 = 1378 is 8.\n\nIn the second example, last digit of 13782 = 1378·1378 = 1898884 is 4.\n\n### Input:\n2\n\n### Output:\n4\n\n\n### Input:\n1\n\n### Output:\n8\n\n\n### Code:\nn = int(input())\nif n == 0:\n print(1)\nif n % 4 == 0 and n!= 0 :\n print(6)\nif n % 4 == 1:\n print(8)\nif n % 4 == 2:\n print(4)\nif n % 4 == 3:\n print(2)\n"}}},{"rowIdx":676,"cells":{"id":{"kind":"string","value":"765_E. Tree Folding_3183"},"description":{"kind":"string","value":"Vanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 = v, a1, ..., ak, and b0 = v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased:\n\n\n\nHelp Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path.\n\nInput\n\nThe first line of input contains the number of vertices n (2 ≤ n ≤ 2·105).\n\nNext n - 1 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 ≤ u, v ≤ n, u ≠ v) — indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree.\n\nOutput\n\nIf it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path.\n\nExamples\n\nInput\n\n6\n1 2\n2 3\n2 4\n4 5\n1 6\n\n\nOutput\n\n3\n\n\nInput\n\n7\n1 2\n1 3\n3 4\n1 5\n5 6\n6 7\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample case, a path of three edges is obtained after merging paths 2 - 1 - 6 and 2 - 4 - 5.\n\nIt is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 - 3 - 4 and 1 - 5 - 6, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path."},"code":{"kind":"string","value":"import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\nmod = 10**9 + 7\n\ndef LI(): return list(map(int, input().split()))\ndef II(): return int(input())\ndef LS(): return input().split()\ndef S(): return input()\n\n\ndef main():\n n = II()\n d = collections.defaultdict(set)\n for _ in range(n-1):\n a,b = LI()\n d[a].add(b)\n d[b].add(a)\n\n memo = [-1] * (n+1)\n def path(t,s):\n ps = set()\n dt = list(d[t])\n for k in dt:\n if memo[k] < 0:\n continue\n ps.add(memo[k])\n\n if s == -1 and len(ps) == 2:\n memo[t] = sum(ps) + 2\n return memo[t]\n\n if len(ps) > 1:\n return -t\n\n if len(ps) == 0:\n memo[t] = 0\n return 0\n\n memo[t] = list(ps)[0] + 1\n return memo[t]\n\n def _path(tt,ss):\n q = [(tt,ss)]\n tq = []\n qi = 0\n while len(q) > qi:\n t,s = q[qi]\n for k in d[t]:\n if k == s:\n continue\n q.append((k,t))\n qi += 1\n for t,s in q[::-1]:\n r = path(t,s)\n if r < 0:\n return r\n return memo[tt]\n\n def _path2(tt,ss):\n q = [(tt,ss)]\n tq = []\n qi = 0\n while len(q) > qi:\n t,s = q[qi]\n for k in d[t]:\n if k == s or memo[k] >= 0:\n continue\n q.append((k,t))\n qi += 1\n for t,s in q[::-1]:\n r = path(t,s)\n if r < 0:\n return r\n return memo[tt]\n\n t = _path(1,-1)\n if t < 0:\n t = _path2(-t,-1)\n\n if t > 0:\n while t%2 == 0:\n t//=2\n return t\n\n return -1\n\nprint(main())\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"6\\n1 2\\n2 3\\n2 4\\n4 5\\n1 6\\n\",\n \"7\\n1 2\\n1 3\\n3 4\\n1 5\\n5 6\\n6 7\\n\",\n \"10\\n4 2\\n7 4\\n2 6\\n2 5\\n4 8\\n10 3\\n2 9\\n9 1\\n5 10\\n\",\n \"10\\n5 10\\n7 8\\n8 3\\n2 6\\n3 2\\n9 7\\n4 5\\n10 1\\n6 4\\n\",\n \"4\\n4 1\\n4 3\\n4 2\\n\",\n \"3\\n3 1\\n1 2\\n\",\n \"9\\n1 2\\n1 3\\n1 4\\n1 5\\n1 6\\n6 7\\n6 8\\n8 9\\n\",\n \"5\\n1 5\\n2 3\\n2 4\\n1 2\\n\",\n \"8\\n6 1\\n4 7\\n4 8\\n8 5\\n7 6\\n4 3\\n4 2\\n\",\n \"7\\n5 6\\n5 7\\n5 1\\n7 4\\n6 3\\n3 2\\n\",\n \"3\\n1 3\\n3 2\\n\",\n \"2\\n1 2\\n\",\n \"5\\n5 4\\n4 3\\n3 1\\n5 2\\n\",\n \"6\\n1 6\\n3 1\\n6 4\\n5 3\\n2 5\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n8 6\\n5 4\\n4 10\\n8 3\\n\",\n \"11\\n11 9\\n6 7\\n7 1\\n8 11\\n5 6\\n3 5\\n9 3\\n10 8\\n2 4\\n4 10\\n\",\n \"12\\n12 6\\n6 7\\n8 11\\n4 8\\n10 4\\n12 3\\n2 10\\n6 2\\n12 9\\n4 1\\n9 5\\n\",\n \"3\\n1 3\\n1 2\\n\",\n \"4\\n2 1\\n4 3\\n4 2\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n8 6\\n1 4\\n4 10\\n8 3\\n\",\n \"6\\n2 6\\n3 1\\n6 4\\n5 3\\n2 5\\n\",\n \"8\\n6 1\\n3 7\\n4 8\\n8 5\\n7 6\\n4 3\\n5 2\\n\",\n \"10\\n5 10\\n9 8\\n8 3\\n2 6\\n3 2\\n9 7\\n4 5\\n10 1\\n6 4\\n\",\n \"8\\n6 1\\n4 7\\n4 8\\n8 5\\n4 6\\n4 3\\n4 2\\n\",\n \"6\\n1 6\\n3 1\\n3 4\\n5 3\\n2 5\\n\",\n \"5\\n1 5\\n4 3\\n2 4\\n1 2\\n\",\n \"8\\n6 1\\n4 7\\n4 8\\n8 5\\n7 6\\n4 3\\n5 2\\n\",\n \"5\\n5 4\\n4 1\\n3 1\\n5 2\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n8 6\\n1 4\\n4 10\\n8 2\\n\",\n \"5\\n5 4\\n4 1\\n3 2\\n5 2\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n1 6\\n1 4\\n4 10\\n8 2\\n\",\n \"4\\n4 1\\n2 3\\n4 2\\n\",\n \"3\\n1 2\\n3 2\\n\",\n \"5\\n5 4\\n4 3\\n4 1\\n5 2\\n\",\n \"6\\n1 4\\n3 1\\n6 4\\n5 3\\n2 5\\n\",\n \"8\\n6 1\\n4 7\\n4 8\\n8 5\\n5 6\\n4 3\\n4 2\\n\",\n \"8\\n6 1\\n4 7\\n7 8\\n8 5\\n5 6\\n4 3\\n4 2\\n\",\n \"10\\n5 10\\n7 8\\n8 3\\n2 6\\n3 2\\n9 8\\n4 5\\n10 1\\n6 4\\n\",\n \"3\\n3 2\\n1 2\\n\",\n \"7\\n1 2\\n1 3\\n3 4\\n2 5\\n5 6\\n6 7\\n\",\n \"6\\n1 6\\n3 1\\n1 4\\n5 3\\n2 5\\n\",\n \"6\\n1 4\\n3 1\\n6 4\\n5 4\\n2 5\\n\",\n \"8\\n6 1\\n4 5\\n7 8\\n8 5\\n5 6\\n4 3\\n4 2\\n\",\n \"5\\n2 5\\n2 3\\n2 4\\n1 2\\n\",\n \"12\\n12 6\\n6 7\\n8 11\\n7 8\\n10 4\\n12 3\\n2 10\\n6 2\\n12 9\\n4 1\\n9 5\\n\",\n \"7\\n1 2\\n1 3\\n2 4\\n1 5\\n5 6\\n6 7\\n\",\n \"8\\n6 1\\n8 7\\n4 8\\n8 5\\n4 6\\n4 3\\n4 2\\n\",\n \"6\\n1 6\\n2 1\\n3 4\\n5 3\\n2 5\\n\",\n \"6\\n2 6\\n6 1\\n6 4\\n5 3\\n2 5\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n9 6\\n1 4\\n4 10\\n8 2\\n\",\n \"7\\n1 2\\n1 4\\n3 4\\n2 5\\n5 6\\n6 7\\n\",\n \"6\\n2 6\\n3 1\\n1 4\\n5 3\\n2 5\\n\",\n \"5\\n2 5\\n2 3\\n2 4\\n1 4\\n\",\n \"6\\n1 6\\n4 1\\n3 4\\n5 3\\n2 5\\n\",\n \"11\\n8 9\\n2 7\\n1 11\\n3 2\\n9 1\\n8 5\\n9 6\\n1 4\\n4 10\\n9 2\\n\",\n \"6\\n4 6\\n3 1\\n1 4\\n5 3\\n2 5\\n\",\n \"2\\n2 1\\n\",\n \"6\\n1 6\\n3 1\\n6 4\\n5 1\\n2 5\\n\",\n \"8\\n6 1\\n4 7\\n4 8\\n8 5\\n4 6\\n4 3\\n7 2\\n\"\n ],\n \"output\": [\n \"3\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"9\\n\",\n \"1\\n\",\n \"1\\n\",\n \"3\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"5\\n\",\n \"1\\n\",\n \"5\\n\",\n \"-1\\n\",\n \"1\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"5\\n\",\n \"7\\n\",\n \"9\\n\",\n \"3\\n\",\n \"3\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"-1\\n\",\n \"1\\n\",\n \"-1\\n\",\n \"3\\n\",\n \"1\\n\",\n \"3\\n\",\n \"5\\n\",\n \"5\\n\",\n \"3\\n\",\n \"1\\n\",\n \"1\\n\",\n \"3\\n\",\n \"1\\n\",\n \"3\\n\",\n \"1\\n\",\n \"1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"3\\n\",\n \"5\\n\",\n \"1\\n\",\n \"-1\\n\",\n \"3\\n\",\n \"5\\n\",\n \"3\\n\",\n \"5\\n\",\n \"-1\\n\",\n \"5\\n\",\n \"1\\n\",\n \"3\\n\",\n \"3\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nVanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 = v, a1, ..., ak, and b0 = v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased:\n\n\n\nHelp Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path.\n\nInput\n\nThe first line of input contains the number of vertices n (2 ≤ n ≤ 2·105).\n\nNext n - 1 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 ≤ u, v ≤ n, u ≠ v) — indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree.\n\nOutput\n\nIf it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path.\n\nExamples\n\nInput\n\n6\n1 2\n2 3\n2 4\n4 5\n1 6\n\n\nOutput\n\n3\n\n\nInput\n\n7\n1 2\n1 3\n3 4\n1 5\n5 6\n6 7\n\n\nOutput\n\n-1\n\nNote\n\nIn the first sample case, a path of three edges is obtained after merging paths 2 - 1 - 6 and 2 - 4 - 5.\n\nIt is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 - 3 - 4 and 1 - 5 - 6, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path.\n\n### Input:\n6\n1 2\n2 3\n2 4\n4 5\n1 6\n\n### Output:\n3\n\n\n### Input:\n7\n1 2\n1 3\n3 4\n1 5\n5 6\n6 7\n\n### Output:\n-1\n\n\n### Code:\nimport math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\nmod = 10**9 + 7\n\ndef LI(): return list(map(int, input().split()))\ndef II(): return int(input())\ndef LS(): return input().split()\ndef S(): return input()\n\n\ndef main():\n n = II()\n d = collections.defaultdict(set)\n for _ in range(n-1):\n a,b = LI()\n d[a].add(b)\n d[b].add(a)\n\n memo = [-1] * (n+1)\n def path(t,s):\n ps = set()\n dt = list(d[t])\n for k in dt:\n if memo[k] < 0:\n continue\n ps.add(memo[k])\n\n if s == -1 and len(ps) == 2:\n memo[t] = sum(ps) + 2\n return memo[t]\n\n if len(ps) > 1:\n return -t\n\n if len(ps) == 0:\n memo[t] = 0\n return 0\n\n memo[t] = list(ps)[0] + 1\n return memo[t]\n\n def _path(tt,ss):\n q = [(tt,ss)]\n tq = []\n qi = 0\n while len(q) > qi:\n t,s = q[qi]\n for k in d[t]:\n if k == s:\n continue\n q.append((k,t))\n qi += 1\n for t,s in q[::-1]:\n r = path(t,s)\n if r < 0:\n return r\n return memo[tt]\n\n def _path2(tt,ss):\n q = [(tt,ss)]\n tq = []\n qi = 0\n while len(q) > qi:\n t,s = q[qi]\n for k in d[t]:\n if k == s or memo[k] >= 0:\n continue\n q.append((k,t))\n qi += 1\n for t,s in q[::-1]:\n r = path(t,s)\n if r < 0:\n return r\n return memo[tt]\n\n t = _path(1,-1)\n if t < 0:\n t = _path2(-t,-1)\n\n if t > 0:\n while t%2 == 0:\n t//=2\n return t\n\n return -1\n\nprint(main())\n"}}},{"rowIdx":677,"cells":{"id":{"kind":"string","value":"789_B. Masha and geometric depression_3187"},"description":{"kind":"string","value":"Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.\n\nYou are given geometric progression b defined by two integers b1 and q. Remind that a geometric progression is a sequence of integers b1, b2, b3, ..., where for each i > 1 the respective term satisfies the condition bi = bi - 1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m \"bad\" integers a1, a2, ..., am, and an integer l.\n\nMasha writes all progression terms one by one onto the board (including repetitive) while condition |bi| ≤ l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the \"bad\" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.\n\nBut the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print \"inf\" in case she needs to write infinitely many integers.\n\nInput\n\nThe first line of input contains four integers b1, q, l, m (-109 ≤ b1, q ≤ 109, 1 ≤ l ≤ 109, 1 ≤ m ≤ 105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of \"bad\" integers, respectively.\n\nThe second line contains m distinct integers a1, a2, ..., am (-109 ≤ ai ≤ 109) — numbers that will never be written on the board.\n\nOutput\n\nPrint the only integer, meaning the number of progression terms that will be written on the board if it is finite, or \"inf\" (without quotes) otherwise.\n\nExamples\n\nInput\n\n3 2 30 4\n6 14 25 48\n\n\nOutput\n\n3\n\nInput\n\n123 1 2143435 4\n123 11 -5453 141245\n\n\nOutput\n\n0\n\nInput\n\n123 1 2143435 4\n54343 -13 6 124\n\n\nOutput\n\ninf\n\nNote\n\nIn the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a \"bad\" integer. Terms bigger than 24 won't be written because they exceed l by absolute value.\n\nIn the second case, Masha won't write any number because all terms are equal 123 and this is a \"bad\" integer.\n\nIn the third case, Masha will write infinitely integers 123. "},"code":{"kind":"string","value":"b1,q,l,m = map(int,input().split())\na = set(map(int,input().split()))\nif q==0:\n if 0 in a:\n if b1 in a:\n print(0)\n elif abs(b1)<=l:\n print(1)\n else:\n print(0)\n elif abs(b1)<=l:\n print(\"inf\")\n else:\n print(0)\nelif q==1:\n if abs(b1)<=l and b1 not in a:\n print(\"inf\")\n else:\n print(0)\nelif q==-1:\n if abs(b1)<=l and (b1 not in a or -b1 not in a):\n print('inf')\n else:\n print(0)\nelif b1==0:\n if 0 in a:\n print(0)\n else:\n print(\"inf\")\nelse:\n cnt = 0\n p = b1\n while abs(p)<=l:\n if p not in a:\n cnt += 1\n p *= q\n print(cnt)"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"123 1 2143435 4\\n123 11 -5453 141245\\n\",\n \"3 2 30 4\\n6 14 25 48\\n\",\n \"123 1 2143435 4\\n54343 -13 6 124\\n\",\n \"-100 0 50 1\\n0\\n\",\n \"-1000 0 10 1\\n5\\n\",\n \"-3 1 100 1\\n3\\n\",\n \"1000000000 100000 1000000000 4\\n5433 13 6 0\\n\",\n \"5 1 5 5\\n1 2 3 4 0\\n\",\n \"2 -1 6 1\\n2\\n\",\n \"3 2 30 3\\n-691070108 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10 14 1\\n123\\n\",\n \"2 0 4 1\\n2\\n\",\n \"0 4 1000 3\\n5 6 2\\n\",\n \"-2 0 2 1\\n1\\n\",\n \"0 10 10 1\\n0\\n\",\n \"3 3 104 17\\n9 -73896485 -290898562 5254410 409659728 -916522518 -435516126 94354167 262981034 -375897180 -80186684 -173062070 -288705544 -410369619 -11447747 320434295 503414250\\n\",\n \"-10 0 5 1\\n1\\n\",\n \"-3 1 100 1\\n-5\\n\",\n \"5 0 12 1\\n5\\n\"\n ],\n \"output\": [\n \"0\\n\",\n \"3\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"4\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"3\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"1\\n\",\n \"4\\n\",\n \"0\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"5\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n 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\"0\\n\",\n \"1\\n\",\n \"2\\n\",\n \"0\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"0\\n\",\n \"5\\n\",\n \"5\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"2\\n\",\n \"0\\n\",\n \"2\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"1\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"inf\\n\",\n \"0\\n\",\n \"3\\n\",\n \"0\\n\",\n \"inf\\n\",\n \"inf\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nMasha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.\n\nYou are given geometric progression b defined by two integers b1 and q. Remind that a geometric progression is a sequence of integers b1, b2, b3, ..., where for each i > 1 the respective term satisfies the condition bi = bi - 1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m \"bad\" integers a1, a2, ..., am, and an integer l.\n\nMasha writes all progression terms one by one onto the board (including repetitive) while condition |bi| ≤ l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the \"bad\" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.\n\nBut the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print \"inf\" in case she needs to write infinitely many integers.\n\nInput\n\nThe first line of input contains four integers b1, q, l, m (-109 ≤ b1, q ≤ 109, 1 ≤ l ≤ 109, 1 ≤ m ≤ 105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of \"bad\" integers, respectively.\n\nThe second line contains m distinct integers a1, a2, ..., am (-109 ≤ ai ≤ 109) — numbers that will never be written on the board.\n\nOutput\n\nPrint the only integer, meaning the number of progression terms that will be written on the board if it is finite, or \"inf\" (without quotes) otherwise.\n\nExamples\n\nInput\n\n3 2 30 4\n6 14 25 48\n\n\nOutput\n\n3\n\nInput\n\n123 1 2143435 4\n123 11 -5453 141245\n\n\nOutput\n\n0\n\nInput\n\n123 1 2143435 4\n54343 -13 6 124\n\n\nOutput\n\ninf\n\nNote\n\nIn the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a \"bad\" integer. Terms bigger than 24 won't be written because they exceed l by absolute value.\n\nIn the second case, Masha won't write any number because all terms are equal 123 and this is a \"bad\" integer.\n\nIn the third case, Masha will write infinitely integers 123. \n\n### Input:\n123 1 2143435 4\n123 11 -5453 141245\n\n### Output:\n0\n\n\n### Input:\n3 2 30 4\n6 14 25 48\n\n### Output:\n3\n\n\n### Code:\nb1,q,l,m = map(int,input().split())\na = set(map(int,input().split()))\nif q==0:\n if 0 in a:\n if b1 in a:\n print(0)\n elif abs(b1)<=l:\n print(1)\n else:\n print(0)\n elif abs(b1)<=l:\n print(\"inf\")\n else:\n print(0)\nelif q==1:\n if abs(b1)<=l and b1 not in a:\n print(\"inf\")\n else:\n print(0)\nelif q==-1:\n if abs(b1)<=l and (b1 not in a or -b1 not in a):\n print('inf')\n else:\n print(0)\nelif b1==0:\n if 0 in a:\n print(0)\n else:\n print(\"inf\")\nelse:\n cnt = 0\n p = b1\n while abs(p)<=l:\n if p not in a:\n cnt += 1\n p *= q\n print(cnt)"}}},{"rowIdx":678,"cells":{"id":{"kind":"string","value":"80_D. Falling Anvils_3191"},"description":{"kind":"string","value":"For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.\n\nAnvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!\n\nIt turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.\n\nLet the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: \n\n\n\nDetermine the probability with which an aim can be successfully hit by an anvil.\n\nYou can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.\n\nInput\n\nThe first line contains integer t (1 ≤ t ≤ 10000) — amount of testcases.\n\nEach of the following t lines contain two space-separated integers a and b (0 ≤ a, b ≤ 106).\n\nPretests contain all the tests with 0 < a < 10, 0 ≤ b < 10.\n\nOutput\n\nPrint t lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed 10 - 6.\n\nExamples\n\nInput\n\n2\n4 2\n1 2\n\n\nOutput\n\n0.6250000000\n0.5312500000"},"code":{"kind":"string","value":"t = int(input())\nfor i in range(t):\n a, b = map(int, input().split())\n denom = a * b * 2\n\n if denom == 0:\n if b == 0:\n print('1')\n else:\n print('0.5')\n continue\n\n if a > 4 * b:\n nom = 2 * b * b\n else:\n nom = (b - a / 4.0 + b) / 2.0 * a\n \n print('%.9f' % ((denom - nom) * 1.0 / denom))\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"2\\n4 2\\n1 2\\n\",\n \"90\\n1 1\\n2 1\\n3 1\\n4 1\\n5 1\\n6 1\\n7 1\\n8 1\\n9 1\\n1 2\\n2 2\\n3 2\\n4 2\\n5 2\\n6 2\\n7 2\\n8 2\\n9 2\\n1 3\\n2 3\\n3 3\\n4 3\\n5 3\\n6 3\\n7 3\\n8 3\\n9 3\\n1 4\\n2 4\\n3 4\\n4 4\\n5 4\\n6 4\\n7 4\\n8 4\\n9 4\\n1 5\\n2 5\\n3 5\\n4 5\\n5 5\\n6 5\\n7 5\\n8 5\\n9 5\\n1 6\\n2 6\\n3 6\\n4 6\\n5 6\\n6 6\\n7 6\\n8 6\\n9 6\\n1 7\\n2 7\\n3 7\\n4 7\\n5 7\\n6 7\\n7 7\\n8 7\\n9 7\\n1 8\\n2 8\\n3 8\\n4 8\\n5 8\\n6 8\\n7 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\"0.5625\\n0.625\\n0.6875\\n0.75\\n0.65625\\n0.8333333333333334\\n0.8571428571428571\\n0.875\\n0.8888888888888888\\n0.53125\\n0.5625\\n0.59375\\n0.625\\n0.65625\\n0.6875\\n0.71875\\n0.625\\n0.7777777777777778\\n0.5208333333333334\\n0.5416666666666666\\n0.5625\\n0.5833333333333334\\n0.6041666666666666\\n0.625\\n0.6458333333333334\\n0.6666666666666666\\n0.6875\\n0.515625\\n0.5625\\n0.546875\\n0.5625\\n0.578125\\n0.59375\\n0.609375\\n0.625\\n0.640625\\n0.5125\\n0.525\\n0.5375\\n0.55\\n0.5625\\n0.575\\n0.5875\\n0.6\\n0.6125\\n0.5104166666666666\\n0.5208333333333334\\n0.53125\\n0.5416666666666666\\n0.5520833333333334\\n0.5625\\n0.5729166666666666\\n0.5833333333333334\\n0.59375\\n0.5089285714285714\\n0.5178571428571429\\n0.5446428571428571\\n0.5357142857142857\\n0.5446428571428571\\n0.5535714285714286\\n0.5625\\n0.5714285714285714\\n0.5803571428571429\\n0.5078125\\n0.515625\\n0.5234375\\n0.53125\\n0.5390625\\n0.546875\\n0.5546875\\n0.5625\\n0.5703125\\n0.5069444444444444\\n0.5138888888888888\\n0.5208333333333334\\n0.5277777777777778\\n0.5347222222222222\\n0.5416666666666666\\n0.5486111111111112\\n0.5555555555555556\\n0.5625\\n1\\n1\\n1\\n1\\n1\\n1\\n0.8571428571428571\\n1\\n1\\n\",\n \"0.625\\n0.5\\n\",\n \"0.525\\n0.546875\\n0.7083333333333334\\n0.6875\\n0.5546875\\n0.525\\n0.5\\n0.9166666666666666\\n0.75\\n0.5694444444444444\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nFor some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.\n\nAnvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!\n\nIt turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.\n\nLet the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: \n\n\n\nDetermine the probability with which an aim can be successfully hit by an anvil.\n\nYou can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.\n\nInput\n\nThe first line contains integer t (1 ≤ t ≤ 10000) — amount of testcases.\n\nEach of the following t lines contain two space-separated integers a and b (0 ≤ a, b ≤ 106).\n\nPretests contain all the tests with 0 < a < 10, 0 ≤ b < 10.\n\nOutput\n\nPrint t lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed 10 - 6.\n\nExamples\n\nInput\n\n2\n4 2\n1 2\n\n\nOutput\n\n0.6250000000\n0.5312500000\n\n### Input:\n2\n4 2\n1 2\n\n### Output:\n0.6250000000\n0.5312500000\n\n\n### Input:\n90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n3 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0\n8 0\n9 0\n\n### Output:\n0.5625000000\n0.6250000000\n0.6875000000\n0.7500000000\n0.8000000000\n0.8333333333\n0.8571428571\n0.8750000000\n0.8888888889\n0.5312500000\n0.5625000000\n0.5937500000\n0.6250000000\n0.6562500000\n0.6875000000\n0.7187500000\n0.7500000000\n0.7777777778\n0.5208333333\n0.5416666667\n0.5625000000\n0.5833333333\n0.6041666667\n0.6250000000\n0.6458333333\n0.6666666667\n0.6875000000\n0.5156250000\n0.5312500000\n0.5468750000\n0.5625000000\n0.5781250000\n0.5937500000\n0.6093750000\n0.6250000000\n0.6406250000\n0.5125000000\n0.5250000000\n0.5375000000\n0.5500000000\n0.5625000000\n0.5750000000\n0.5875000000\n0.6000000000\n0.6125000000\n0.5104166667\n0.5208333333\n0.5312500000\n0.5416666667\n0.5520833333\n0.5625000000\n0.5729166667\n0.5833333333\n0.5937500000\n0.5089285714\n0.5178571429\n0.5267857143\n0.5357142857\n0.5446428571\n0.5535714286\n0.5625000000\n0.5714285714\n0.5803571429\n0.5078125000\n0.5156250000\n0.5234375000\n0.5312500000\n0.5390625000\n0.5468750000\n0.5546875000\n0.5625000000\n0.5703125000\n0.5069444444\n0.5138888889\n0.5208333333\n0.5277777778\n0.5347222222\n0.5416666667\n0.5486111111\n0.5555555556\n0.5625000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n1.0000000000\n\n\n### Code:\nt = int(input())\nfor i in range(t):\n a, b = map(int, input().split())\n denom = a * b * 2\n\n if denom == 0:\n if b == 0:\n print('1')\n else:\n print('0.5')\n continue\n\n if a > 4 * b:\n nom = 2 * b * b\n else:\n nom = (b - a / 4.0 + b) / 2.0 * a\n \n print('%.9f' % ((denom - nom) * 1.0 / denom))\n"}}},{"rowIdx":679,"cells":{"id":{"kind":"string","value":"835_B. The number on the board_3195"},"description":{"kind":"string","value":"Some natural number was written on the board. Its sum of digits was not less than k. But you were distracted a bit, and someone changed this number to n, replacing some digits with others. It's known that the length of the number didn't change.\n\nYou have to find the minimum number of digits in which these two numbers can differ.\n\nInput\n\nThe first line contains integer k (1 ≤ k ≤ 109).\n\nThe second line contains integer n (1 ≤ n < 10100000).\n\nThere are no leading zeros in n. It's guaranteed that this situation is possible.\n\nOutput\n\nPrint the minimum number of digits in which the initial number and n can differ.\n\nExamples\n\nInput\n\n3\n11\n\n\nOutput\n\n1\n\n\nInput\n\n3\n99\n\n\nOutput\n\n0\n\nNote\n\nIn the first example, the initial number could be 12.\n\nIn the second example the sum of the digits of n is not less than k. The initial number could be equal to n."},"code":{"kind":"string","value":"\"\"\"\n\tAuthor\t\t: Arif Ahmad\n\tDate \t\t: \n\tAlgo \t\t: \n\tDifficulty\t: \n\"\"\"\nfrom sys import stdin, stdout\n\ndef main():\n\tk = int(stdin.readline().strip())\n\tn = stdin.readline().strip()\n\tn = sorted(n)\n\n\ttotal = 0\n\tfor c in n:\n\t\td = ord(c) - 48\n\t\ttotal += d\n\n\tans = 0\n\tfor c in n:\n\t\tif total >= k: break\n\t\td = ord(c) - 48\n\t\ttotal = total - d + 9\n\t\tans += 1\n\n\tstdout.write(str(ans) + '\\n')\n\n\nif __name__ == '__main__':\n main()\n "},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3\\n11\\n\",\n \"3\\n99\\n\",\n \"3\\n21\\n\",\n \"3\\n111\\n\",\n \"6\\n33\\n\",\n \"6\\n222\\n\",\n \"5\\n5\\n\",\n \"2\\n11\\n\",\n \"1\\n1\\n\",\n \"500\\n1899337170458531693764539600958943248270674811247191310452938511077656066239840703432499357537079035\\n\",\n \"900\\n7570423817272967027553082464863962024635217372307919506594193055572300657732661146354209508997483330\\n\",\n \"10\\n5205602270\\n\",\n \"45\\n23456\\n\",\n \"700\\n9307216756404590162143344901558545760612901767837570518638460182990196397856220673189163417019781185\\n\",\n \"9\\n9\\n\",\n \"23\\n12138\\n\",\n \"16\\n333\\n\",\n \"108\\n199999899899\\n\",\n \"2\\n2\\n\",\n \"27\\n888\\n\",\n \"1\\n100\\n\",\n \"70\\n3326631213\\n\",\n \"3\\n12\\n\",\n \"200\\n1000000010000000000000000000010000000000000001000001000000000000000000000000000000000000000000000000\\n\",\n \"42\\n97779\\n\",\n \"18\\n900\\n\",\n \"18\\n99\\n\",\n \"17\\n89\\n\",\n \"3\\n25\\n\",\n \"3\\n101\\n\",\n \"500\\n912847954554043759533641650753636547262846968194243986164624835115915995453205463032991863345362751\\n\",\n \"900\\n13595314340746721027884681972026445045155446054797436718350397773609081581610067818125738383867204953\\n\",\n \"700\\n2827909885153614209536247937255907342223529877703181259853581714521705348785489110836222257304902083\\n\",\n \"108\\n279537836291\\n\",\n \"27\\n1303\\n\",\n \"70\\n635283927\\n\",\n \"200\\n1000000010000000000000000000010000000000000001000001000000000000010000000000000000000000000000000000\\n\",\n \"18\\n117\\n\",\n \"500\\n1518579087340116288937736599162465305202624412337518488197055281340561153696250883915352521725279445\\n\",\n \"900\\n6761684374671474145370041824653392630068380810733017147939339046240643056768246793418122862717043873\\n\",\n \"700\\n1820440427472754654005505510201511734837415681159646159223568238325009995518405552958176518558890038\\n\",\n \"700\\n2421044298803518599175491131519646231498861226117474903459340692958777078643419274468107065406155492\\n\",\n \"108\\n187335325377\\n\",\n \"6\\n16\\n\",\n \"6\\n344\\n\",\n \"5\\n7\\n\",\n \"2\\n4\\n\",\n \"1\\n0\\n\",\n \"10\\n9380242707\\n\",\n \"45\\n31025\\n\",\n \"9\\n17\\n\",\n \"23\\n15494\\n\",\n \"16\\n183\\n\",\n \"2\\n3\\n\",\n \"1\\n110\\n\",\n \"3\\n13\\n\",\n \"42\\n113672\\n\",\n \"18\\n1685\\n\",\n \"17\\n139\\n\",\n \"3\\n0\\n\",\n \"3\\n128\\n\",\n \"3\\n1\\n\",\n \"3\\n001\\n\",\n \"6\\n0\\n\",\n \"6\\n663\\n\",\n \"5\\n14\\n\",\n \"2\\n6\\n\",\n \"1\\n2\\n\",\n \"10\\n2517720454\\n\",\n \"9\\n11\\n\",\n \"23\\n28482\\n\",\n \"16\\n77\\n\",\n \"108\\n497278643619\\n\",\n \"2\\n0\\n\",\n \"1\\n010\\n\",\n \"70\\n809579535\\n\",\n \"3\\n2\\n\",\n \"200\\n1000000010000000000000010000010000000000000001000001000000000000010000000000000000000000000000000000\\n\",\n \"42\\n131479\\n\",\n \"18\\n2752\\n\",\n \"18\\n125\\n\",\n \"17\\n115\\n\",\n \"3\\n3\\n\",\n \"3\\n221\\n\",\n \"3\\n011\\n\",\n \"6\\n1\\n\",\n \"6\\n371\\n\",\n \"5\\n15\\n\",\n \"2\\n9\\n\",\n \"1\\n3\\n\",\n \"500\\n706462677389562675710135048975711250288549200563479007435388895878083268783135485467203952858871003\\n\",\n \"10\\n1686851186\\n\",\n \"9\\n2\\n\",\n \"23\\n5804\\n\",\n \"16\\n94\\n\",\n \"108\\n139869568358\\n\",\n \"1\\n000\\n\",\n \"70\\n1461608712\\n\",\n \"3\\n4\\n\",\n \"200\\n1000000010000000000000010000010000000000000001000001000000000000010000000000000000000000000001000000\\n\",\n \"42\\n226492\\n\",\n \"18\\n3119\\n\",\n \"17\\n163\\n\",\n \"3\\n5\\n\",\n \"3\\n406\\n\",\n \"3\\n100\\n\",\n \"6\\n2\\n\",\n \"6\\n178\\n\",\n \"5\\n23\\n\",\n \"2\\n17\\n\",\n \"1\\n4\\n\",\n \"500\\n1365351811047316638577374736626193617865087279070847955122380370886930562732083201005251181562770410\\n\",\n \"10\\n3124775247\\n\",\n \"700\\n3993473126639854893598610789929709225198013139466801565924318044702332535342574254011166104230940309\\n\",\n \"9\\n1\\n\",\n \"23\\n11505\\n\",\n \"16\\n75\\n\",\n \"1\\n001\\n\",\n \"70\\n165202738\\n\",\n \"200\\n1000000010000000000000010000010000000000000001000001000000000010010000000000000000000000000001000000\\n\",\n \"42\\n335392\\n\",\n \"18\\n2219\\n\",\n \"17\\n276\\n\",\n \"3\\n6\\n\",\n \"3\\n261\\n\"\n ],\n \"output\": [\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"6\\n\",\n \"91\\n\",\n \"0\\n\",\n \"5\\n\",\n \"32\\n\",\n \"0\\n\",\n \"1\\n\",\n \"2\\n\",\n \"3\\n\",\n \"0\\n\",\n \"3\\n\",\n \"0\\n\",\n \"6\\n\",\n \"0\\n\",\n \"22\\n\",\n \"2\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"5\\n\",\n \"86\\n\",\n \"34\\n\",\n \"10\\n\",\n \"3\\n\",\n \"4\\n\",\n \"22\\n\",\n \"2\\n\",\n \"8\\n\",\n \"95\\n\",\n \"35\\n\",\n \"32\\n\",\n \"12\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"5\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"10\\n\",\n \"1\\n\",\n \"0\\n\",\n \"3\\n\",\n \"1\\n\",\n \"22\\n\",\n \"3\\n\",\n \"1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"4\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"10\\n\",\n \"1\\n\",\n \"5\\n\",\n \"0\\n\",\n \"22\\n\",\n \"3\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"10\\n\",\n \"0\\n\",\n \"35\\n\",\n \"1\\n\",\n \"2\\n\",\n \"1\\n\",\n \"0\\n\",\n \"5\\n\",\n \"22\\n\",\n \"3\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nSome natural number was written on the board. Its sum of digits was not less than k. But you were distracted a bit, and someone changed this number to n, replacing some digits with others. It's known that the length of the number didn't change.\n\nYou have to find the minimum number of digits in which these two numbers can differ.\n\nInput\n\nThe first line contains integer k (1 ≤ k ≤ 109).\n\nThe second line contains integer n (1 ≤ n < 10100000).\n\nThere are no leading zeros in n. It's guaranteed that this situation is possible.\n\nOutput\n\nPrint the minimum number of digits in which the initial number and n can differ.\n\nExamples\n\nInput\n\n3\n11\n\n\nOutput\n\n1\n\n\nInput\n\n3\n99\n\n\nOutput\n\n0\n\nNote\n\nIn the first example, the initial number could be 12.\n\nIn the second example the sum of the digits of n is not less than k. The initial number could be equal to n.\n\n### Input:\n3\n11\n\n### Output:\n1\n\n\n### Input:\n3\n99\n\n### Output:\n0\n\n\n### Code:\n\"\"\"\n\tAuthor\t\t: Arif Ahmad\n\tDate \t\t: \n\tAlgo \t\t: \n\tDifficulty\t: \n\"\"\"\nfrom sys import stdin, stdout\n\ndef main():\n\tk = int(stdin.readline().strip())\n\tn = stdin.readline().strip()\n\tn = sorted(n)\n\n\ttotal = 0\n\tfor c in n:\n\t\td = ord(c) - 48\n\t\ttotal += d\n\n\tans = 0\n\tfor c in n:\n\t\tif total >= k: break\n\t\td = ord(c) - 48\n\t\ttotal = total - d + 9\n\t\tans += 1\n\n\tstdout.write(str(ans) + '\\n')\n\n\nif __name__ == '__main__':\n main()\n "}}},{"rowIdx":680,"cells":{"id":{"kind":"string","value":"87_C. Interesting Game_3202"},"description":{"kind":"string","value":"Two best friends Serozha and Gena play a game.\n\nInitially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.\n\nThe friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?\n\nInput\n\nThe single line contains a single integer n (1 ≤ n ≤ 105).\n\nOutput\n\nIf Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.\n\nIf Gena wins, print \"-1\" (without the quotes).\n\nExamples\n\nInput\n\n3\n\n\nOutput\n\n2\n\n\nInput\n\n6\n\n\nOutput\n\n-1\n\n\nInput\n\n100\n\n\nOutput\n\n8"},"code":{"kind":"string","value":"import math\nfrom collections import Counter\n\nn = int(input())\ng = [0 for i in range(n + 1)]\nprefix_xor = g.copy()\n\n\ndef in_range(d, k):\n if (2 * k - d * d + d) % (2 * d) != 0:\n return -1\n x = (2 * k - d * d + d) / (2 * d)\n return int(x) if x > 0 else -1\n\n\ndef mex(arr):\n counter = Counter()\n for i in arr:\n counter[i] += 1\n for i in range(0, len(arr) + 1):\n if counter[i] == 0:\n return i\n\n\ndef find_move(arr):\n for i in range(0, len(arr)):\n if arr[i] == 0:\n return i\n return -1\n\n\nif n < 3:\n print(-1)\n exit(0)\nfor i in range(3, n + 1):\n for_range = range(2, int(math.sqrt(2 * i)) + 1)\n filter_range = [l for l in for_range if in_range(l, i) > 0]\n branches = [prefix_xor[in_range(d, i) + d - 1] ^ prefix_xor[in_range(d, i) - 1] for d in filter_range]\n g[i] = mex(branches)\n prefix_xor[i] = prefix_xor[i - 1] ^ g[i]\n if i == n:\n print(-1 if g[i] == 0 else filter_range[find_move(branches)])\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"6\\n\",\n \"100\\n\",\n \"3\\n\",\n \"56\\n\",\n \"1\\n\",\n \"46\\n\",\n \"63478\\n\",\n \"7578\\n\",\n \"56056\\n\",\n \"78\\n\",\n \"66873\\n\",\n \"8149\\n\",\n \"35708\\n\",\n \"81207\\n\",\n \"41385\\n\",\n \"37317\\n\",\n \"74424\\n\",\n \"67817\\n\",\n \"684\\n\",\n \"15\\n\",\n \"96992\\n\",\n \"38798\\n\",\n \"19715\\n\",\n \"627\\n\",\n \"39509\\n\",\n \"45899\\n\",\n \"31893\\n\",\n \"1515\\n\",\n \"33\\n\",\n \"95298\\n\",\n \"27443\\n\",\n \"60879\\n\",\n \"99\\n\",\n \"34378\\n\",\n \"57113\\n\",\n \"36655\\n\",\n \"63359\\n\",\n \"873\\n\",\n \"67341\\n\",\n \"100000\\n\",\n \"42863\\n\",\n \"35\\n\",\n \"250\\n\",\n \"573\\n\",\n \"23\\n\",\n \"871\\n\",\n \"15748\\n\",\n \"92763\\n\",\n \"9564\\n\",\n \"42602\\n\",\n \"38\\n\",\n \"42237\\n\",\n \"70878\\n\",\n \"93764\\n\",\n \"303\\n\",\n \"28\\n\",\n \"43624\\n\",\n \"13800\\n\",\n \"60989\\n\",\n \"977\\n\",\n \"45190\\n\",\n \"90035\\n\",\n \"43956\\n\",\n \"72801\\n\",\n \"370\\n\",\n \"792\\n\",\n \"14577\\n\",\n \"10259\\n\",\n \"20\\n\",\n \"61946\\n\",\n \"74488\\n\",\n \"67748\\n\",\n \"2347\\n\",\n \"36488\\n\",\n \"14\\n\",\n \"64619\\n\",\n \"4083\\n\",\n \"707\\n\",\n \"34566\\n\",\n \"3359\\n\",\n \"2640\\n\",\n \"51\\n\",\n \"3947\\n\",\n \"43151\\n\",\n \"16\\n\",\n \"27223\\n\",\n \"52861\\n\",\n \"29112\\n\",\n \"1378\\n\",\n \"94967\\n\",\n \"13\\n\",\n \"36\\n\",\n \"653\\n\",\n \"19486\\n\",\n \"41407\\n\",\n \"6183\\n\",\n \"19\\n\",\n \"18133\\n\",\n \"3096\\n\",\n \"262\\n\",\n \"11\\n\",\n \"9\\n\",\n \"47\\n\",\n \"4055\\n\"\n ],\n \"output\": [\n \"-1\\n\",\n \"8\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"4\\n\",\n \"-1\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"4\\n\",\n \"2\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"6\\n\",\n \"15\\n\",\n \"-1\\n\",\n \"21\\n\",\n \"73\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"76\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"3\\n\",\n \"2\\n\",\n \"2\\n\",\n \"4\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"34\\n\",\n \"18\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"5\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"8\\n\",\n \"22\\n\",\n \"3\\n\",\n \"17\\n\",\n \"-1\\n\",\n \"18\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"16\\n\",\n \"15\\n\",\n \"142\\n\",\n \"2\\n\",\n \"4\\n\",\n \"22\\n\",\n \"9\\n\",\n \"6\\n\",\n \"20\\n\",\n \"3\\n\",\n \"113\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"16\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"3\\n\",\n \"-1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"-1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nTwo best friends Serozha and Gena play a game.\n\nInitially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.\n\nThe friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?\n\nInput\n\nThe single line contains a single integer n (1 ≤ n ≤ 105).\n\nOutput\n\nIf Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.\n\nIf Gena wins, print \"-1\" (without the quotes).\n\nExamples\n\nInput\n\n3\n\n\nOutput\n\n2\n\n\nInput\n\n6\n\n\nOutput\n\n-1\n\n\nInput\n\n100\n\n\nOutput\n\n8\n\n### Input:\n6\n\n### Output:\n-1\n\n\n### Input:\n100\n\n### Output:\n8\n\n\n### Code:\nimport math\nfrom collections import Counter\n\nn = int(input())\ng = [0 for i in range(n + 1)]\nprefix_xor = g.copy()\n\n\ndef in_range(d, k):\n if (2 * k - d * d + d) % (2 * d) != 0:\n return -1\n x = (2 * k - d * d + d) / (2 * d)\n return int(x) if x > 0 else -1\n\n\ndef mex(arr):\n counter = Counter()\n for i in arr:\n counter[i] += 1\n for i in range(0, len(arr) + 1):\n if counter[i] == 0:\n return i\n\n\ndef find_move(arr):\n for i in range(0, len(arr)):\n if arr[i] == 0:\n return i\n return -1\n\n\nif n < 3:\n print(-1)\n exit(0)\nfor i in range(3, n + 1):\n for_range = range(2, int(math.sqrt(2 * i)) + 1)\n filter_range = [l for l in for_range if in_range(l, i) > 0]\n branches = [prefix_xor[in_range(d, i) + d - 1] ^ prefix_xor[in_range(d, i) - 1] for d in filter_range]\n g[i] = mex(branches)\n prefix_xor[i] = prefix_xor[i - 1] ^ g[i]\n if i == n:\n print(-1 if g[i] == 0 else filter_range[find_move(branches)])\n"}}},{"rowIdx":681,"cells":{"id":{"kind":"string","value":"903_E. Swapping Characters_3206"},"description":{"kind":"string","value":"We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string).\n\nYou are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, k·n ≤ 5000).\n\nInput\n\nThe first line contains two integers k and n (1 ≤ k ≤ 2500, 2 ≤ n ≤ 5000, k · n ≤ 5000) — the number of strings we obtained, and the length of each of these strings.\n\nNext k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters.\n\nOutput\n\nPrint any suitable string s, or -1 if such string doesn't exist.\n\nExamples\n\nInput\n\n3 4\nabac\ncaab\nacba\n\n\nOutput\n\nacab\n\n\nInput\n\n3 4\nkbbu\nkbub\nubkb\n\n\nOutput\n\nkbub\n\n\nInput\n\n5 4\nabcd\ndcba\nacbd\ndbca\nzzzz\n\n\nOutput\n\n-1\n\nNote\n\nIn the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character.\n\nIn the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 — by swapping the second and the fourth, and s3 — by swapping the first and the third.\n\nIn the third example it's impossible to obtain given strings by aforementioned operations."},"code":{"kind":"string","value":"import collections\n\ndef swapCharacters(strings, k, n):\n\t\"\"\"\n\tTime: O(n^2 * k)\n\tSpace: O(1)\n\t\"\"\"\n\tif k == 1:\n\t\ts0 = list(strings[0])\n\t\ts0[0], s0[1] = s0[1], s0[0]\n\t\treturn ''.join(s0)\n\n\t# Initial check for validity\n\tfreq = collections.Counter(strings[0])\n\tcanSame = (max(freq.values()) >= 2)\t\t# could swap two of the same characters ==> same string\n\tfor s in strings:\n\t\tif collections.Counter(s) != freq:\n\t\t\treturn -1\n\n\t# Find diff indices between first two strings\n\tmax_dist = 0\n\tmax_dist_s = None\n\ts0 = strings[0]\n\tfor s1 in strings[1:]:\n\t\tdist = HammingDistance(s0, s1, n)\n\t\tif dist > max_dist:\n\t\t\tmax_dist = dist\n\t\t\tmax_dist_s = s1\n\n\t# Hamming distance <= 2*2 between input strings to be valid\n\tif max_dist > 4:\n\t\treturn -1\n\tdiffs = [i for i in range(n) if s0[i] != s1[i]]\n\n\t# Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN))\n\ts0 = list(s0)\n\tfor i in diffs:\n\t\tfor j in range(n):\n\t\t\t# try swapping\n\t\t\ts0[i], s0[j] = s0[j], s0[i]\n\t\t\t# see if matches second string now\n\t\t\t#dist = sum([s0[i] != s1[i] for i in diffs])\n\t\t\tdist = HammingDistance(s0, s1, n)\n\t\t\tif dist == 2 or (dist == 0 and canSame):\n\t\t\t\tcand = ''.join(s0)\n\t\t\t\tif verifyAll(strings, k, n, cand, canSame):\n\t\t\t\t\treturn cand\n\t\t\t# revert\n\t\t\ts0[i], s0[j] = s0[j], s0[i]\n\n\t# nothing works\n\treturn -1\n\n\ndef HammingDistance(s0, s1, n):\n\tcount = 0\n\tfor i in range(n):\n\t\tif s0[i] != s1[i]:\n\t\t\tcount += 1\n\treturn count\n\n\ndef verifyAll(strings, k, n, cand, canSame):\n\tfor s in strings:\n\t\tdist = HammingDistance(s, cand, n)\n\t\tif (dist != 0 or not canSame) and dist != 2:\n\t\t\treturn False\n\treturn True\n\n\n\nk, n = [int(x) for x in input().split()]\nstrings = set()\t\t# discard duplicates\nfor _ in range(k):\n\tstrings.add(input())\nstrings = list(strings)\nk = len(strings)\nres = swapCharacters(strings, k, n)\nprint(res)"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"5 4\\nabcd\\ndcba\\nacbd\\ndbca\\nzzzz\\n\",\n \"3 4\\nabac\\ncaab\\nacba\\n\",\n \"3 4\\nkbbu\\nkbub\\nubkb\\n\",\n \"3 4\\nkbub\\nkbbu\\nubkb\\n\",\n \"5 5\\nzbibx\\nzbbix\\nzbibx\\nxbibz\\nxbibz\\n\",\n \"100 2\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"5 5\\neellh\\nehlle\\nehlle\\nhelle\\nhlele\\n\",\n \"2 3\\nghn\\nghn\\n\",\n \"2 4\\nayax\\nabac\\n\",\n \"2 6\\nabcdef\\nbadcef\\n\",\n \"1 2\\nyu\\n\",\n \"2 4\\najax\\nazad\\n\",\n \"2 2\\nnm\\nnm\\n\",\n \"2 2\\nac\\nca\\n\",\n \"5 5\\ngyvnn\\ngnvny\\nvygnn\\ngynvn\\ngnvny\\n\",\n \"2 2\\nab\\ncd\\n\",\n \"3 3\\nuvh\\nvhu\\nhuv\\n\",\n \"3 2\\nxh\\nxh\\nxh\\n\",\n \"3 2\\ncg\\ncg\\ncg\\n\",\n \"8 23\\nmgiomcytqdvoihhcirldmuj\\nmgmoicytqdvoihhicrldmuj\\nmgmomcytqdvoihhicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuj\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"8 6\\nmnionk\\nmnikno\\ninmkno\\nmnnkio\\noniknm\\noniknm\\nmkinno\\nmnikon\\n\",\n \"1 3\\nvts\\n\",\n \"2 3\\nabc\\nabz\\n\",\n \"2 4\\nabcd\\nccdc\\n\",\n \"2 5\\ndbcag\\nacbdh\\n\",\n \"2 16\\nhmlqgaepsgpdbzyk\\nchhhburuvnyirrim\\n\",\n \"5 5\\nzbibx\\nzbbix\\nxbibz\\nxbibz\\nxbibz\\n\",\n \"100 2\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nzq\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\nqz\\n\",\n \"1 2\\nnm\\nnm\\n\",\n \"2 2\\nac\\nac\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"5 5\\neellh\\nehlle\\nehlke\\nhelle\\nhlele\\n\",\n \"2 4\\najax\\ndaza\\n\",\n \"2 2\\nab\\ncc\\n\",\n \"3 3\\nuvh\\nvhv\\nhuv\\n\",\n \"3 2\\ncg\\ncg\\ngc\\n\",\n \"8 23\\nmgiomcytqdvoihhcirldmuj\\nogmmicytqdvoihhicrldmuj\\nmgmomcytqdvoihhicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuj\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"8 6\\nmnionk\\nmnikno\\ninmkno\\nmnnkio\\noniknm\\noniknm\\nmkjnno\\nmnikon\\n\",\n \"2 3\\ncba\\nabz\\n\",\n \"2 5\\ndbcag\\nabbdh\\n\",\n \"5 4\\nabcd\\ndcba\\nacbd\\nebca\\nzzzz\\n\",\n \"3 4\\nkbbu\\nkbub\\nubka\\n\",\n \"5 5\\nzbibx\\nzbbix\\nxbibz\\nxzibb\\nxbibz\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"2 4\\najax\\nzada\\n\",\n \"2 2\\nac\\nba\\n\",\n \"3 3\\nuvh\\nwhv\\nhuv\\n\",\n \"8 21\\nmgiomcytqdvoihhcirldmuj\\nogmmicytqdvoihhicrldmuj\\nmgmomcytqdvoihhicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuj\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"8 6\\nmnionk\\nmnikno\\nimmkno\\nmnnkio\\noniknm\\noniknm\\nmkjnno\\nmnikon\\n\",\n \"2 5\\ndbbag\\nabbdh\\n\",\n \"3 4\\nkbbu\\nkbbu\\nubka\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"2 2\\najax\\nzada\\n\",\n \"2 2\\nac\\naa\\n\",\n \"3 3\\nhvu\\nwhv\\nhuv\\n\",\n \"8 21\\nmgiomcytqdvoihhcirldmuj\\nogmmicytqdvoihhicrldmuj\\nmgmomcytqdvoihhicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuk\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"3 4\\nkbbu\\nkbbu\\nbuka\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nszk\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"2 2\\nxaja\\nzada\\n\",\n \"2 2\\nbc\\naa\\n\",\n \"3 3\\nhvu\\nvhw\\nhuv\\n\",\n \"8 21\\nmgiomcytqdvoihhcirldmuj\\nogmmicytqdvoihhicrldmuj\\nmghomcytqdvoihmicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuk\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"3 1\\nkbbu\\nkbbu\\nbuka\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nszk\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsk\\nskz\\nzsk\\nkzs\\nszk\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"3 3\\nhuu\\nvhw\\nhuv\\n\",\n \"8 21\\nmgiomcytqdvoihjcirldmuh\\nogmmicytqdvoihhicrldmuj\\nmghomcytqdvoihmicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuk\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nszk\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsj\\nskz\\nzsk\\nkzs\\nszk\\nskz\\nkzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"3 3\\nhuu\\nvhw\\nvuh\\n\",\n \"8 21\\nmgiomcytqdvoihjcirldmuh\\nogmmicysqdvoihhicrldmuj\\nmghomcytqdvoihmicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuk\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nszk\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsj\\nskz\\nzsk\\nkzs\\nszk\\nskz\\njzs\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"3 3\\nhut\\nvhw\\nvuh\\n\",\n \"8 21\\nmgiomcytqdvoihjcirldmuh\\nogmmicysqdvoihhicrldmuj\\nmgholcytqdvoihmicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nmgiimcytqdvoihhocrldmuk\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\",\n \"100 3\\nzsk\\nzsk\\nzsk\\nzsk\\nskz\\nskz\\nkzt\\nskz\\nkzs\\nkzs\\nzsk\\nkzs\\nkzs\\nlzs\\nskz\\nkzs\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nkzs\\nskz\\nskz\\nskz\\nzsk\\nskz\\nzsk\\nskz\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nzsk\\nkzs\\nskz\\nskz\\nszk\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nskz\\nkzs\\nkzs\\nskz\\nkzs\\nkzs\\nkzs\\nkzr\\nskz\\nkzs\\nskz\\nskz\\nskz\\nskz\\nzsk\\nkzs\\nskz\\nzsk\\nkzs\\nskz\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nskz\\nkzs\\nkzs\\nskz\\nzsj\\nskz\\nzsk\\nkzs\\nszk\\nskz\\njzs\\nszk\\nkzs\\nzsk\\nkzs\\nkzs\\nzsk\\nkzs\\nskz\\nzsk\\nskz\\nskz\\nskz\\nkzs\\nzsk\\nkzs\\nkzs\\nskz\\n\",\n \"3 3\\nhvt\\nvhw\\nvuh\\n\",\n \"8 21\\nmgiomcytqdvoihjcirldmuh\\nogmmicysqdvoihhicrldmuj\\nmgholcytqdvoihmicrldiuj\\nmgcomcytqdvoihhiirldmuj\\nkumdlrcohhiovdqtycmiigm\\nmgioicytqdvoihhmcrldmuj\\nmgiomcytqdvodhhicrlimuj\\nmgiomcytjdvoihhicrldmuq\\n\"\n ],\n \"output\": [\n \"-1\\n\",\n \"acab\\n\",\n \"kbub\\n\",\n \"kbub\\n\",\n \"zbibx\\n\",\n \"zq\\n\",\n \"szk\\n\",\n \"helle\\n\",\n \"hgn\\n\",\n \"-1\\n\",\n \"bacdef\\n\",\n \"uy\\n\",\n \"-1\\n\",\n \"mn\\n\",\n \"-1\\n\",\n \"gyvnn\\n\",\n \"-1\\n\",\n \"vuh\\n\",\n \"hx\\n\",\n \"gc\\n\",\n \"mgiomcytqdvoihhicrldmuj\\n\",\n \"mnikno\\n\",\n \"tvs\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"zbibx\\n\",\n \"-1\\n\",\n \"mn\\n\",\n \"ca\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\",\n \"-1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nWe had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string).\n\nYou are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, k·n ≤ 5000).\n\nInput\n\nThe first line contains two integers k and n (1 ≤ k ≤ 2500, 2 ≤ n ≤ 5000, k · n ≤ 5000) — the number of strings we obtained, and the length of each of these strings.\n\nNext k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters.\n\nOutput\n\nPrint any suitable string s, or -1 if such string doesn't exist.\n\nExamples\n\nInput\n\n3 4\nabac\ncaab\nacba\n\n\nOutput\n\nacab\n\n\nInput\n\n3 4\nkbbu\nkbub\nubkb\n\n\nOutput\n\nkbub\n\n\nInput\n\n5 4\nabcd\ndcba\nacbd\ndbca\nzzzz\n\n\nOutput\n\n-1\n\nNote\n\nIn the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character.\n\nIn the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 — by swapping the second and the fourth, and s3 — by swapping the first and the third.\n\nIn the third example it's impossible to obtain given strings by aforementioned operations.\n\n### Input:\n5 4\nabcd\ndcba\nacbd\ndbca\nzzzz\n\n### Output:\n-1\n\n\n### Input:\n3 4\nabac\ncaab\nacba\n\n### Output:\nacab\n\n\n### Code:\nimport collections\n\ndef swapCharacters(strings, k, n):\n\t\"\"\"\n\tTime: O(n^2 * k)\n\tSpace: O(1)\n\t\"\"\"\n\tif k == 1:\n\t\ts0 = list(strings[0])\n\t\ts0[0], s0[1] = s0[1], s0[0]\n\t\treturn ''.join(s0)\n\n\t# Initial check for validity\n\tfreq = collections.Counter(strings[0])\n\tcanSame = (max(freq.values()) >= 2)\t\t# could swap two of the same characters ==> same string\n\tfor s in strings:\n\t\tif collections.Counter(s) != freq:\n\t\t\treturn -1\n\n\t# Find diff indices between first two strings\n\tmax_dist = 0\n\tmax_dist_s = None\n\ts0 = strings[0]\n\tfor s1 in strings[1:]:\n\t\tdist = HammingDistance(s0, s1, n)\n\t\tif dist > max_dist:\n\t\t\tmax_dist = dist\n\t\t\tmax_dist_s = s1\n\n\t# Hamming distance <= 2*2 between input strings to be valid\n\tif max_dist > 4:\n\t\treturn -1\n\tdiffs = [i for i in range(n) if s0[i] != s1[i]]\n\n\t# Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN))\n\ts0 = list(s0)\n\tfor i in diffs:\n\t\tfor j in range(n):\n\t\t\t# try swapping\n\t\t\ts0[i], s0[j] = s0[j], s0[i]\n\t\t\t# see if matches second string now\n\t\t\t#dist = sum([s0[i] != s1[i] for i in diffs])\n\t\t\tdist = HammingDistance(s0, s1, n)\n\t\t\tif dist == 2 or (dist == 0 and canSame):\n\t\t\t\tcand = ''.join(s0)\n\t\t\t\tif verifyAll(strings, k, n, cand, canSame):\n\t\t\t\t\treturn cand\n\t\t\t# revert\n\t\t\ts0[i], s0[j] = s0[j], s0[i]\n\n\t# nothing works\n\treturn -1\n\n\ndef HammingDistance(s0, s1, n):\n\tcount = 0\n\tfor i in range(n):\n\t\tif s0[i] != s1[i]:\n\t\t\tcount += 1\n\treturn count\n\n\ndef verifyAll(strings, k, n, cand, canSame):\n\tfor s in strings:\n\t\tdist = HammingDistance(s, cand, n)\n\t\tif (dist != 0 or not canSame) and dist != 2:\n\t\t\treturn False\n\treturn True\n\n\n\nk, n = [int(x) for x in input().split()]\nstrings = set()\t\t# discard duplicates\nfor _ in range(k):\n\tstrings.add(input())\nstrings = list(strings)\nk = len(strings)\nres = swapCharacters(strings, k, n)\nprint(res)"}}},{"rowIdx":682,"cells":{"id":{"kind":"string","value":"954_G. Castle Defense_3210"},"description":{"kind":"string","value":"Today you are going to lead a group of elven archers to defend the castle that is attacked by an army of angry orcs. Three sides of the castle are protected by impassable mountains and the remaining side is occupied by a long wall that is split into n sections. At this moment there are exactly ai archers located at the i-th section of this wall. You know that archer who stands at section i can shoot orcs that attack section located at distance not exceeding r, that is all such sections j that |i - j| ≤ r. In particular, r = 0 means that archers are only capable of shooting at orcs who attack section i.\n\nDenote as defense level of section i the total number of archers who can shoot at the orcs attacking this section. Reliability of the defense plan is the minimum value of defense level of individual wall section.\n\nThere is a little time left till the attack so you can't redistribute archers that are already located at the wall. However, there is a reserve of k archers that you can distribute among wall sections in arbitrary way. You would like to achieve maximum possible reliability of the defence plan.\n\nInput\n\nThe first line of the input contains three integers n, r and k (1 ≤ n ≤ 500 000, 0 ≤ r ≤ n, 0 ≤ k ≤ 1018) — the number of sections of the wall, the maximum distance to other section archers can still shoot and the number of archers yet to be distributed along the wall. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the current number of archers at each section.\n\nOutput\n\nPrint one integer — the maximum possible value of defense plan reliability, i.e. the maximum possible value of minimum defense level if we distribute k additional archers optimally.\n\nExamples\n\nInput\n\n5 0 6\n5 4 3 4 9\n\n\nOutput\n\n5\n\n\nInput\n\n4 2 0\n1 2 3 4\n\n\nOutput\n\n6\n\n\nInput\n\n5 1 1\n2 1 2 1 2\n\n\nOutput\n\n3"},"code":{"kind":"string","value":"import sys\n\nborder = 1 << 30\n\n\ndef build(x=0):\n res = [0, 0]\n\n i = 0\n while x and i < 30:\n if x & 1:\n res[1] += (1 << i)\n x >>= 1\n i += 1\n\n i = 0\n while x:\n if x & 1:\n res[0] += (1 << i)\n x >>= 1\n i += 1\n\n return res\n\n\nn, r, k = map(int, sys.stdin.buffer.readline().decode('utf-8').split())\na = list(map(int, sys.stdin.buffer.readline().decode('utf-8').split()))\n\nk_big, k_small = build(k)\nleft = build(sum(a[:r]))\nminus_big, minus_small = [0]*n, [0]*n\nw = 2*r+1\n\n\ndef solve(level_big, level_small):\n used_big = used_small = 0\n acc_big, acc_small = left\n\n for i in range(n):\n if minus_small[i] or minus_big[i]:\n acc_big -= minus_big[i]\n acc_small -= minus_small[i]\n if acc_small < 0:\n acc_small += border\n acc_big -= 1\n elif acc_small >= border:\n acc_small -= border\n acc_big += 1\n\n minus_big[i] = minus_small[i] = 0\n\n acc_small += (a[i+r] if i+r < n else 0) - (a[i-r-1] if i-r >= 1 else 0)\n if acc_small >= border:\n acc_small -= border\n acc_big += 1\n elif acc_small < 0:\n acc_small += border\n acc_big -= 1\n\n if acc_big < level_big or acc_big == level_big and acc_small < level_small:\n used_big += level_big - acc_big\n used_small += level_small - acc_small\n if used_small >= border:\n used_small -= border\n used_big += 1\n elif used_small < 0:\n used_small += border\n used_big -= 1\n\n if used_big > k_big or used_big == k_big and used_small > k_small:\n break\n if i+w < n:\n minus_big[i+w] = level_big - acc_big\n minus_small[i+w] = level_small - acc_small\n\n acc_big = level_big\n acc_small = level_small\n\n for i in range(i+1, n):\n if minus_small[i] or minus_big[i]:\n minus_small[i] = minus_big[i] = 0\n\n return used_big < k_big or used_big == k_big and used_small <= k_small\n\n\nok, ng = min(a), k + sum(a) + 1\nwhile abs(ok - ng) > 1:\n mid = (ok + ng) >> 1\n if solve(*build(mid)):\n ok = mid\n else:\n ng = mid\n\nprint(ok)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4 2 0\\n1 2 3 4\\n\",\n \"5 0 6\\n5 4 3 4 9\\n\",\n \"5 1 1\\n2 1 2 1 2\\n\",\n \"1 0 0\\n1\\n\",\n \"1 1 10\\n23\\n\",\n \"100 0 0\\n607 169 477 518 368 54 15 471 604 138 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 752 446 204 509 816 313 900 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\\n\",\n \"100 100 0\\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 64 804 441 957 288 112 790 239 919 216 885 527 381 749 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\\n\",\n \"2 0 100\\n98 2\\n\",\n \"100 1 0\\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 883 524 46 542 898 984 859 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 934 320 331 700 638\\n\",\n \"100 100 1000\\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 141 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 69 522 104 451 443 239 171 22 346 227 525 807\\n\",\n \"1 0 0\\n0\\n\",\n \"100 0 1000\\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 702 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 589 563 905 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\\n\",\n \"100 3 1000\\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 616 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 359 405 927 934 211 828 587 896 722 34 936 355 958 541 308 463 404 709 654 248\\n\",\n \"1 0 1000000000000000000\\n1000000000\\n\",\n \"2 0 1\\n1 1\\n\",\n \"100 3 0\\n483 655 856 10 354 917 853 843 968 309 819 150 532 993 693 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 932 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\\n\",\n \"3 1 1000\\n0 0 0\\n\",\n \"100 1 1000\\n923 286 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 5 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 604 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\\n\",\n \"1 1 10\\n20\\n\",\n \"100 0 0\\n607 169 477 518 368 54 15 471 604 138 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 900 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\\n\",\n \"100 100 0\\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 64 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\\n\",\n \"100 1 0\\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 96 524 46 542 898 984 859 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 934 320 331 700 638\\n\",\n \"100 100 1000\\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 141 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 52 522 104 451 443 239 171 22 346 227 525 807\\n\",\n \"1 1 0\\n0\\n\",\n \"100 0 1000\\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 702 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 589 563 609 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\\n\",\n \"100 3 1000\\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 616 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 355 958 541 308 463 404 709 654 248\\n\",\n \"1 0 1000000000000000000\\n1010000000\\n\",\n \"2 0 1\\n1 0\\n\",\n \"100 3 0\\n483 655 856 10 354 917 853 843 968 309 819 150 532 993 646 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 932 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\\n\",\n \"3 1 1000\\n0 0 1\\n\",\n \"100 1 1000\\n923 286 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 5 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\\n\",\n \"5 0 6\\n5 4 3 4 11\\n\",\n \"5 1 1\\n0 1 2 1 2\\n\",\n \"100 100 0\\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\\n\",\n \"100 100 1000\\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 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153 980 848 910 219 876 581 35 756 513 314 804 887\\n\",\n \"100 1 0\\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 784 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 718 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 1348 320 331 700 638\\n\",\n \"100 3 1000\\n391 145 605 150 641 788 1000 471 328 15 753 161 472 385 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 35 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 266 958 541 308 463 404 709 654 248\\n\",\n \"100 3 0\\n483 655 856 10 55 917 853 843 968 309 819 150 532 993 646 729 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 564 39 278 866 866 515 942 151 110 991 725 989 96 21 931 653\\n\",\n \"5 1 0\\n5 6 3 4 9\\n\",\n \"5 0 2\\n0 2 3 1 2\\n\",\n \"100 0 0\\n607 169 477 518 368 54 29 117 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 661 669 86 400 186 565 578 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\\n\",\n \"100 3 1000\\n391 145 605 150 641 788 1000 471 357 15 753 161 472 385 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 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\"2050\",\n \"1701\",\n \"740\",\n \"1\",\n \"14\",\n \"279\",\n \"2050\",\n \"1701\",\n \"11\",\n \"1\",\n \"14\",\n \"2050\"\n ]\n}"},"source":{"kind":"class label","value":"2","name":"CODEFORCES"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nToday you are going to lead a group of elven archers to defend the castle that is attacked by an army of angry orcs. Three sides of the castle are protected by impassable mountains and the remaining side is occupied by a long wall that is split into n sections. At this moment there are exactly ai archers located at the i-th section of this wall. You know that archer who stands at section i can shoot orcs that attack section located at distance not exceeding r, that is all such sections j that |i - j| ≤ r. In particular, r = 0 means that archers are only capable of shooting at orcs who attack section i.\n\nDenote as defense level of section i the total number of archers who can shoot at the orcs attacking this section. Reliability of the defense plan is the minimum value of defense level of individual wall section.\n\nThere is a little time left till the attack so you can't redistribute archers that are already located at the wall. However, there is a reserve of k archers that you can distribute among wall sections in arbitrary way. You would like to achieve maximum possible reliability of the defence plan.\n\nInput\n\nThe first line of the input contains three integers n, r and k (1 ≤ n ≤ 500 000, 0 ≤ r ≤ n, 0 ≤ k ≤ 1018) — the number of sections of the wall, the maximum distance to other section archers can still shoot and the number of archers yet to be distributed along the wall. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the current number of archers at each section.\n\nOutput\n\nPrint one integer — the maximum possible value of defense plan reliability, i.e. the maximum possible value of minimum defense level if we distribute k additional archers optimally.\n\nExamples\n\nInput\n\n5 0 6\n5 4 3 4 9\n\n\nOutput\n\n5\n\n\nInput\n\n4 2 0\n1 2 3 4\n\n\nOutput\n\n6\n\n\nInput\n\n5 1 1\n2 1 2 1 2\n\n\nOutput\n\n3\n\n### Input:\n4 2 0\n1 2 3 4\n\n### Output:\n6\n\n\n### Input:\n5 0 6\n5 4 3 4 9\n\n### Output:\n5\n\n\n### Code:\nimport sys\n\nborder = 1 << 30\n\n\ndef build(x=0):\n res = [0, 0]\n\n i = 0\n while x and i < 30:\n if x & 1:\n res[1] += (1 << i)\n x >>= 1\n i += 1\n\n i = 0\n while x:\n if x & 1:\n res[0] += (1 << i)\n x >>= 1\n i += 1\n\n return res\n\n\nn, r, k = map(int, sys.stdin.buffer.readline().decode('utf-8').split())\na = list(map(int, sys.stdin.buffer.readline().decode('utf-8').split()))\n\nk_big, k_small = build(k)\nleft = build(sum(a[:r]))\nminus_big, minus_small = [0]*n, [0]*n\nw = 2*r+1\n\n\ndef solve(level_big, level_small):\n used_big = used_small = 0\n acc_big, acc_small = left\n\n for i in range(n):\n if minus_small[i] or minus_big[i]:\n acc_big -= minus_big[i]\n acc_small -= minus_small[i]\n if acc_small < 0:\n acc_small += border\n acc_big -= 1\n elif acc_small >= border:\n acc_small -= border\n acc_big += 1\n\n minus_big[i] = minus_small[i] = 0\n\n acc_small += (a[i+r] if i+r < n else 0) - (a[i-r-1] if i-r >= 1 else 0)\n if acc_small >= border:\n acc_small -= border\n acc_big += 1\n elif acc_small < 0:\n acc_small += border\n acc_big -= 1\n\n if acc_big < level_big or acc_big == level_big and acc_small < level_small:\n used_big += level_big - acc_big\n used_small += level_small - acc_small\n if used_small >= border:\n used_small -= border\n used_big += 1\n elif used_small < 0:\n used_small += border\n used_big -= 1\n\n if used_big > k_big or used_big == k_big and used_small > k_small:\n break\n if i+w < n:\n minus_big[i+w] = level_big - acc_big\n minus_small[i+w] = level_small - acc_small\n\n acc_big = level_big\n acc_small = level_small\n\n for i in range(i+1, n):\n if minus_small[i] or minus_big[i]:\n minus_small[i] = minus_big[i] = 0\n\n return used_big < k_big or used_big == k_big and used_small <= k_small\n\n\nok, ng = min(a), k + sum(a) + 1\nwhile abs(ok - ng) > 1:\n mid = (ok + ng) >> 1\n if solve(*build(mid)):\n ok = mid\n else:\n ng = mid\n\nprint(ok)\n"}}},{"rowIdx":683,"cells":{"id":{"kind":"string","value":"p02549 AtCoder Beginner Contest 179 - Leaping Tak_3226"},"description":{"kind":"string","value":"There are N cells arranged in a row, numbered 1, 2, \\ldots, N from left to right.\n\nTak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.\n\nYou are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \\ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \\leq i \\leq r.\n\n* \bWhen you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.\n\n\n\nTo help Tak, find the number of ways to go to Cell N, modulo 998244353.\n\nConstraints\n\n* 2 \\leq N \\leq 2 \\times 10^5\n* 1 \\leq K \\leq \\min(N, 10)\n* 1 \\leq L_i \\leq R_i \\leq N\n* [L_i, R_i] and [L_j, R_j] do not intersect (i \\neq j)\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\nL_1 R_1\nL_2 R_2\n:\nL_K R_K\n\n\nOutput\n\nPrint the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.\n\nExamples\n\nInput\n\n5 2\n1 1\n3 4\n\n\nOutput\n\n4\n\n\nInput\n\n5 2\n3 3\n5 5\n\n\nOutput\n\n0\n\n\nInput\n\n5 1\n1 2\n\n\nOutput\n\n5\n\n\nInput\n\n60 3\n5 8\n1 3\n10 15\n\n\nOutput\n\n221823067"},"code":{"kind":"string","value":"import sys\ninput = sys.stdin.readline\n\nN,K=map(int,input().split())\nK=[tuple(map(int,input().split())) for i in range(K)]\nmod=998244353\n\nDP=[0]*(4*10**5+100)\nDP[1]=1\nDP[2]=-1\n\nfor i in range(1,N+1):\n DP[i]+=DP[i-1]\n DP[i]%=mod\n \n for l,r in K:\n DP[i+l]+=DP[i]\n DP[i+l]%=mod\n DP[i+r+1]-=DP[i]\n DP[i+r+1]%=mod\n \n\n #print(DP[:10])\n\nprint(DP[N])\n \n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"5 2\\n3 3\\n5 5\",\n \"5 1\\n1 2\",\n \"60 3\\n5 8\\n1 3\\n10 15\",\n \"5 2\\n1 1\\n3 4\",\n \"5 2\\n3 3\\n5 9\",\n \"60 3\\n5 4\\n1 3\\n10 15\",\n \"10 2\\n1 1\\n3 4\",\n \"60 3\\n5 4\\n1 3\\n10 20\",\n \"50 3\\n5 4\\n1 3\\n10 20\",\n \"5 1\\n1 2\\n5 9\",\n \"60 3\\n5 8\\n1 0\\n10 15\",\n \"3 2\\n1 1\\n3 4\",\n \"60 3\\n5 4\\n1 6\\n10 15\",\n \"10 2\\n1 2\\n3 4\",\n \"5 2\\n1 3\\n5 9\",\n \"60 3\\n5 4\\n1 1\\n10 20\",\n \"50 3\\n5 4\\n1 3\\n1 20\",\n \"15 2\\n1 2\\n3 4\",\n \"5 2\\n1 3\\n4 9\",\n \"60 3\\n5 4\\n2 1\\n10 20\",\n \"84 3\\n5 4\\n1 3\\n1 20\",\n \"60 3\\n2 4\\n2 1\\n10 20\",\n \"84 3\\n5 4\\n1 2\\n1 20\",\n \"5 2\\n1 3\\n3 9\",\n \"60 3\\n2 4\\n2 1\\n9 20\",\n \"84 3\\n5 4\\n1 2\\n1 27\",\n \"60 3\\n2 4\\n2 1\\n12 20\",\n \"84 3\\n5 4\\n1 1\\n1 27\",\n \"60 3\\n2 4\\n2 2\\n12 20\",\n \"84 3\\n5 4\\n2 1\\n1 27\",\n \"45 3\\n2 4\\n2 2\\n12 20\",\n \"45 3\\n2 4\\n2 2\\n13 20\",\n \"45 3\\n2 4\\n2 1\\n13 20\",\n \"45 3\\n2 2\\n2 1\\n13 20\",\n \"45 3\\n2 2\\n2 1\\n13 35\",\n \"45 3\\n2 2\\n2 1\\n5 35\",\n \"5 2\\n3 3\\n2 5\",\n \"60 3\\n5 8\\n1 3\\n10 9\",\n \"60 2\\n5 4\\n1 3\\n10 15\",\n \"60 3\\n5 4\\n1 4\\n10 20\",\n \"49 3\\n5 8\\n1 0\\n10 15\",\n \"60 3\\n5 4\\n2 6\\n10 15\",\n \"10 2\\n1 2\\n5 4\",\n \"50 3\\n5 4\\n2 3\\n1 20\",\n \"84 3\\n5 4\\n1 3\\n1 10\",\n \"60 3\\n2 4\\n2 1\\n9 10\",\n \"60 3\\n2 3\\n2 1\\n12 20\",\n \"45 3\\n2 4\\n1 1\\n13 20\",\n \"45 3\\n2 2\\n2 1\\n13 47\",\n \"5 2\\n1 3\\n2 5\",\n \"60 3\\n5 8\\n1 3\\n10 11\",\n \"103 2\\n5 4\\n1 3\\n10 15\",\n \"60 3\\n5 4\\n1 6\\n10 20\",\n \"60 3\\n5 4\\n2 6\\n3 15\",\n \"50 3\\n5 4\\n4 3\\n1 20\",\n \"15 1\\n1 2\\n0 21\",\n \"14 1\\n1 2\\n-1 21\",\n \"60 3\\n2 3\\n2 1\\n14 20\",\n \"16 3\\n2 2\\n2 1\\n13 47\",\n \"60 3\\n5 8\\n1 6\\n10 20\",\n \"5 2\\n1 4\\n3 9\",\n \"50 3\\n5 4\\n4 5\\n1 20\",\n \"5 2\\n1 4\\n2 9\",\n \"60 3\\n5 8\\n1 3\\n10 20\",\n \"50 3\\n5 4\\n3 5\\n1 20\",\n \"60 3\\n5 8\\n1 3\\n10 26\",\n \"10 2\\n3 4\\n5 17\",\n \"96 3\\n5 4\\n3 5\\n1 20\",\n \"4 1\\n1 3\\n0 4\",\n \"60 3\\n5 8\\n1 2\\n10 26\",\n \"15 2\\n1 0\\n3 33\",\n \"96 3\\n4 4\\n3 5\\n1 20\",\n \"60 3\\n9 8\\n1 2\\n10 26\",\n \"17 2\\n1 0\\n3 33\",\n \"96 3\\n4 4\\n3 4\\n1 20\",\n \"60 3\\n9 16\\n1 2\\n10 26\",\n \"96 3\\n4 4\\n3 4\\n1 5\",\n \"60 3\\n11 16\\n1 2\\n10 26\",\n \"93 3\\n4 4\\n3 4\\n1 5\",\n \"5 0\\n1 2\",\n \"5 1\\n3 3\\n5 9\",\n \"5 1\\n3 2\\n5 9\",\n \"5 1\\n1 2\\n5 17\",\n \"5 1\\n1 0\\n5 17\",\n \"10 1\\n1 0\\n5 17\",\n \"10 1\\n1 0\\n7 17\",\n \"10 1\\n1 0\\n7 24\",\n \"10 1\\n1 0\\n7 21\",\n \"5 2\\n3 3\\n5 4\",\n \"5 0\\n3 3\\n5 9\",\n \"5 0\\n1 3\",\n \"5 1\\n3 2\\n0 9\",\n \"5 1\\n1 2\\n5 13\",\n \"5 0\\n1 2\\n5 17\",\n \"5 1\\n1 0\\n2 17\",\n \"10 1\\n1 0\\n7 30\",\n \"10 1\\n1 0\\n7 45\",\n \"16 1\\n1 0\\n7 21\",\n \"5 2\\n2 3\\n5 4\",\n \"3 0\\n1 1\\n3 4\",\n \"8 0\\n3 3\\n5 9\",\n \"5 1\\n3 2\\n0 6\",\n \"5 0\\n1 2\\n5 13\",\n \"5 0\\n1 2\\n2 17\"\n ],\n \"output\": [\n \"0\",\n \"5\",\n \"221823067\",\n \"4\",\n \"0\\n\",\n \"903929718\\n\",\n \"40\\n\",\n \"917017175\\n\",\n \"614976987\\n\",\n \"5\\n\",\n \"742066\\n\",\n \"1\\n\",\n \"980971792\\n\",\n \"208\\n\",\n \"7\\n\",\n \"3543464\\n\",\n \"465231607\\n\",\n \"5536\\n\",\n \"8\\n\",\n \"1598\\n\",\n \"613452135\\n\",\n \"292126669\\n\",\n \"281307714\\n\",\n \"10\\n\",\n \"693162917\\n\",\n \"282478460\\n\",\n \"690528981\\n\",\n \"894733340\\n\",\n \"877034906\\n\",\n \"425974918\\n\",\n \"866471222\\n\",\n \"694270313\\n\",\n \"9189590\\n\",\n \"974\\n\",\n \"1423\\n\",\n \"2168498\\n\",\n \"2\\n\",\n \"768416799\\n\",\n \"430890364\\n\",\n \"560835629\\n\",\n \"40986\\n\",\n \"887645468\\n\",\n \"55\\n\",\n \"421969935\\n\",\n \"679877201\\n\",\n \"622019656\\n\",\n \"35661246\\n\",\n \"508986960\\n\",\n \"1438\\n\",\n \"16\\n\",\n \"294018064\\n\",\n \"883576557\\n\",\n \"266040191\\n\",\n \"754365377\\n\",\n \"981187987\\n\",\n \"610\\n\",\n \"377\\n\",\n \"17712531\\n\",\n \"3\\n\",\n \"190978532\\n\",\n \"11\\n\",\n \"951713208\\n\",\n \"17\\n\",\n \"217313924\\n\",\n \"335832333\\n\",\n \"749094228\\n\",\n \"6\\n\",\n \"180683974\\n\",\n \"4\\n\",\n \"397629130\\n\",\n \"41\\n\",\n \"310942914\\n\",\n \"944871132\\n\",\n \"88\\n\",\n \"112718204\\n\",\n \"634479161\\n\",\n \"76115092\\n\",\n \"469563953\\n\",\n \"754902149\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"5\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"5\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nThere are N cells arranged in a row, numbered 1, 2, \\ldots, N from left to right.\n\nTak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.\n\nYou are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \\ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \\leq i \\leq r.\n\n* \bWhen you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.\n\n\n\nTo help Tak, find the number of ways to go to Cell N, modulo 998244353.\n\nConstraints\n\n* 2 \\leq N \\leq 2 \\times 10^5\n* 1 \\leq K \\leq \\min(N, 10)\n* 1 \\leq L_i \\leq R_i \\leq N\n* [L_i, R_i] and [L_j, R_j] do not intersect (i \\neq j)\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\nL_1 R_1\nL_2 R_2\n:\nL_K R_K\n\n\nOutput\n\nPrint the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.\n\nExamples\n\nInput\n\n5 2\n1 1\n3 4\n\n\nOutput\n\n4\n\n\nInput\n\n5 2\n3 3\n5 5\n\n\nOutput\n\n0\n\n\nInput\n\n5 1\n1 2\n\n\nOutput\n\n5\n\n\nInput\n\n60 3\n5 8\n1 3\n10 15\n\n\nOutput\n\n221823067\n\n### Input:\n5 2\n3 3\n5 5\n### Output:\n0\n\n### Input:\n5 1\n1 2\n### Output:\n5\n\n### Code:\nimport sys\ninput = sys.stdin.readline\n\nN,K=map(int,input().split())\nK=[tuple(map(int,input().split())) for i in range(K)]\nmod=998244353\n\nDP=[0]*(4*10**5+100)\nDP[1]=1\nDP[2]=-1\n\nfor i in range(1,N+1):\n DP[i]+=DP[i-1]\n DP[i]%=mod\n \n for l,r in K:\n DP[i+l]+=DP[i]\n DP[i+l]%=mod\n DP[i+r+1]-=DP[i]\n DP[i+r+1]%=mod\n \n\n #print(DP[:10])\n\nprint(DP[N])\n \n"}}},{"rowIdx":684,"cells":{"id":{"kind":"string","value":"p02680 AtCoder Beginner Contest 168 - . (Single Dot)_3229"},"description":{"kind":"string","value":"There is a grass field that stretches infinitely.\n\nIn this field, there is a negligibly small cow. Let (x, y) denote the point that is x\\ \\mathrm{cm} south and y\\ \\mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).\n\nThere are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).\n\nWhat is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print `INF` instead.\n\nConstraints\n\n* All values in input are integers between -10^9 and 10^9 (inclusive).\n* 1 \\leq N, M \\leq 1000\n* A_i < B_i\\ (1 \\leq i \\leq N)\n* E_j < F_j\\ (1 \\leq j \\leq M)\n* The point (0, 0) does not lie on any of the given segments.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M\nA_1 B_1 C_1\n:\nA_N B_N C_N\nD_1 E_1 F_1\n:\nD_M E_M F_M\n\n\nOutput\n\nIf the area of the region the cow can reach is infinite, print `INF`; otherwise, print an integer representing the area in \\mathrm{cm^2}.\n\n(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)\n\nExamples\n\nInput\n\n5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4\n\n\nOutput\n\n13\n\n\nInput\n\n6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4\n\n\nOutput\n\nINF"},"code":{"kind":"string","value":"I=lambda:map(int,input().split());F=1e21;r=range;n,m=I();f=[-F,F];X=[0]+f;Y=X[:];R=[(f,F),(f,-F)];H=[(F,f),(-F,f)]\nfor i in r(n):*a,c=I();R+=[(a,c)];Y+=c,;X+=a\nfor i in r(m):a,*b=I();H+=[(a,b)];X+=a,;Y+=b\ndef g(X):s=dict(enumerate(sorted(set(X))));return{s[i]:i for i in s},s,len(s)+1\nh,s,K=g(X);w,t,L=g(Y);j=lambda:[[0]*-~K for i in r(L+1)];V=j();U=j();v=j()\nfor(a,b),c in R:U[w[c]][h[a]]+=1;U[w[c]][h[b]]+=-1\nfor d,(e,f)in H:V[w[e]][h[d]]+=1;V[w[f]][h[d]]+=-1\nfor i in r(L):\n for j in r(K):U[i][j+1]+=U[i][j];V[i+1][j]+=V[i][j]\nq=[(h[0],w[0])];v[w[0]][h[0]]=1;a=0\nwhile q:\n x,y=q.pop();a+=(s[x]-s[x+1])*(t[y]-t[y+1])\n for e,f in[(-1,0),(1,0),(0,1),(0,-1)]:\n c=x+e;d=y+f\n if 0==v[d][c]and(U[(f>0)+y][x]|e==0)|(V[y][(e>0)+x]|f==0):q+=[(c,d)];v[d][c]=1\nprint([a,'INF'][a>F])"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"6 1\\n-3 -1 -2\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 4\\n1 2 4\",\n \"6 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"5 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 4 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 5\\n3 -2 6\\n1 2 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 4 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 10\\n6 -2 6\\n1 2 4\",\n \"5 6\\n2 0 0\\n-1 1 1\\n0 4 2\\n-2 7 -1\\n0 2 3\\n1 -1 1\\n1 1 1\\n1 0 2\\n-1 -7 10\\n3 -2 6\\n1 4 6\",\n \"3 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"3 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-3 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-6 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 2 -1\\n1 4 1\\n3 1 0\",\n \"6 1\\n-3 -1 -2\\n-3 -1 1\\n-2 -1 2\\n1 4 -3\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 6\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 4\\n1 2 4\",\n \"6 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -4\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 4 4\",\n \"3 1\\n-3 0 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"2 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -5\\n-3 -1 1\\n-2 -1 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"4 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-3 -1 1\\n-2 0 2\\n1 1 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"2 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-3 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 1 1\\n3 1 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n6 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -7\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 10\\n3 -2 6\\n1 2 4\",\n \"3 0\\n-3 -1 0\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -13 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 4 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 10\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n0 4 1\\n3 1 0\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 2 -1\\n1 4 2\\n3 1 0\",\n \"6 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -3\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 6\\n2 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 4\\n1 2 4\",\n \"5 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n1 4 -4\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 1\\n-1 -4 5\\n3 -2 6\\n1 4 4\",\n \"3 1\\n-3 0 -4\\n-3 -1 1\\n-2 0 2\\n1 4 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"2 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n4 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -5\\n-3 0 1\\n-2 -1 2\\n1 4 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"4 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 0\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-3 -1 1\\n-2 0 2\\n1 1 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"2 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n4 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 1 1\\n3 1 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n6 -2 6\\n1 2 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 10\\n3 -2 6\\n1 2 4\",\n \"3 0\\n-3 -1 0\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 1 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 0 1\\n0 2 2\\n-3 4 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -13 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n2 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 4 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 10\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 12 -1\\n0 4 1\\n3 1 0\",\n \"6 1\\n-3 -1 -4\\n-3 -1 1\\n-2 -1 2\\n0 4 -3\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 3 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 6\\n2 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n3 -2 4\\n1 2 4\",\n \"5 1\\n-3 -1 -4\\n-3 -1 1\\n-3 -1 2\\n1 4 -4\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 2 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 1\\n-1 -1 5\\n3 -2 6\\n1 4 4\",\n \"3 1\\n-3 0 -4\\n-3 -1 1\\n-2 0 2\\n1 5 -2\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"2 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n4 0 6\\n1 2 4\",\n \"3 1\\n-3 -1 -5\\n-3 0 1\\n-2 -1 2\\n1 1 -2\\n1 6 -1\\n1 4 1\\n3 1 4\",\n \"4 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n1 0 0\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-3 -1 1\\n-2 0 2\\n1 1 -2\\n1 6 -1\\n1 6 1\\n3 1 4\",\n \"2 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -2\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n4 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 -4\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n1 1 1\\n3 0 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n8 -2 6\\n1 2 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n1 0 2\\n-1 -4 10\\n3 -2 6\\n1 2 4\",\n \"3 0\\n-3 -1 0\\n-3 0 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n2 1 1\\n3 1 0\",\n \"3 1\\n-3 -2 0\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n2 4 1\\n3 1 0\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 12 -1\\n0 4 1\\n4 1 0\",\n \"6 1\\n-3 0 -4\\n-3 -1 1\\n-2 -1 2\\n0 4 -3\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 3 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 6\\n2 0 1\\n0 2 2\\n2 0 2\\n-1 -4 5\\n3 -2 4\\n1 2 4\",\n \"5 1\\n-3 -1 -8\\n-3 -1 1\\n-3 -1 2\\n1 4 -4\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 1\\n-1 -1 5\\n3 -2 6\\n1 4 4\",\n \"3 1\\n-3 0 -4\\n-3 -1 1\\n-2 0 2\\n1 5 -2\\n1 4 -1\\n1 4 2\\n3 1 4\",\n \"2 6\\n1 0 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n4 0 6\\n1 2 4\",\n \"3 1\\n-3 -1 -5\\n-3 0 1\\n-2 -1 2\\n1 1 -2\\n1 6 -1\\n1 4 1\\n5 1 4\",\n \"4 6\\n2 1 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n1 0 0\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-3 -1 1\\n-2 0 2\\n1 1 -2\\n1 9 -1\\n1 6 1\\n3 1 4\",\n \"2 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -2\\n-2 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n4 -2 6\\n0 2 4\",\n \"3 1\\n-3 -1 -4\\n-6 -1 1\\n-2 0 2\\n0 4 -2\\n1 6 -1\\n1 1 1\\n3 0 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n1 0 2\\n-1 -4 17\\n3 -2 6\\n1 2 4\",\n \"2 1\\n-3 -2 0\\n-6 -1 1\\n-2 0 2\\n1 4 -2\\n1 6 -1\\n2 4 1\\n3 1 0\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 4 2\\n-3 7 -1\\n-1 6 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -7 10\\n6 -2 6\\n1 2 6\",\n \"3 1\\n-3 -1 0\\n-6 1 1\\n-2 0 2\\n1 4 -2\\n1 12 -1\\n0 4 0\\n4 1 0\",\n \"6 1\\n-3 0 -4\\n-3 -1 1\\n-2 -1 2\\n0 8 -3\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 1\\n-3 0 -8\\n-3 -1 1\\n-3 -1 2\\n1 4 -4\\n1 4 -1\\n1 4 1\\n3 1 4\",\n \"5 6\\n1 1 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 1\\n-1 -1 5\\n3 -1 6\\n1 4 4\",\n \"3 1\\n-2 0 -4\\n-3 -1 1\\n-2 0 2\\n1 5 -2\\n1 4 -1\\n1 4 2\\n3 1 4\",\n \"2 6\\n1 0 0\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n2 0 2\\n-1 -4 5\\n4 0 6\\n1 0 4\",\n \"3 1\\n-3 -1 -5\\n-3 0 1\\n-2 -1 2\\n1 1 -2\\n1 6 -1\\n1 4 1\\n5 1 7\",\n \"4 6\\n2 0 1\\n0 1 1\\n0 2 2\\n-3 4 -1\\n-2 6 3\\n1 0 1\\n0 1 2\\n1 0 0\\n-1 -4 5\\n3 -2 6\\n1 2 4\",\n \"3 1\\n-3 -1 0\\n-3 -1 1\\n-2 0 2\\n1 1 -2\\n1 14 -1\\n1 6 1\\n3 1 4\",\n \"2 6\\n1 1 1\\n0 1 1\\n0 2 2\\n-3 4 -2\\n-2 0 3\\n1 0 1\\n1 1 2\\n2 0 2\\n-1 -4 5\\n4 -2 6\\n0 2 4\",\n \"3 1\\n-3 -1 -4\\n-6 -1 1\\n-2 0 2\\n0 4 -2\\n2 6 -1\\n1 1 1\\n3 0 4\",\n \"5 6\\n1 0 1\\n0 1 1\\n0 2 2\\n-3 7 -1\\n-1 9 3\\n1 0 1\\n1 1 2\\n1 0 2\\n-1 -4 17\\n3 -2 6\\n1 2 4\"\n ],\n \"output\": [\n \"INF\",\n \"13\",\n \"INF\\n\",\n \"13\\n\",\n \"16\\n\",\n \"14\\n\",\n \"28\\n\",\n \"4\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"13\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"14\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"14\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"28\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"INF\\n\",\n \"16\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nThere is a grass field that stretches infinitely.\n\nIn this field, there is a negligibly small cow. Let (x, y) denote the point that is x\\ \\mathrm{cm} south and y\\ \\mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).\n\nThere are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).\n\nWhat is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print `INF` instead.\n\nConstraints\n\n* All values in input are integers between -10^9 and 10^9 (inclusive).\n* 1 \\leq N, M \\leq 1000\n* A_i < B_i\\ (1 \\leq i \\leq N)\n* E_j < F_j\\ (1 \\leq j \\leq M)\n* The point (0, 0) does not lie on any of the given segments.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M\nA_1 B_1 C_1\n:\nA_N B_N C_N\nD_1 E_1 F_1\n:\nD_M E_M F_M\n\n\nOutput\n\nIf the area of the region the cow can reach is infinite, print `INF`; otherwise, print an integer representing the area in \\mathrm{cm^2}.\n\n(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)\n\nExamples\n\nInput\n\n5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4\n\n\nOutput\n\n13\n\n\nInput\n\n6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4\n\n\nOutput\n\nINF\n\n### Input:\n6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4\n### Output:\nINF\n\n### Input:\n5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4\n### Output:\n13\n\n### Code:\nI=lambda:map(int,input().split());F=1e21;r=range;n,m=I();f=[-F,F];X=[0]+f;Y=X[:];R=[(f,F),(f,-F)];H=[(F,f),(-F,f)]\nfor i in r(n):*a,c=I();R+=[(a,c)];Y+=c,;X+=a\nfor i in r(m):a,*b=I();H+=[(a,b)];X+=a,;Y+=b\ndef g(X):s=dict(enumerate(sorted(set(X))));return{s[i]:i for i in s},s,len(s)+1\nh,s,K=g(X);w,t,L=g(Y);j=lambda:[[0]*-~K for i in r(L+1)];V=j();U=j();v=j()\nfor(a,b),c in R:U[w[c]][h[a]]+=1;U[w[c]][h[b]]+=-1\nfor d,(e,f)in H:V[w[e]][h[d]]+=1;V[w[f]][h[d]]+=-1\nfor i in r(L):\n for j in r(K):U[i][j+1]+=U[i][j];V[i+1][j]+=V[i][j]\nq=[(h[0],w[0])];v[w[0]][h[0]]=1;a=0\nwhile q:\n x,y=q.pop();a+=(s[x]-s[x+1])*(t[y]-t[y+1])\n for e,f in[(-1,0),(1,0),(0,1),(0,-1)]:\n c=x+e;d=y+f\n if 0==v[d][c]and(U[(f>0)+y][x]|e==0)|(V[y][(e>0)+x]|f==0):q+=[(c,d)];v[d][c]=1\nprint([a,'INF'][a>F])"}}},{"rowIdx":685,"cells":{"id":{"kind":"string","value":"p02808 Dwango Programming Contest 6th - Cookie Distribution_3232"},"description":{"kind":"string","value":"There are N children, numbered 1,2,\\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)\n\nLet us define the happiness of the children as c_1 \\times c_2 \\times \\ldots \\times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \\binom{N}{a_1} \\times \\binom{N}{a_2} \\times \\ldots \\times \\binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).\n\nConstraints\n\n* 1 \\leq N \\leq 1000\n* 1 \\leq K \\leq 20\n* 1 \\leq a_i \\leq N\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\na_1 a_2 \\ldots a_K\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 2\n3 2\n\n\nOutput\n\n12\n\n\nInput\n\n856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63\n\n\nOutput\n\n337587117"},"code":{"kind":"string","value":"n,k = map(int,input().split())\na = tuple(map(int,input().split()))\nmod = 10**9+7\nrng = 1001\nfctr = [1]\nfinv = [1]\nfor i in range(1,rng):\n fctr.append(fctr[-1]*i%mod)\n finv.append(pow(fctr[i],mod-2,mod))\ndp = [[0 for i in range(n+1)] for j in range(k+1)]\ndp[0][0] = 1\nfor i in range(1,k+1):\n x = a[i-1]\n for j in range(n+1):\n if dp[i-1][j] == 0:\n continue\n y = dp[i-1][j]*fctr[n-j]*finv[n-x]%mod\n for t in range(min(n-j,x)+1):\n dp[i][j+t]=(dp[i][j+t]+y*fctr[n-t]*finv[n-j-t]*finv[t]*finv[x-t])%mod\nprint(dp[k][n])"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3 2\\n3 2\",\n \"856 16\\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63\",\n \"3 2\\n1 2\",\n \"856 16\\n399 491 665 432 206 61 784 548 422 313 848 478 827 26 398 63\",\n \"4 2\\n1 2\",\n \"856 16\\n399 491 665 432 206 0 784 548 422 313 848 478 827 26 398 63\",\n \"2 2\\n1 2\",\n \"856 16\\n399 491 665 432 206 0 784 548 422 514 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 0 784 548 422 514 94 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 0 784 548 143 514 94 478 827 26 398 63\",\n \"3 2\\n3 3\",\n \"856 16\\n399 263 665 432 206 61 784 548 422 24 848 478 827 26 398 63\",\n \"3 2\\n2 2\",\n \"856 16\\n399 491 665 432 206 61 784 548 422 313 848 478 827 23 398 63\",\n \"4 2\\n2 2\",\n \"856 16\\n399 491 665 432 206 0 784 246 422 313 848 478 827 26 398 63\",\n \"2 2\\n1 1\",\n \"856 16\\n399 491 665 432 206 0 784 548 422 514 848 478 827 2 398 63\",\n \"856 16\\n399 833 665 432 206 0 784 548 422 514 94 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 107 0 784 548 143 514 94 478 827 26 398 63\",\n \"856 16\\n399 263 747 432 206 61 784 548 422 24 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 61 784 548 422 313 848 478 827 23 222 63\",\n \"4 2\\n2 3\",\n \"856 16\\n399 491 665 329 206 0 784 246 422 313 848 478 827 26 398 63\",\n \"856 16\\n399 833 665 432 206 0 784 548 422 514 70 478 827 26 398 63\",\n \"856 16\\n399 263 747 432 206 61 784 548 422 47 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 61 784 548 422 79 848 478 827 23 222 63\",\n \"856 16\\n399 491 665 329 206 0 784 246 508 313 848 478 827 26 398 63\",\n \"2 1\\n2 8\",\n \"856 16\\n399 263 747 432 206 61 784 548 422 30 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 61 784 548 422 79 848 478 827 23 222 94\",\n \"856 16\\n399 263 747 432 206 61 784 548 422 40 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 564 206 61 784 548 422 79 848 478 827 23 222 94\",\n \"856 16\\n399 263 747 376 206 61 784 548 422 40 848 478 827 26 398 63\",\n \"856 16\\n399 263 234 376 206 61 784 548 422 40 848 478 827 26 398 63\",\n \"856 16\\n399 263 234 376 206 61 784 548 774 40 848 478 827 26 398 63\",\n \"856 16\\n399 350 234 376 206 61 784 548 774 40 848 478 827 26 398 63\",\n \"856 16\\n214 350 234 376 206 61 784 548 774 40 848 478 827 26 398 63\",\n \"7 2\\n1 7\",\n \"856 16\\n399 263 665 432 206 61 816 548 422 313 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 170 0 784 548 422 313 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 1 784 548 422 514 848 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 0 784 548 422 514 60 478 827 26 398 63\",\n \"856 16\\n399 491 665 432 206 0 784 855 143 514 94 478 827 26 398 63\",\n \"856 16\\n399 263 665 418 206 61 784 548 422 313 848 478 827 26 398 63\",\n \"856 16\\n399 263 665 418 206 61 784 315 422 313 848 478 827 26 398 63\",\n \"856 16\\n399 263 11 418 206 61 354 315 82 313 848 478 827 26 398 64\",\n \"856 16\\n399 263 11 418 206 61 354 315 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 11 418 206 61 201 315 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 11 418 206 61 201 530 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 11 418 206 61 201 13 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 11 418 206 61 201 6 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 21 418 206 61 201 6 82 313 848 478 827 42 398 64\",\n \"856 16\\n399 263 21 204 206 61 201 6 82 313 848 478 827 42 398 64\",\n \"856 7\\n399 263 21 204 206 61 201 6 82 313 848 478 827 42 398 64\",\n \"856 7\\n399 389 21 204 206 61 201 6 82 313 848 478 827 42 398 64\",\n \"856 14\\n399 389 21 204 206 61 201 5 82 313 848 478 631 42 398 64\",\n \"856 14\\n399 389 21 204 206 61 201 5 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 21 204 206 61 201 5 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 37 204 206 61 201 5 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 37 204 206 61 201 1 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 37 204 206 61 195 1 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 37 204 366 61 195 1 39 313 848 478 631 42 398 64\",\n \"856 12\\n399 389 24 204 366 61 195 1 39 313 848 478 631 42 398 80\",\n \"2 2\\n2 2\",\n \"2 2\\n2 3\",\n \"2 2\\n2 5\",\n \"2 4\\n2 5\",\n \"2 5\\n2 5\",\n \"2 5\\n0 5\",\n \"2 5\\n0 8\",\n \"2 5\\n1 8\",\n \"2 5\\n1 16\",\n \"2 5\\n1 22\",\n \"2 9\\n1 22\",\n \"1 9\\n1 22\",\n \"1 9\\n2 22\",\n \"1 9\\n3 22\",\n \"1 9\\n4 22\",\n \"1 9\\n6 22\",\n \"1 9\\n6 31\",\n \"1 9\\n6 26\",\n \"1 1\\n6 26\",\n \"1 0\\n6 26\",\n \"2 2\\n4 2\",\n \"2 2\\n3 5\",\n \"2 2\\n1 5\",\n \"2 4\\n4 5\",\n \"2 6\\n2 5\",\n \"2 5\\n1 5\",\n \"1 5\\n0 8\",\n \"1 5\\n1 8\",\n \"2 5\\n1 30\",\n \"2 5\\n1 28\",\n \"2 9\\n1 8\",\n \"2 9\\n2 22\",\n \"1 9\\n2 14\",\n \"1 14\\n3 22\",\n \"1 9\\n1 29\",\n \"0 9\\n6 22\",\n \"1 14\\n6 31\",\n \"0 9\\n6 26\"\n ],\n \"output\": [\n \"12\",\n \"337587117\",\n \"3\\n\",\n \"652418319\\n\",\n \"0\\n\",\n \"860269823\\n\",\n \"4\\n\",\n \"293299401\\n\",\n \"366370911\\n\",\n \"24060500\\n\",\n \"8\\n\",\n \"310476415\\n\",\n \"12\\n\",\n \"25729710\\n\",\n \"6\\n\",\n \"314510353\\n\",\n \"2\\n\",\n \"25600194\\n\",\n \"23647064\\n\",\n \"973833970\\n\",\n \"756052596\\n\",\n \"293415485\\n\",\n \"24\\n\",\n \"281860830\\n\",\n \"150176430\\n\",\n \"944589618\\n\",\n \"731138031\\n\",\n \"601992298\\n\",\n \"1\\n\",\n \"279486415\\n\",\n \"452204876\\n\",\n \"816722626\\n\",\n \"68373623\\n\",\n \"397893539\\n\",\n \"368478426\\n\",\n \"983214695\\n\",\n \"654286888\\n\",\n \"726149561\\n\",\n \"14\\n\",\n \"307328341\\n\",\n \"421014311\\n\",\n \"5274556\\n\",\n \"305060096\\n\",\n \"957106834\\n\",\n \"800357371\\n\",\n \"772960854\\n\",\n \"453626014\\n\",\n \"928059710\\n\",\n \"872873967\\n\",\n \"292836983\\n\",\n \"351295606\\n\",\n \"509183906\\n\",\n \"727532698\\n\",\n \"591111976\\n\",\n \"113519286\\n\",\n \"557731190\\n\",\n \"691045396\\n\",\n \"129825796\\n\",\n \"830635867\\n\",\n \"959556031\\n\",\n \"280903391\\n\",\n \"634652159\\n\",\n \"418267134\\n\",\n \"767801877\\n\",\n \"4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nThere are N children, numbered 1,2,\\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)\n\nLet us define the happiness of the children as c_1 \\times c_2 \\times \\ldots \\times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \\binom{N}{a_1} \\times \\binom{N}{a_2} \\times \\ldots \\times \\binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).\n\nConstraints\n\n* 1 \\leq N \\leq 1000\n* 1 \\leq K \\leq 20\n* 1 \\leq a_i \\leq N\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN K\na_1 a_2 \\ldots a_K\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 2\n3 2\n\n\nOutput\n\n12\n\n\nInput\n\n856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63\n\n\nOutput\n\n337587117\n\n### Input:\n3 2\n3 2\n### Output:\n12\n\n### Input:\n856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63\n### Output:\n337587117\n\n### Code:\nn,k = map(int,input().split())\na = tuple(map(int,input().split()))\nmod = 10**9+7\nrng = 1001\nfctr = [1]\nfinv = [1]\nfor i in range(1,rng):\n fctr.append(fctr[-1]*i%mod)\n finv.append(pow(fctr[i],mod-2,mod))\ndp = [[0 for i in range(n+1)] for j in range(k+1)]\ndp[0][0] = 1\nfor i in range(1,k+1):\n x = a[i-1]\n for j in range(n+1):\n if dp[i-1][j] == 0:\n continue\n y = dp[i-1][j]*fctr[n-j]*finv[n-x]%mod\n for t in range(min(n-j,x)+1):\n dp[i][j+t]=(dp[i][j+t]+y*fctr[n-t]*finv[n-j-t]*finv[t]*finv[x-t])%mod\nprint(dp[k][n])"}}},{"rowIdx":686,"cells":{"id":{"kind":"string","value":"p03081 ExaWizards 2019 - Snuke the Wizard_3238"},"description":{"kind":"string","value":"There are N squares numbered 1 to N from left to right. Each square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.\n\nSnuke cast Q spells to move the golems.\n\nThe i-th spell consisted of two characters t_i and d_i, where d_i is `L` or `R`. When Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is `L`, and moved to the square adjacent to the right if d_i is `R`.\n\nHowever, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.\n\nFind the number of golems remaining after Snuke cast the Q spells.\n\nConstraints\n\n* 1 \\leq N,Q \\leq 2 \\times 10^{5}\n* |s| = N\n* s_i and t_i are uppercase English letters.\n* d_i is `L` or `R`.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN Q\ns\nt_1 d_1\n\\vdots\nt_{Q} d_Q\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 4\nABC\nA L\nB L\nB R\nA R\n\n\nOutput\n\n2\n\n\nInput\n\n8 3\nAABCBDBA\nA L\nB R\nA R\n\n\nOutput\n\n5\n\n\nInput\n\n10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L\n\n\nOutput\n\n3"},"code":{"kind":"string","value":"n, q = map(int, input().split())\ns = input()\n\no = []\nfor _ in range(q):\n t, d = input().split()\n o.append((t, d))\n\n\ndef check(x):\n cur = s[x]\n ind = x\n for i in range(q):\n if o[i][0] == cur:\n if o[i][1] == 'L':\n ind -= 1\n if ind < 0:\n return \"LEFT\"\n cur = s[ind]\n else:\n ind += 1\n if ind > n-1:\n return \"RIGHT\"\n cur = s[ind]\n return \"MID\"\n\n\nans = n\n\nbottom = -1\ntop = n\n\nwhile top - bottom > 1:\n mid = (top+bottom)//2\n if check(mid) == \"LEFT\":\n bottom = mid\n else:\n top = mid\n\nans -= 1+bottom\n\nbottom = -1\ntop = n\n\nwhile top - bottom > 1:\n mid = (top+bottom)//2\n if check(mid) == \"RIGHT\":\n top = mid\n else:\n bottom = mid\n\nans -= n-top\n\nprint(ans)"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"10 15\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nW R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nA L\\nN L\\nE R\\nZ L\\nS L\",\n \"3 4\\nABC\\nA L\\nB L\\nB R\\nA R\",\n \"8 3\\nAABCBDBA\\nA L\\nB R\\nA R\",\n \"10 15\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nW R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nA L\\nN L\\nE R\\nZ L\\nR L\",\n \"3 4\\nACB\\nA L\\nB L\\nB R\\nA R\",\n \"8 3\\nAABBBDBA\\nA L\\nB R\\nA R\",\n \"3 3\\nACB\\nB L\\nB L\\nA R\\n@ S\",\n \"3 3\\nBCA\\nB L\\nB L\\nA R\\n@ S\",\n \"8 0\\nAABCBDBA\\nA L\\nB R\\n@ S\",\n \"8 3\\nAABCBDBA\\nC L\\nB R\\nA R\",\n \"10 15\\nBWECRWZCNS\\nB R\\nR R\\nE R\\nW R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nA L\\nN L\\nE R\\nZ L\\nR L\",\n \"10 0\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nX R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nB L\\nN L\\nE R\\nZ L\\nS L\",\n \"3 4\\nCBB\\nA L\\nC L\\nB R\\nB R\",\n \"8 3\\nAABCBDBA\\nA L\\nB R\\n@ R\",\n \"3 4\\nACB\\nA L\\nB L\\nB R\\n@ R\",\n \"8 3\\nAABCBDCA\\nA L\\nB R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nB R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nA R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nA R\\n@ S\",\n \"10 15\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nW R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nD L\\nA L\\nN L\\nE R\\nZ L\\nR L\",\n \"3 4\\nACB\\nA L\\nB L\\nB Q\\nA R\",\n \"8 3\\nAABCBDBA\\nA L\\nB R\\n@ S\",\n \"3 4\\nADB\\nA L\\nB L\\nB R\\n@ R\",\n \"8 3\\nAABCBDCA\\nA L\\nB R\\n@ S\",\n \"3 3\\nBCA\\nA L\\nB L\\nB R\\n@ R\",\n \"3 4\\nACB\\nA L\\nB L\\nB Q\\nA S\",\n \"8 3\\nAACCBDBA\\nA L\\nB R\\nA R\",\n \"3 4\\nBCA\\nA L\\nB L\\nB R\\nA R\",\n \"3 4\\nABB\\nA L\\nB L\\nB R\\n@ R\",\n \"3 3\\nABC\\nA L\\nB L\\nA R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nB R\\n@ S\",\n \"8 3\\nAABBBDBA\\nA L\\nB R\\nB R\",\n \"3 4\\nACC\\nA L\\nB L\\nB Q\\nA R\",\n \"3 4\\nADB\\nA L\\nB L\\nB Q\\n@ R\",\n \"3 3\\nCCA\\nA L\\nB L\\nB R\\n@ R\",\n \"3 3\\nACB\\nB L\\nB K\\nA R\\n@ S\",\n \"3 4\\nBCA\\nA L\\nB L\\nB Q\\nA S\",\n \"8 3\\nACCABDBA\\nA L\\nB R\\nA R\",\n \"3 4\\nABB\\nA L\\nB L\\nB R\\nA R\",\n \"3 3\\nBAC\\nA L\\nB L\\nA R\\n@ R\",\n \"8 3\\nAABBBDAA\\nA L\\nB R\\nB R\",\n \"8 0\\nAABCBDBA\\n@ L\\nB R\\n@ S\",\n \"3 4\\nACB\\nA L\\nB L\\nB Q\\n@ R\",\n \"3 3\\nCCA\\nA L\\nB L\\nA R\\n@ R\",\n \"3 3\\nBCA\\nA L\\nB L\\nB Q\\nA S\",\n \"3 3\\nBBC\\nA L\\nB L\\nA R\\n@ R\",\n \"8 3\\nAABBBDAA\\nB L\\nB R\\nB R\",\n \"8 0\\nAABCBDBA\\n@ L\\nB S\\n@ S\",\n \"3 3\\nCCA\\nA L\\nB L\\nA R\\n@ Q\",\n \"3 3\\nCBB\\nA L\\nB L\\nA R\\n@ R\",\n \"8 1\\nAABCBDBA\\n@ L\\nB S\\n@ S\",\n \"3 3\\nCBB\\nA L\\nC L\\nA R\\n@ R\",\n \"8 1\\nAABCBDBA\\n@ L\\nA S\\n@ S\",\n \"3 3\\nCBB\\nA L\\nC L\\nA R\\n@ S\",\n \"8 1\\nAABCBDBA\\n? L\\nA S\\n@ S\",\n \"8 1\\nAABCBDBA\\n? K\\nA S\\n@ S\",\n \"8 1\\nBABCBDBA\\n? K\\nA S\\n@ S\",\n \"8 0\\nBABCBDBA\\n? K\\nA S\\n@ S\",\n \"10 15\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nW R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nB L\\nN L\\nE R\\nZ L\\nS L\",\n \"3 4\\nBBC\\nA L\\nB L\\nB R\\nA R\",\n \"8 3\\nAABCBDBA\\nB L\\nB R\\nA R\",\n \"3 4\\nACB\\nA L\\nB L\\nB S\\nA R\",\n \"3 4\\nACB\\nA L\\nB L\\nB R\\n@ Q\",\n \"3 1\\nACB\\nA L\\nB L\\nB R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nA R\\n@ Q\",\n \"3 3\\nACB\\nA L\\nB L\\nA Q\\n@ S\",\n \"3 4\\nADB\\nA L\\nB L\\nB R\\nA R\",\n \"8 1\\nAABCBDCA\\nA L\\nB R\\n@ S\",\n \"3 3\\nACB\\nB L\\nC L\\nA R\\n@ S\",\n \"3 4\\nACB\\nA L\\nB L\\nB Q\\nB S\",\n \"3 3\\nBCA\\nB L\\nB K\\nA R\\n@ S\",\n \"8 2\\nAACCBDBA\\nA L\\nB R\\nA R\",\n \"3 4\\nBCA\\nA L\\nB L\\nB R\\nB R\",\n \"3 4\\nABB\\nA L\\nB L\\nB R\\n@ S\",\n \"3 3\\nABC\\nA L\\nC L\\nA R\\n@ R\",\n \"3 4\\nACC\\nB L\\nB L\\nB Q\\nA R\",\n \"8 0\\nAABCBDBA\\nA L\\nA R\\n@ S\",\n \"3 4\\nADB\\n@ L\\nB L\\nB Q\\n@ R\",\n \"3 3\\nCCA\\nA L\\nB L\\nC R\\n@ R\",\n \"3 3\\nACB\\nB L\\nB K\\nA R\\n@ T\",\n \"3 4\\nBCA\\nA L\\nB L\\nB P\\nA S\",\n \"8 3\\nAACABDBC\\nA L\\nB R\\nA R\",\n \"3 4\\nABB\\nB L\\nB L\\nB R\\nA R\",\n \"8 3\\nAABBBDAA\\nA L\\nA R\\nB R\",\n \"8 0\\nAABCBDBA\\n@ L\\nB R\\n? S\",\n \"3 3\\nCCA\\nA L\\nB L\\nA R\\n? R\",\n \"3 3\\nBBC\\nA L\\nA L\\nA R\\n@ R\",\n \"8 0\\nAABCBDBA\\n@ L\\nB T\\n@ S\",\n \"3 3\\nACC\\nA L\\nB L\\nA R\\n@ Q\",\n \"3 3\\nCBB\\nA L\\nC L\\n@ R\\n@ R\",\n \"3 3\\nCBB\\nA L\\nB L\\nA R\\n@ S\",\n \"8 1\\nAABCBDBB\\n? L\\nA S\\n@ S\",\n \"8 1\\nBABCBDBA\\n? K\\nA R\\n@ S\",\n \"10 15\\nSNCZWRCEWB\\nB R\\nR R\\nE R\\nX R\\nZ L\\nS R\\nQ L\\nW L\\nB R\\nC L\\nB L\\nN L\\nE R\\nZ L\\nS L\",\n \"3 4\\nBCB\\nA L\\nB L\\nB R\\nA R\",\n \"3 4\\nACC\\nA L\\nB L\\nB S\\nA R\",\n \"3 4\\nACB\\nA L\\nB L\\nB R\\nA Q\",\n \"3 1\\nACB\\n@ L\\nB L\\nB R\\n@ R\",\n \"3 3\\nACB\\nA L\\nB L\\nA Q\\n@ T\",\n \"3 4\\nBDA\\nA L\\nB L\\nB R\\nA R\",\n \"8 1\\nAABCBDCA\\nA L\\nC R\\n@ S\",\n \"3 4\\nBCA\\nA L\\nB L\\nC R\\nB R\",\n \"3 2\\nABC\\nA L\\nC L\\nA R\\n@ R\"\n ],\n \"output\": [\n \"3\",\n \"2\",\n \"5\",\n \"7\\n\",\n \"2\\n\",\n \"5\\n\",\n \"3\\n\",\n \"1\\n\",\n \"8\\n\",\n \"6\\n\",\n \"9\\n\",\n \"10\\n\",\n \"0\\n\",\n \"7\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\",\n \"5\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\",\n \"3\\n\",\n \"3\\n\",\n \"2\\n\",\n \"5\\n\",\n \"2\\n\",\n \"1\\n\",\n \"7\\n\",\n \"8\\n\",\n \"2\\n\",\n \"3\\n\",\n \"2\\n\",\n \"2\\n\",\n \"8\\n\",\n \"8\\n\",\n \"3\\n\",\n \"3\\n\",\n \"8\\n\",\n \"2\\n\",\n \"8\\n\",\n \"2\\n\",\n \"8\\n\",\n \"8\\n\",\n \"8\\n\",\n \"8\\n\",\n \"3\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"7\\n\",\n \"3\\n\",\n \"2\\n\",\n \"1\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"3\\n\",\n \"8\\n\",\n \"3\\n\",\n \"3\\n\",\n \"3\\n\",\n \"2\\n\",\n \"7\\n\",\n \"3\\n\",\n \"7\\n\",\n \"8\\n\",\n \"3\\n\",\n \"3\\n\",\n \"8\\n\",\n \"2\\n\",\n \"2\\n\",\n \"3\\n\",\n \"8\\n\",\n \"8\\n\",\n \"5\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"3\\n\",\n \"2\\n\",\n \"2\\n\",\n \"7\\n\",\n \"2\\n\",\n \"2\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nThere are N squares numbered 1 to N from left to right. Each square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.\n\nSnuke cast Q spells to move the golems.\n\nThe i-th spell consisted of two characters t_i and d_i, where d_i is `L` or `R`. When Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is `L`, and moved to the square adjacent to the right if d_i is `R`.\n\nHowever, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.\n\nFind the number of golems remaining after Snuke cast the Q spells.\n\nConstraints\n\n* 1 \\leq N,Q \\leq 2 \\times 10^{5}\n* |s| = N\n* s_i and t_i are uppercase English letters.\n* d_i is `L` or `R`.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN Q\ns\nt_1 d_1\n\\vdots\nt_{Q} d_Q\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 4\nABC\nA L\nB L\nB R\nA R\n\n\nOutput\n\n2\n\n\nInput\n\n8 3\nAABCBDBA\nA L\nB R\nA R\n\n\nOutput\n\n5\n\n\nInput\n\n10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L\n\n\nOutput\n\n3\n\n### Input:\n10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L\n### Output:\n3\n\n### Input:\n3 4\nABC\nA L\nB L\nB R\nA R\n### Output:\n2\n\n### Code:\nn, q = map(int, input().split())\ns = input()\n\no = []\nfor _ in range(q):\n t, d = input().split()\n o.append((t, d))\n\n\ndef check(x):\n cur = s[x]\n ind = x\n for i in range(q):\n if o[i][0] == cur:\n if o[i][1] == 'L':\n ind -= 1\n if ind < 0:\n return \"LEFT\"\n cur = s[ind]\n else:\n ind += 1\n if ind > n-1:\n return \"RIGHT\"\n cur = s[ind]\n return \"MID\"\n\n\nans = n\n\nbottom = -1\ntop = n\n\nwhile top - bottom > 1:\n mid = (top+bottom)//2\n if check(mid) == \"LEFT\":\n bottom = mid\n else:\n top = mid\n\nans -= 1+bottom\n\nbottom = -1\ntop = n\n\nwhile top - bottom > 1:\n mid = (top+bottom)//2\n if check(mid) == \"RIGHT\":\n top = mid\n else:\n bottom = mid\n\nans -= n-top\n\nprint(ans)"}}},{"rowIdx":687,"cells":{"id":{"kind":"string","value":"p03226 Tenka1 Programmer Contest - Circular_3241"},"description":{"kind":"string","value":"You are given a sequence of N integers: A_1,A_2,...,A_N.\n\nFind the number of permutations p_1,p_2,...,p_N of 1,2,...,N that can be changed to A_1,A_2,...,A_N by performing the following operation some number of times (possibly zero), modulo 998244353:\n\n* For each 1\\leq i\\leq N, let q_i=min(p_{i-1},p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.\n\nConstraints\n\n* 1 \\leq N \\leq 3 × 10^5\n* 1 \\leq A_i \\leq N\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1\n:\nA_N\n\n\nOutput\n\nPrint the number of the sequences that satisfy the condition, modulo 998244353.\n\nExamples\n\nInput\n\n3\n1\n2\n1\n\n\nOutput\n\n2\n\n\nInput\n\n5\n3\n1\n4\n1\n5\n\n\nOutput\n\n0\n\n\nInput\n\n8\n4\n4\n4\n1\n1\n1\n2\n2\n\n\nOutput\n\n24\n\n\nInput\n\n6\n1\n1\n6\n2\n2\n2\n\n\nOutput\n\n0"},"code":{"kind":"string","value":"import sys\nread = sys.stdin.buffer.read\nreadline = sys.stdin.buffer.readline\nreadlines = sys.stdin.buffer.readlines\nsys.setrecursionlimit(10 ** 7)\n\nfrom operator import itemgetter\n\nMOD = 998244353\n\nN,*A = map(int,read().split())\n\nT = A.count(1)\nif T == 0:\n print(0)\n exit()\nif T == 1:\n answer = 1 if len(set(A)) == N else 0\n print(answer)\n exit()\nif T == N:\n answer = 1\n for n in range(1,N+1):\n answer *= n\n answer %= MOD\n print(answer)\n exit()\n\nn = A.index(1)\nwhile A[n-1] == 1:\n n -= 1\nA = A[n:] + A[:n]\n\n# assert len(A) == N and A[0] == 1 and A[-1] != 1\n\nL = [0] * (N+1)\nR = [-1] * (N+1)\nctr = [0] * (N+1)\nnums = []\nprev = 0\nfor i,x in enumerate(A):\n ctr[x] += 1\n R[x] = i\n if prev != x:\n nums.append(x)\n L[x] = i\n prev = x\n\nif any(y - x + 1 != z for x,y,z in zip(L,R,ctr)):\n print(0)\n exit()\nif any(x > T for x in ctr[2:]):\n print(0)\n exit()\n\nfree = [0] * (N+1) # ある数値を書き込んだ時点で、死亡確定になってるマス数\nanswer = 1\nfor x,y,z in zip(nums,nums[1:],nums[2:]+[1]):\n if x > y < z:\n if ctr[y] != T:\n answer = 0\n break\n elif x < y < z:\n free[y] += ctr[y] - 1\n elif x > y > z:\n free[y] += ctr[y] - 1\n else:\n # x < y > z\n answer *= (T + 1 - ctr[y])\n answer %= MOD\n free[y] += ctr[y] + T - 2\n\nf = 0\nfor n in range(1,N+1):\n if ctr[n] >= 1:\n f += free[n]\n continue\n answer *= f\n answer %= MOD\n f -= 1\n\nprint(answer)"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3\\n1\\n2\\n1\",\n \"8\\n4\\n4\\n4\\n1\\n1\\n1\\n2\\n2\",\n \"6\\n1\\n1\\n6\\n2\\n2\\n2\",\n \"5\\n3\\n1\\n4\\n1\\n5\",\n \"8\\n4\\n4\\n4\\n1\\n2\\n1\\n2\\n2\",\n \"5\\n3\\n1\\n4\\n2\\n5\",\n \"6\\n4\\n1\\n1\\n2\\n2\\n4\",\n \"6\\n1\\n1\\n1\\n2\\n2\\n2\",\n \"6\\n1\\n1\\n1\\n2\\n2\\n1\",\n \"6\\n1\\n1\\n1\\n1\\n2\\n1\",\n \"6\\n1\\n1\\n1\\n1\\n1\\n1\",\n \"3\\n1\\n1\\n1\",\n \"8\\n4\\n4\\n5\\n1\\n1\\n1\\n2\\n3\",\n \"5\\n1\\n2\\n2\\n1\\n1\",\n \"6\\n1\\n1\\n6\\n2\\n2\\n4\",\n \"5\\n3\\n1\\n4\\n1\\n9\",\n \"8\\n4\\n4\\n3\\n1\\n2\\n1\\n2\\n2\",\n \"6\\n1\\n1\\n12\\n2\\n2\\n4\",\n \"5\\n3\\n1\\n4\\n1\\n2\",\n \"6\\n2\\n1\\n12\\n2\\n2\\n4\",\n \"5\\n3\\n2\\n4\\n1\\n2\",\n \"6\\n2\\n1\\n12\\n2\\n2\\n1\",\n \"5\\n3\\n2\\n8\\n1\\n2\",\n \"5\\n3\\n2\\n5\\n1\\n2\",\n \"8\\n8\\n4\\n4\\n1\\n1\\n1\\n2\\n2\",\n \"6\\n2\\n1\\n6\\n2\\n2\\n2\",\n \"8\\n5\\n4\\n3\\n1\\n2\\n1\\n2\\n2\",\n \"5\\n3\\n1\\n4\\n1\\n3\",\n \"6\\n4\\n1\\n12\\n2\\n2\\n4\",\n \"5\\n5\\n2\\n4\\n1\\n2\",\n \"6\\n2\\n1\\n12\\n2\\n2\\n2\",\n \"5\\n3\\n2\\n8\\n1\\n1\",\n \"6\\n2\\n1\\n13\\n2\\n2\\n2\",\n \"5\\n3\\n2\\n4\\n2\\n5\",\n \"8\\n5\\n7\\n3\\n1\\n2\\n1\\n2\\n2\",\n \"5\\n2\\n1\\n4\\n1\\n3\",\n \"6\\n3\\n1\\n6\\n2\\n2\\n2\",\n \"6\\n2\\n1\\n1\\n2\\n2\\n2\",\n \"5\\n3\\n3\\n4\\n2\\n5\",\n \"5\\n3\\n1\\n4\\n1\\n1\",\n \"5\\n3\\n4\\n4\\n2\\n5\",\n \"5\\n3\\n4\\n4\\n2\\n10\",\n \"6\\n1\\n1\\n1\\n2\\n3\\n1\",\n \"5\\n3\\n4\\n4\\n2\\n16\",\n \"6\\n1\\n1\\n1\\n1\\n3\\n1\",\n \"5\\n3\\n4\\n4\\n3\\n16\",\n \"6\\n1\\n2\\n1\\n2\\n3\\n1\",\n \"5\\n3\\n8\\n4\\n3\\n16\",\n \"5\\n3\\n8\\n7\\n3\\n16\",\n \"3\\n1\\n3\\n1\",\n \"8\\n4\\n4\\n4\\n1\\n1\\n1\\n1\\n2\",\n \"6\\n1\\n1\\n6\\n2\\n1\\n2\",\n \"5\\n3\\n1\\n3\\n1\\n5\",\n \"8\\n4\\n4\\n2\\n1\\n2\\n1\\n2\\n2\",\n \"6\\n1\\n1\\n7\\n2\\n2\\n2\",\n \"5\\n3\\n1\\n5\\n1\\n9\",\n \"8\\n4\\n1\\n3\\n1\\n2\\n1\\n2\\n2\",\n \"6\\n2\\n1\\n19\\n2\\n2\\n4\",\n \"6\\n2\\n1\\n12\\n2\\n4\\n4\",\n \"5\\n2\\n2\\n8\\n1\\n2\",\n \"8\\n8\\n4\\n4\\n1\\n1\\n1\\n2\\n3\",\n \"6\\n2\\n2\\n6\\n2\\n2\\n2\",\n \"5\\n1\\n1\\n4\\n2\\n5\",\n \"5\\n3\\n1\\n5\\n1\\n1\",\n \"5\\n5\\n3\\n4\\n1\\n2\",\n \"5\\n4\\n2\\n8\\n1\\n1\",\n \"6\\n3\\n1\\n1\\n2\\n2\\n2\",\n \"5\\n3\\n2\\n4\\n2\\n10\",\n \"8\\n5\\n11\\n3\\n1\\n2\\n1\\n2\\n2\",\n \"5\\n2\\n1\\n4\\n1\\n2\",\n \"6\\n2\\n1\\n1\\n2\\n2\\n4\",\n \"5\\n3\\n3\\n5\\n2\\n5\",\n \"5\\n3\\n1\\n3\\n1\\n1\",\n \"6\\n1\\n1\\n1\\n2\\n1\\n1\",\n \"5\\n3\\n3\\n4\\n2\\n16\",\n \"5\\n3\\n4\\n4\\n3\\n32\",\n \"5\\n3\\n8\\n4\\n3\\n24\",\n \"5\\n3\\n8\\n7\\n4\\n16\",\n \"8\\n4\\n1\\n2\\n1\\n2\\n1\\n2\\n2\",\n \"5\\n3\\n1\\n5\\n2\\n9\",\n \"6\\n3\\n1\\n12\\n2\\n4\\n4\",\n \"5\\n4\\n2\\n8\\n1\\n2\",\n \"8\\n8\\n8\\n4\\n1\\n1\\n1\\n2\\n3\",\n \"6\\n2\\n2\\n6\\n2\\n3\\n2\",\n \"5\\n1\\n2\\n4\\n2\\n5\",\n \"5\\n3\\n1\\n5\\n1\\n2\",\n \"5\\n8\\n2\\n8\\n1\\n1\",\n \"6\\n3\\n1\\n2\\n2\\n2\\n2\",\n \"5\\n3\\n2\\n4\\n2\\n8\",\n \"8\\n5\\n11\\n3\\n1\\n2\\n1\\n4\\n2\",\n \"5\\n2\\n2\\n4\\n1\\n2\",\n \"6\\n2\\n1\\n2\\n2\\n2\\n4\",\n \"5\\n3\\n5\\n5\\n2\\n5\",\n \"5\\n5\\n1\\n3\\n1\\n1\",\n \"6\\n1\\n2\\n1\\n1\\n2\\n1\",\n \"5\\n3\\n4\\n4\\n3\\n8\",\n \"5\\n1\\n8\\n7\\n4\\n16\",\n \"3\\n1\\n1\\n2\",\n \"8\\n4\\n1\\n2\\n1\\n4\\n1\\n2\\n2\",\n \"5\\n3\\n1\\n5\\n2\\n14\",\n \"6\\n3\\n2\\n12\\n2\\n4\\n4\",\n \"5\\n4\\n2\\n15\\n1\\n2\",\n \"6\\n2\\n2\\n6\\n2\\n6\\n2\",\n \"5\\n1\\n2\\n4\\n3\\n5\"\n ],\n \"output\": [\n \"2\",\n \"24\",\n \"0\",\n \"0\",\n \"0\\n\",\n \"1\\n\",\n \"2\\n\",\n \"24\\n\",\n \"72\\n\",\n \"120\\n\",\n \"720\\n\",\n \"6\\n\",\n \"18\\n\",\n \"12\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"24\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"120\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"2\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nYou are given a sequence of N integers: A_1,A_2,...,A_N.\n\nFind the number of permutations p_1,p_2,...,p_N of 1,2,...,N that can be changed to A_1,A_2,...,A_N by performing the following operation some number of times (possibly zero), modulo 998244353:\n\n* For each 1\\leq i\\leq N, let q_i=min(p_{i-1},p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.\n\nConstraints\n\n* 1 \\leq N \\leq 3 × 10^5\n* 1 \\leq A_i \\leq N\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1\n:\nA_N\n\n\nOutput\n\nPrint the number of the sequences that satisfy the condition, modulo 998244353.\n\nExamples\n\nInput\n\n3\n1\n2\n1\n\n\nOutput\n\n2\n\n\nInput\n\n5\n3\n1\n4\n1\n5\n\n\nOutput\n\n0\n\n\nInput\n\n8\n4\n4\n4\n1\n1\n1\n2\n2\n\n\nOutput\n\n24\n\n\nInput\n\n6\n1\n1\n6\n2\n2\n2\n\n\nOutput\n\n0\n\n### Input:\n3\n1\n2\n1\n### Output:\n2\n\n### Input:\n8\n4\n4\n4\n1\n1\n1\n2\n2\n### Output:\n24\n\n### Code:\nimport sys\nread = sys.stdin.buffer.read\nreadline = sys.stdin.buffer.readline\nreadlines = sys.stdin.buffer.readlines\nsys.setrecursionlimit(10 ** 7)\n\nfrom operator import itemgetter\n\nMOD = 998244353\n\nN,*A = map(int,read().split())\n\nT = A.count(1)\nif T == 0:\n print(0)\n exit()\nif T == 1:\n answer = 1 if len(set(A)) == N else 0\n print(answer)\n exit()\nif T == N:\n answer = 1\n for n in range(1,N+1):\n answer *= n\n answer %= MOD\n print(answer)\n exit()\n\nn = A.index(1)\nwhile A[n-1] == 1:\n n -= 1\nA = A[n:] + A[:n]\n\n# assert len(A) == N and A[0] == 1 and A[-1] != 1\n\nL = [0] * (N+1)\nR = [-1] * (N+1)\nctr = [0] * (N+1)\nnums = []\nprev = 0\nfor i,x in enumerate(A):\n ctr[x] += 1\n R[x] = i\n if prev != x:\n nums.append(x)\n L[x] = i\n prev = x\n\nif any(y - x + 1 != z for x,y,z in zip(L,R,ctr)):\n print(0)\n exit()\nif any(x > T for x in ctr[2:]):\n print(0)\n exit()\n\nfree = [0] * (N+1) # ある数値を書き込んだ時点で、死亡確定になってるマス数\nanswer = 1\nfor x,y,z in zip(nums,nums[1:],nums[2:]+[1]):\n if x > y < z:\n if ctr[y] != T:\n answer = 0\n break\n elif x < y < z:\n free[y] += ctr[y] - 1\n elif x > y > z:\n free[y] += ctr[y] - 1\n else:\n # x < y > z\n answer *= (T + 1 - ctr[y])\n answer %= MOD\n free[y] += ctr[y] + T - 2\n\nf = 0\nfor n in range(1,N+1):\n if ctr[n] >= 1:\n f += free[n]\n continue\n answer *= f\n answer %= MOD\n f -= 1\n\nprint(answer)"}}},{"rowIdx":688,"cells":{"id":{"kind":"string","value":"p03374 AtCoder Regular Contest 096 - Static Sushi_3244"},"description":{"kind":"string","value":"\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\n\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\n\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\n\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger.\n\nConstraints\n\n* 1 ≤ N ≤ 10^5\n* 2 ≤ C ≤ 10^{14}\n* 1 ≤ x_1 < x_2 < ... < x_N < C\n* 1 ≤ v_i ≤ 10^9\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N\n\n\nOutput\n\nIf Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.\n\nExamples\n\nInput\n\n3 20\n2 80\n9 120\n16 1\n\n\nOutput\n\n191\n\n\nInput\n\n3 20\n2 80\n9 1\n16 120\n\n\nOutput\n\n192\n\n\nInput\n\n1 100000000000000\n50000000000000 1\n\n\nOutput\n\n0\n\n\nInput\n\n15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000\n\n\nOutput\n\n6500000000"},"code":{"kind":"string","value":"N, C = map(int, input().split())\nxv = [[int(i) for i in input().split()] for _ in range(N)]\n\nav = 0\nfa1 = 0\nbv = 0\nfb1 = 0\nfa = []\nfb = []\nga = []\ngb = []\nfor i in range(N):\n ax = xv[i][0]\n av += xv[i][1]\n bx = C - xv[-(i+1)][0]\n bv += xv[-(i+1)][1]\n fa1 = max(fa1, av-ax)\n fa.append(fa1)\n ga.append(av - 2*ax)\n fb1 = max(fb1, bv-bx)\n fb.append(fb1)\n gb.append(bv - 2*bx)\n\np = max(0, fa[-1], fb[-1])\n\nfor i in range(N-1):\n p = max(p, fa[i]+gb[N-i-2], ga[i]+fb[N-i-2])\n\nprint(p)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"15 10000000000\\n400000000 1000000000\\n800000000 1000000000\\n1900000000 1000000000\\n2400000000 1000000000\\n2900000000 1000000000\\n3300000000 1000000000\\n3700000000 1000000000\\n3800000000 1000000000\\n4000000000 1000000000\\n4100000000 1000000000\\n5200000000 1000000000\\n6600000000 1000000000\\n8000000000 1000000000\\n9300000000 1000000000\\n9700000000 1000000000\",\n \"3 20\\n2 80\\n9 120\\n16 1\",\n \"3 20\\n2 80\\n9 1\\n16 120\",\n \"1 100000000000000\\n50000000000000 1\",\n \"3 20\\n2 80\\n5 120\\n16 1\",\n \"3 20\\n2 1\\n9 120\\n16 1\",\n \"3 20\\n0 80\\n9 1\\n16 120\",\n \"1 100100000000000\\n50000000000000 1\",\n \"15 10000000000\\n400000000 1000000000\\n800000000 1000000000\\n1900000000 1000000000\\n2400000000 1000000000\\n2900000000 1000000000\\n3300000000 1000000000\\n3700000000 1000000000\\n3800000000 1000000000\\n4000000000 1000000000\\n4100000000 1000000000\\n5200000000 1000000000\\n6600000000 1000000000\\n8000000000 1000000001\\n9300000000 1000000000\\n9700000000 1000000000\",\n \"3 20\\n4 80\\n9 120\\n16 1\",\n \"3 20\\n2 80\\n8 1\\n16 120\",\n \"3 20\\n2 80\\n8 1\\n16 82\",\n \"3 20\\n2 80\\n9 1\\n20 120\",\n \"3 20\\n4 50\\n9 120\\n16 1\",\n \"3 20\\n2 101\\n8 1\\n16 120\",\n \"3 21\\n2 80\\n8 1\\n16 82\",\n \"3 20\\n2 001\\n8 1\\n16 120\",\n \"3 20\\n2 80\\n3 2\\n20 120\",\n \"3 20\\n2 72\\n8 120\\n16 -1\",\n \"3 20\\n2 80\\n3 2\\n20 114\",\n \"3 20\\n2 72\\n8 188\\n16 -1\",\n \"3 20\\n4 80\\n9 1\\n16 120\",\n \"15 10000000000\\n400000000 1000000000\\n800000000 1000000000\\n1900000000 1000000000\\n2400000000 1000000000\\n2900000000 1000000000\\n3300000000 1000000000\\n3700000000 1000000000\\n3800000000 1000000000\\n4000000000 1000000000\\n4100000000 1000000000\\n5200000000 1000000000\\n6600000000 1000000000\\n8000000000 1000000001\\n9300000000 1000000100\\n9700000000 1000000000\",\n \"3 20\\n4 80\\n9 120\\n29 1\",\n \"3 20\\n2 80\\n9 165\\n16 0\",\n \"3 20\\n3 80\\n9 1\\n20 120\",\n \"3 20\\n2 100\\n8 1\\n16 120\",\n \"3 10\\n2 80\\n9 120\\n16 0\",\n \"3 20\\n2 80\\n3 2\\n8 120\",\n \"3 20\\n2 101\\n8 188\\n16 -1\",\n \"3 20\\n4 80\\n9 17\\n29 1\",\n \"3 20\\n2 80\\n9 327\\n16 0\",\n \"3 20\\n3 66\\n9 120\\n16 1\",\n \"3 20\\n2 101\\n8 316\\n16 -1\",\n \"3 22\\n4 80\\n9 17\\n29 1\",\n \"3 20\\n3 66\\n9 229\\n16 1\",\n \"3 24\\n4 80\\n9 17\\n29 1\",\n \"3 20\\n8 80\\n9 445\\n16 0\",\n \"3 24\\n7 80\\n9 17\\n13 1\",\n \"3 20\\n0 66\\n9 65\\n16 2\",\n \"3 20\\n0 66\\n4 65\\n16 2\",\n \"3 20\\n0 56\\n4 65\\n16 2\",\n \"3 20\\n0 56\\n2 65\\n16 2\",\n \"3 7\\n0 56\\n2 65\\n16 2\",\n \"3 7\\n0 56\\n2 65\\n25 2\",\n \"3 11\\n0 56\\n2 85\\n25 2\",\n \"3 13\\n0 56\\n2 85\\n25 2\",\n \"3 20\\n2 80\\n5 120\\n16 2\",\n \"1 100100000000000\\n50000000000000 2\",\n \"1 100100000100000\\n50000000000000 2\",\n \"1 100100000100000\\n50000000000000 4\",\n \"1 100100000100000\\n46089894256444 4\",\n \"1 100100000100000\\n54080308945825 4\",\n \"1 100100000100000\\n54080308945825 7\",\n \"1 100100000100000\\n97477316051591 7\",\n \"1 100000000000000\\n50000000000000 0\",\n \"1 100100000000000\\n90630560822492 2\",\n \"1 100100000100000\\n50000000000000 1\",\n \"1 100100000100000\\n50000000000000 5\",\n \"1 100100000100000\\n36435423729333 4\",\n \"1 100100010100000\\n54080308945825 4\",\n \"1 100000000000000\\n50000000000000 -1\",\n \"1 100100000000000\\n7505783473189 2\",\n \"1 100100000100010\\n50000000000000 1\",\n \"1 100100000100000\\n50000000000000 8\",\n \"1 100100000100000\\n36435423729333 2\",\n \"1 100100010100000\\n54080308945825 1\",\n \"1 100000000000000\\n50000000000000 -2\",\n \"1 100100000000000\\n7505783473189 4\",\n \"1 100100100100000\\n50000000000000 4\",\n \"1 100100000100000\\n36435423729333 1\",\n \"1 100000000000000\\n2421261197873 -2\",\n \"1 100100000000000\\n7505783473189 8\",\n \"1 100100100100000\\n58327321578744 4\",\n \"1 100100000100000\\n19822786627217 1\",\n \"1 100000000000000\\n1741598310499 -2\",\n \"1 100100000000000\\n7505783473189 3\",\n \"1 100100100100000\\n22913237067823 4\",\n \"1 100000000000000\\n1741598310499 -3\",\n \"1 100100001000000\\n7505783473189 3\",\n \"1 100100100100000\\n41461083252438 4\",\n \"1 100000000000000\\n2678773713496 -3\",\n \"1 100100001000000\\n7505783473189 0\",\n \"1 100000000000000\\n2801735506425 -3\",\n \"1 100100001000000\\n4623623015161 0\",\n \"1 100100001010000\\n4623623015161 0\",\n \"1 100100001110000\\n4623623015161 0\",\n \"1 100100001110000\\n2938818569659 0\",\n \"1 100100011110000\\n2938818569659 0\",\n \"3 20\\n2 80\\n9 120\\n16 0\",\n \"1 100000000100000\\n50000000000000 1\",\n \"1 100100000000000\\n6783797980409 1\",\n \"1 100100000000000\\n54911871768050 2\",\n \"1 100100000100000\\n10677651247468 4\",\n \"1 100100000100000\\n42933082280305 4\",\n \"15 10000000000\\n400000000 1000000000\\n800000000 1000000000\\n1900000000 1000000000\\n2400000000 1000000000\\n2900000000 1000000000\\n3300000000 1000000000\\n3700000000 1000000000\\n3800000000 1000000000\\n4000000000 1000000000\\n4100000000 1000000000\\n5200000000 1000000001\\n6600000000 1000000000\\n8000000000 1000000001\\n9300000000 1000000000\\n9700000000 1000000000\",\n \"1 100000000000000\\n74834431600491 0\",\n \"1 100100000000000\\n21109961939239 2\",\n \"1 100100001100000\\n50000000000000 5\",\n \"1 100100000100000\\n66407103008160 4\",\n \"1 100100010100000\\n56740499990362 4\",\n \"1 100100000000000\\n50000000000000 -1\",\n \"1 100100000000000\\n1198784427126 2\",\n \"1 100000000100010\\n50000000000000 1\"\n ],\n \"output\": [\n \"6500000000\",\n \"191\",\n \"192\",\n \"0\",\n \"195\\n\",\n \"112\\n\",\n \"196\\n\",\n \"0\\n\",\n \"6500000000\\n\",\n \"191\\n\",\n \"192\\n\",\n \"154\\n\",\n \"198\\n\",\n \"161\\n\",\n \"213\\n\",\n \"153\\n\",\n \"116\\n\",\n \"199\\n\",\n \"184\\n\",\n \"193\\n\",\n \"252\\n\",\n \"188\\n\",\n \"6500000100\\n\",\n \"210\\n\",\n \"236\\n\",\n \"197\\n\",\n \"212\\n\",\n \"203\\n\",\n \"194\\n\",\n \"281\\n\",\n \"107\\n\",\n \"398\\n\",\n \"177\\n\",\n \"409\\n\",\n \"103\\n\",\n \"286\\n\",\n \"99\\n\",\n \"516\\n\",\n \"88\\n\",\n \"122\\n\",\n \"127\\n\",\n \"117\\n\",\n \"119\\n\",\n \"139\\n\",\n \"157\\n\",\n \"169\\n\",\n \"165\\n\",\n \"195\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"191\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"6500000000\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\n\"Teishi-zushi\", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.\n\nNakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.\n\nNakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.\n\nWhenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger.\n\nConstraints\n\n* 1 ≤ N ≤ 10^5\n* 2 ≤ C ≤ 10^{14}\n* 1 ≤ x_1 < x_2 < ... < x_N < C\n* 1 ≤ v_i ≤ 10^9\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN C\nx_1 v_1\nx_2 v_2\n:\nx_N v_N\n\n\nOutput\n\nIf Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.\n\nExamples\n\nInput\n\n3 20\n2 80\n9 120\n16 1\n\n\nOutput\n\n191\n\n\nInput\n\n3 20\n2 80\n9 1\n16 120\n\n\nOutput\n\n192\n\n\nInput\n\n1 100000000000000\n50000000000000 1\n\n\nOutput\n\n0\n\n\nInput\n\n15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000\n\n\nOutput\n\n6500000000\n\n### Input:\n15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000\n### Output:\n6500000000\n\n### Input:\n3 20\n2 80\n9 120\n16 1\n### Output:\n191\n\n### Code:\nN, C = map(int, input().split())\nxv = [[int(i) for i in input().split()] for _ in range(N)]\n\nav = 0\nfa1 = 0\nbv = 0\nfb1 = 0\nfa = []\nfb = []\nga = []\ngb = []\nfor i in range(N):\n ax = xv[i][0]\n av += xv[i][1]\n bx = C - xv[-(i+1)][0]\n bv += xv[-(i+1)][1]\n fa1 = max(fa1, av-ax)\n fa.append(fa1)\n ga.append(av - 2*ax)\n fb1 = max(fb1, bv-bx)\n fb.append(fb1)\n gb.append(bv - 2*bx)\n\np = max(0, fa[-1], fb[-1])\n\nfor i in range(N-1):\n p = max(p, fa[i]+gb[N-i-2], ga[i]+fb[N-i-2])\n\nprint(p)\n"}}},{"rowIdx":689,"cells":{"id":{"kind":"string","value":"p03535 CODE FESTIVAL 2017 Final (Parallel) - Time Gap_3248"},"description":{"kind":"string","value":"In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\n\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours. The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours. Here, we are using 24-hour notation. That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\n\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\n\nFind the maximum possible value of s.\n\nConstraints\n\n* 1 \\leq N \\leq 50\n* 0 \\leq D_i \\leq 12\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nD_1 D_2 ... D_N\n\n\nOutput\n\nPrint the maximum possible value of s.\n\nExamples\n\nInput\n\n3\n7 12 8\n\n\nOutput\n\n4\n\n\nInput\n\n2\n11 11\n\n\nOutput\n\n2\n\n\nInput\n\n1\n0\n\n\nOutput\n\n0"},"code":{"kind":"string","value":"N = int(input())\nD = [int(x) for x in input().split()]\nD.append(0)\nD.sort()\nans = []\nfor i in range(N + 1):\n if i % 2 == 0:\n ans.append(D[i])\n else:\n ans.append((24 - D[i]) % 24)\nans.sort()\nprint(min(min(ans[i + 1] - ans[i] for i in range(N)), 24 - ans[-1]))\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"2\\n11 11\",\n \"3\\n7 12 8\",\n \"1\\n0\",\n \"2\\n11 8\",\n \"3\\n7 12 11\",\n \"2\\n8 8\",\n \"2\\n10 2\",\n \"2\\n2 0\",\n \"3\\n9 12 8\",\n \"2\\n6 8\",\n \"2\\n12 8\",\n \"2\\n9 7\",\n \"1\\n11\",\n \"1\\n9\",\n \"1\\n10\",\n \"3\\n8 12 11\",\n \"2\\n8 1\",\n \"2\\n10 1\",\n \"2\\n4 2\",\n \"2\\n8 2\",\n \"2\\n2 1\",\n \"2\\n3 0\",\n \"2\\n8 6\",\n \"3\\n8 12 0\",\n \"2\\n8 0\",\n \"2\\n17 1\",\n \"2\\n10 0\",\n \"2\\n4 1\",\n \"2\\n14 1\",\n \"2\\n2 2\",\n \"2\\n3 1\",\n \"2\\n5 0\",\n \"2\\n6 6\",\n \"2\\n9 1\",\n \"2\\n0 1\",\n \"2\\n15 0\",\n \"2\\n4 0\",\n \"2\\n14 0\",\n \"2\\n4 3\",\n \"2\\n3 2\",\n \"2\\n12 12\",\n \"2\\n6 11\",\n \"2\\n1 1\",\n \"2\\n11 0\",\n \"2\\n6 0\",\n \"2\\n0 3\",\n \"2\\n3 3\",\n \"2\\n3 12\",\n \"2\\n0 0\",\n \"2\\n19 0\",\n \"2\\n0 4\",\n \"2\\n6 3\",\n \"2\\n5 12\",\n \"2\\n17 0\",\n \"2\\n1 4\",\n \"2\\n6 1\",\n \"2\\n12 0\",\n \"2\\n7 0\",\n \"2\\n12 1\",\n \"2\\n7 1\",\n \"2\\n12 2\",\n \"2\\n21 1\",\n \"2\\n11 7\",\n \"3\\n10 12 8\",\n \"2\\n0 8\",\n \"2\\n13 1\",\n \"2\\n16 1\",\n \"2\\n10 4\",\n \"2\\n1 2\",\n \"2\\n1 0\",\n \"2\\n5 1\",\n \"3\\n4 12 8\",\n \"2\\n8 11\",\n \"2\\n9 0\",\n \"2\\n13 0\",\n \"2\\n4 6\",\n \"2\\n11 1\",\n \"2\\n5 2\",\n \"2\\n6 2\",\n \"2\\n1 8\",\n \"2\\n1 6\",\n \"2\\n16 2\",\n \"2\\n2 11\",\n \"2\\n7 2\",\n \"2\\n20 1\",\n \"2\\n0 5\",\n \"2\\n5 3\",\n \"2\\n5 7\",\n \"2\\n0 2\",\n \"2\\n0 6\",\n \"2\\n7 12\",\n \"2\\n1 7\",\n \"2\\n7 3\",\n \"2\\n12 4\",\n \"2\\n0 7\",\n \"2\\n0 15\",\n \"2\\n16 0\",\n \"2\\n5 4\",\n \"2\\n14 2\",\n \"2\\n1 3\",\n \"2\\n2 4\",\n \"2\\n24 0\",\n \"2\\n11 2\"\n ],\n \"output\": [\n \"2\",\n \"4\",\n \"0\",\n \"5\\n\",\n \"1\\n\",\n \"8\\n\",\n \"2\\n\",\n \"0\\n\",\n \"3\\n\",\n \"6\\n\",\n \"4\\n\",\n \"7\\n\",\n \"11\\n\",\n \"9\\n\",\n \"10\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"1\\n\",\n \"0\\n\",\n \"6\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"1\\n\",\n \"0\\n\",\n \"6\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n\",\n \"2\\n\",\n \"0\\n\",\n \"6\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n\",\n \"3\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n\",\n \"5\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"1\\n\",\n \"6\\n\",\n \"2\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"4\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"4\\n\",\n \"5\\n\",\n \"0\\n\",\n \"0\\n\",\n \"4\\n\",\n \"1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"2\\n\",\n \"2\\n\",\n \"1\\n\",\n \"0\\n\",\n \"3\\n\",\n \"5\\n\",\n \"0\\n\",\n \"0\\n\",\n \"5\\n\",\n \"1\\n\",\n \"3\\n\",\n \"4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"4\\n\",\n \"2\\n\",\n \"1\\n\",\n \"2\\n\",\n \"0\\n\",\n \"2\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nIn CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.\n\nTakahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours. The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours. Here, we are using 24-hour notation. That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.\n\nThen, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.\n\nFind the maximum possible value of s.\n\nConstraints\n\n* 1 \\leq N \\leq 50\n* 0 \\leq D_i \\leq 12\n* All input values are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nD_1 D_2 ... D_N\n\n\nOutput\n\nPrint the maximum possible value of s.\n\nExamples\n\nInput\n\n3\n7 12 8\n\n\nOutput\n\n4\n\n\nInput\n\n2\n11 11\n\n\nOutput\n\n2\n\n\nInput\n\n1\n0\n\n\nOutput\n\n0\n\n### Input:\n2\n11 11\n### Output:\n2\n\n### Input:\n3\n7 12 8\n### Output:\n4\n\n### Code:\nN = int(input())\nD = [int(x) for x in input().split()]\nD.append(0)\nD.sort()\nans = []\nfor i in range(N + 1):\n if i % 2 == 0:\n ans.append(D[i])\n else:\n ans.append((24 - D[i]) % 24)\nans.sort()\nprint(min(min(ans[i + 1] - ans[i] for i in range(N)), 24 - ans[-1]))\n"}}},{"rowIdx":690,"cells":{"id":{"kind":"string","value":"p03695 AtCoder Beginner Contest 064 - Colorful Leaderboard_3252"},"description":{"kind":"string","value":"In AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:\n\n* Rating 1-399 : gray\n* Rating 400-799 : brown\n* Rating 800-1199 : green\n* Rating 1200-1599 : cyan\n* Rating 1600-1999 : blue\n* Rating 2000-2399 : yellow\n* Rating 2400-2799 : orange\n* Rating 2800-3199 : red\n\n\n\nOther than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.\nCurrently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.\nFind the minimum and maximum possible numbers of different colors of the users.\n\nConstraints\n\n* 1 ≤ N ≤ 100\n* 1 ≤ a_i ≤ 4800\n* a_i is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\na_1 a_2 ... a_N\n\n\nOutput\n\nPrint the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.\n\nExamples\n\nInput\n\n4\n2100 2500 2700 2700\n\n\nOutput\n\n2 2\n\n\nInput\n\n5\n1100 1900 2800 3200 3200\n\n\nOutput\n\n3 5\n\n\nInput\n\n20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990\n\n\nOutput\n\n1 1"},"code":{"kind":"string","value":"n,a=open(0)\ns=set();x=0\nfor i in map(int,a.split()):\n\tj=i//400\n\tif j<8:s.add(j)\n\telse:x+=1\nprint(max(1,len(s)),len(s)+x)"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4\\n2100 2500 2700 2700\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990\",\n \"5\\n1100 1900 2800 3200 3200\",\n \"4\\n2100 2500 4217 2700\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 1771 920 930 940 950 960 970 980 990\",\n \"5\\n1100 3348 2800 3200 3200\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 1771 920 930 120 950 960 970 980 990\",\n \"5\\n1101 3348 2955 3200 2889\",\n \"5\\n1101 3348 2302 3200 2889\",\n \"4\\n2100 4691 248 409\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 950 960 970 980 990\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 2243 960 970 980 990\",\n \"20\\n800 2108 443 830 840 1093 116 614 398 92 399 1139 1229 646 92 2243 960 970 1914 990\",\n \"20\\n800 990 78 2271 36 2722 116 68 620 99 118 1335 454 486 157 1328 82 1387 1914 573\",\n \"20\\n975 990 000 2271 28 3273 196 38 68 22 118 1335 875 971 3 1328 65 1173 1914 573\",\n \"20\\n975 290 000 3026 28 3273 372 38 48 22 255 1335 875 1250 3 2010 79 1173 1914 573\",\n \"20\\n975 147 000 4828 55 3273 372 38 48 22 255 754 875 1250 3 2010 79 1173 1914 890\",\n \"20\\n975 147 000 4828 55 3273 372 38 9 22 255 754 875 1703 3 2010 79 1173 1914 890\",\n \"4\\n3422 2500 2700 2700\",\n \"20\\n800 2054 820 830 840 850 116 433 398 259 399 1139 920 1007 92 2243 960 970 3670 990\",\n \"20\\n975 990 000 290 28 3273 196 38 68 22 118 1335 875 971 3 1328 65 1173 1914 573\",\n \"20\\n1304 147 010 4828 55 3273 372 3 9 22 255 754 875 3080 0 2010 79 512 1914 427\",\n \"4\\n2100 3371 4217 2127\",\n \"20\\n975 990 000 2271 28 3273 372 53 68 22 118 1335 875 1250 3 3842 79 1173 3241 573\",\n \"20\\n975 147 000 4828 55 3273 372 6 9 22 255 163 875 44 3 2010 79 1173 1914 356\",\n \"5\\n1111 1141 830 1005 946\",\n \"4\\n2100 2500 4217 2612\",\n \"5\\n1100 3348 2800 3200 5007\",\n \"4\\n2100 2500 248 2612\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 1771 920 1028 120 950 960 970 980 990\",\n \"5\\n1100 3348 2955 3200 5007\",\n \"4\\n2100 2500 248 2218\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 1303 920 1028 120 950 960 970 980 990\",\n \"5\\n1101 3348 2955 3200 5007\",\n \"4\\n2100 4691 248 2218\",\n \"20\\n800 810 820 830 840 850 860 870 880 890 900 1303 920 1028 92 950 960 970 980 990\",\n \"4\\n2100 4691 248 3862\",\n \"20\\n800 810 820 830 840 850 860 870 1213 890 900 1303 920 1028 92 950 960 970 980 990\",\n \"20\\n800 1586 820 830 840 850 860 870 1213 890 900 1303 920 1028 92 950 960 970 980 990\",\n \"5\\n1101 3348 2302 1173 2889\",\n \"4\\n2100 3230 248 409\",\n \"20\\n800 1586 820 830 840 850 860 870 1213 259 900 1303 920 1028 92 950 960 970 980 990\",\n \"5\\n1001 3348 2302 1173 2889\",\n \"4\\n2100 3230 248 21\",\n \"5\\n1001 3348 2302 2089 2889\",\n \"4\\n2100 3230 248 26\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 1189 960 970 980 990\",\n \"5\\n1001 831 2302 2089 2889\",\n \"4\\n2100 3992 248 26\",\n \"5\\n1011 831 2302 2089 2889\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1138 920 1028 92 2243 960 970 980 990\",\n \"5\\n1011 1444 2302 2089 2889\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1138 920 1052 92 2243 960 970 980 990\",\n \"5\\n1010 1444 2302 2089 2889\",\n \"20\\n800 1586 820 830 840 850 860 433 1213 259 900 1139 920 1052 92 2243 960 970 980 990\",\n \"5\\n1011 1444 2302 2089 2555\",\n \"20\\n800 1586 820 830 840 850 384 433 1213 259 900 1139 920 1052 92 2243 960 970 980 990\",\n \"5\\n0011 1444 2302 2089 2555\",\n \"20\\n800 1586 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 980 990\",\n \"5\\n0011 1444 2302 2089 1070\",\n \"20\\n800 2054 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 980 990\",\n \"5\\n0011 1444 2302 2089 344\",\n \"20\\n800 2054 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 1357 990\",\n \"5\\n0001 1444 2302 2089 344\",\n \"20\\n800 2054 820 830 840 850 384 433 398 259 900 1139 920 1007 92 2243 960 970 1357 990\",\n \"5\\n0001 1444 2302 2089 194\",\n \"20\\n800 2054 820 830 840 850 116 433 398 259 900 1139 920 1007 92 2243 960 970 1357 990\",\n \"5\\n0001 1444 2302 1373 194\",\n \"20\\n800 2054 820 830 840 850 116 433 398 259 900 1139 920 1007 92 2243 960 970 1914 990\",\n \"5\\n0001 2597 2302 1373 194\",\n \"20\\n800 2054 820 830 840 850 116 433 398 259 399 1139 920 1007 92 2243 960 970 1914 990\",\n \"5\\n0001 2597 2302 1585 194\",\n \"20\\n800 2054 820 830 840 850 116 433 398 92 399 1139 920 1007 92 2243 960 970 1914 990\",\n \"5\\n0001 2396 2302 1585 194\",\n \"20\\n800 2054 820 830 840 850 116 614 398 92 399 1139 920 1007 92 2243 960 970 1914 990\",\n \"5\\n0001 2396 1904 1585 194\",\n \"20\\n800 2054 820 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990\",\n \"5\\n0001 3918 1904 1585 194\",\n \"20\\n800 2108 820 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990\",\n \"5\\n0001 3918 1904 1005 194\",\n \"20\\n800 2108 443 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990\",\n \"5\\n0001 3918 2121 1005 194\",\n \"20\\n800 2108 443 830 840 1093 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990\",\n \"5\\n0001 3918 3916 1005 194\",\n \"20\\n800 2108 443 830 840 1093 116 614 398 92 399 1139 768 646 92 2243 960 970 1914 990\",\n \"5\\n0001 2696 3916 1005 194\",\n \"5\\n0101 2696 3916 1005 194\",\n \"20\\n800 2108 443 830 840 1093 116 614 398 92 399 1139 1229 646 92 2243 96 970 1914 990\",\n \"5\\n0101 2696 3916 1005 379\",\n \"20\\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 96 970 1914 990\",\n \"5\\n1101 2696 3916 1005 379\",\n \"20\\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 174 970 1914 990\",\n \"5\\n1101 1141 3916 1005 379\",\n \"20\\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 174 857 1914 990\",\n \"5\\n1111 1141 3916 1005 379\",\n \"20\\n800 2108 443 830 840 1093 116 614 620 92 399 1139 1229 646 92 2243 174 857 1914 990\",\n \"5\\n1111 1141 3916 1005 185\",\n \"20\\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 857 1914 990\",\n \"20\\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 1254 1914 990\",\n \"20\\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 1254 1914 625\",\n \"20\\n800 2108 443 830 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 625\",\n \"20\\n800 2108 443 1329 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 625\",\n \"20\\n800 2108 443 1329 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 573\"\n ],\n \"output\": [\n \"2 2\",\n \"1 1\",\n \"3 5\",\n \"2 3\\n\",\n \"2 2\\n\",\n \"2 5\\n\",\n \"3 3\\n\",\n \"2 4\\n\",\n \"3 5\\n\",\n \"3 4\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"6 6\\n\",\n \"7 7\\n\",\n \"6 7\\n\",\n \"7 8\\n\",\n \"6 8\\n\",\n \"5 7\\n\",\n \"1 2\\n\",\n \"4 5\\n\",\n \"5 6\\n\",\n \"7 9\\n\",\n \"1 3\\n\",\n \"5 8\\n\",\n \"4 6\\n\",\n \"1 1\\n\",\n \"2 3\\n\",\n \"2 5\\n\",\n \"3 3\\n\",\n \"3 3\\n\",\n \"2 5\\n\",\n \"3 3\\n\",\n \"3 3\\n\",\n \"2 5\\n\",\n \"2 3\\n\",\n \"3 3\\n\",\n \"2 4\\n\",\n \"3 3\\n\",\n \"3 3\\n\",\n \"3 4\\n\",\n \"3 4\\n\",\n \"3 3\\n\",\n \"3 4\\n\",\n \"2 3\\n\",\n \"3 4\\n\",\n \"2 3\\n\",\n \"4 4\\n\",\n \"3 3\\n\",\n \"2 3\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"3 3\\n\",\n \"5 5\\n\",\n \"4 4\\n\",\n \"5 5\\n\",\n \"3 4\\n\",\n \"5 5\\n\",\n \"3 4\\n\",\n \"5 5\\n\",\n \"3 4\\n\",\n \"5 5\\n\",\n \"2 4\\n\",\n \"5 5\\n\",\n \"3 4\\n\",\n \"3 4\\n\",\n \"6 6\\n\",\n \"3 4\\n\",\n \"6 6\\n\",\n \"3 4\\n\",\n \"6 6\\n\",\n \"2 3\\n\",\n \"6 6\\n\",\n \"2 3\\n\",\n \"6 6\\n\",\n \"2 3\\n\",\n \"6 6\\n\",\n \"6 6\\n\",\n \"6 6\\n\",\n \"6 6\\n\",\n \"6 6\\n\",\n \"6 6\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nIn AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:\n\n* Rating 1-399 : gray\n* Rating 400-799 : brown\n* Rating 800-1199 : green\n* Rating 1200-1599 : cyan\n* Rating 1600-1999 : blue\n* Rating 2000-2399 : yellow\n* Rating 2400-2799 : orange\n* Rating 2800-3199 : red\n\n\n\nOther than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.\nCurrently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.\nFind the minimum and maximum possible numbers of different colors of the users.\n\nConstraints\n\n* 1 ≤ N ≤ 100\n* 1 ≤ a_i ≤ 4800\n* a_i is an integer.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\na_1 a_2 ... a_N\n\n\nOutput\n\nPrint the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.\n\nExamples\n\nInput\n\n4\n2100 2500 2700 2700\n\n\nOutput\n\n2 2\n\n\nInput\n\n5\n1100 1900 2800 3200 3200\n\n\nOutput\n\n3 5\n\n\nInput\n\n20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990\n\n\nOutput\n\n1 1\n\n### Input:\n4\n2100 2500 2700 2700\n### Output:\n2 2\n\n### Input:\n20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990\n### Output:\n1 1\n\n### Code:\nn,a=open(0)\ns=set();x=0\nfor i in map(int,a.split()):\n\tj=i//400\n\tif j<8:s.add(j)\n\telse:x+=1\nprint(max(1,len(s)),len(s)+x)"}}},{"rowIdx":691,"cells":{"id":{"kind":"string","value":"p03850 AtCoder Regular Contest 066 - Addition and Subtraction Hard_3256"},"description":{"kind":"string","value":"Joisino has a formula consisting of N terms: A_1 op_1 A_2 ... op_{N-1} A_N. Here, A_i is an integer, and op_i is an binary operator either `+` or `-`. Because Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula. Opening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer. It is allowed to insert any number of parentheses at a position. Your task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\n\nConstraints\n\n* 1≦N≦10^5\n* 1≦A_i≦10^9\n* op_i is either `+` or `-`.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\nA_1 op_1 A_2 ... op_{N-1} A_N\n\n\nOutput\n\nPrint the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\n\nExamples\n\nInput\n\n3\n5 - 1 - 3\n\n\nOutput\n\n7\n\n\nInput\n\n5\n1 - 2 + 3 - 4 + 5\n\n\nOutput\n\n5\n\n\nInput\n\n5\n1 - 20 - 13 + 14 - 5\n\n\nOutput\n\n13"},"code":{"kind":"string","value":"#!/usr/bin/env python3\n\n\ndef solve(n):\n\n s = input()\n sum_a = 0\n sum_n = 0\n sum_np = 0\n min_sum_np = 10 ** 15\n\n j = s.find('-')\n if j < 0:\n return sum(list(map(int, s.split(' + '))))\n\n sum_a = sum(list(map(int, s[:j - 1].split(' + '))))\n j += 2\n s += ' '\n len_s = len(s)\n sign = -1\n w = ''\n while j < len_s:\n ch = s[j]\n j += 1\n if ch == ' ':\n if len(w):\n a = int(w)\n sum_a += a\n w = ''\n if sign < 0:\n sum_n += a\n sum_np = 0\n else:\n sum_np += a\n elif ch == '+':\n sign = 1\n elif ch == '-':\n min_sum_np = min(min_sum_np, sum_n + sum_np)\n sign = -1\n else:\n w += ch\n\n min_sum_np = min(min_sum_np, sum_n + sum_np)\n return sum_a - 2 * min_sum_np\n\n\ndef main():\n n = input()\n n = int(n)\n\n print(solve(n))\n\n\nif __name__ == '__main__':\n main()\n\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"5\\n1 - 2 + 3 - 4 + 5\",\n \"3\\n5 - 1 - 3\",\n \"5\\n1 - 20 - 13 + 14 - 5\",\n \"5\\n1 - 2 + 2 - 4 + 5\",\n \"5\\n1 - 38 - 13 + 14 - 5\",\n \"5\\n1 - 45 - 13 + 14 - 5\",\n \"5\\n2 - 45 - 13 + 14 - 5\",\n \"5\\n2 - 80 - 13 + 14 - 5\",\n \"5\\n2 - 57 - 13 + 14 - 5\",\n \"5\\n2 - 39 - 13 + 9 - 5\",\n \"5\\n1 - 2 + 0 - 4 + 5\",\n \"5\\n1 - 6 - 13 + 14 - 5\",\n \"5\\n2 - 45 - 7 + 14 - 5\",\n \"5\\n2 - 119 - 13 + 14 - 5\",\n \"5\\n2 - 39 - 14 + 14 - 5\",\n \"5\\n2 - 15 - 13 + 9 - 4\",\n \"5\\n1 - 9 - 6 + 14 - 5\",\n \"5\\n1 - 2 + 1 - 4 + 5\",\n \"5\\n1 - 6 - 13 + 14 - 4\",\n \"5\\n2 - 119 - 13 + 19 - 5\",\n \"5\\n2 - 39 - 14 + 14 - 9\",\n \"5\\n1 - 6 - 13 + 4 - 4\",\n \"5\\n1 - 119 - 13 + 19 - 5\",\n \"5\\n1 - 6 - 13 + 4 - 6\",\n \"5\\n1 - 119 - 13 + 19 - 9\",\n \"5\\n2 - 39 - 14 + 3 - 4\",\n \"5\\n1 - 6 - 13 + 6 - 6\",\n \"5\\n2 - 39 - 19 + 5 - 4\",\n \"3\\n5 - 1 - 6\",\n \"5\\n1 - 20 - 22 + 14 - 5\",\n \"5\\n1 - 2 + 2 - 7 + 5\",\n \"5\\n1 - 38 - 10 + 14 - 5\",\n \"5\\n0 - 45 - 13 + 14 - 5\",\n \"5\\n2 - 49 - 13 + 14 - 5\",\n \"5\\n2 - 80 - 13 + 21 - 5\",\n \"5\\n1 - 119 - 13 + 14 - 5\",\n \"5\\n4 - 39 - 14 + 14 - 5\",\n \"5\\n3 - 15 - 13 + 9 - 4\",\n \"5\\n1 - 4 + 1 - 4 + 5\",\n \"5\\n1 - 6 - 24 + 14 - 4\",\n \"5\\n1 - 119 - 13 + 2 - 5\",\n \"5\\n1 - 6 - 13 + 5 - 6\",\n \"5\\n1 - 119 - 13 + 1 - 9\",\n \"5\\n1 - 6 - 13 + 9 - 6\",\n \"3\\n5 - 1 - 8\",\n \"5\\n0 - 45 - 13 + 14 - 0\",\n \"5\\n2 - 159 - 13 + 21 - 5\",\n \"5\\n1 - 119 - 8 + 14 - 5\",\n \"5\\n0 - 4 + 1 - 4 + 5\",\n \"5\\n2 - 119 - 9 + 19 - 5\",\n \"5\\n1 - 119 - 13 + 4 - 5\",\n \"5\\n1 - 6 - 13 + 18 - 6\",\n \"3\\n4 - 1 - 8\",\n \"5\\n1 - 38 - 1 + 14 - 3\",\n \"5\\n0 - 45 - 6 + 14 - 0\",\n \"5\\n0 - 49 - 13 + 24 - 5\",\n \"5\\n0 - 6 - 13 + 18 - 6\",\n \"5\\n0 - 45 - 0 + 14 - 0\",\n \"5\\n0 - 49 - 6 + 24 - 5\",\n \"5\\n2 - 119 - 13 + 6 - 5\",\n \"5\\n1 - 5 - 13 + 18 - 6\",\n \"5\\n0 - 45 - 0 + 3 - 0\",\n \"5\\n1 - 2 + 3 - 4 + 3\",\n \"5\\n0 - 38 - 13 + 14 - 5\",\n \"5\\n1 - 20 - 6 + 14 - 1\",\n \"5\\n2 - 80 - 7 + 14 - 5\",\n \"5\\n2 - 119 - 13 + 9 - 5\",\n \"5\\n2 - 119 - 13 + 30 - 5\",\n \"5\\n1 - 119 - 1 + 19 - 9\",\n \"5\\n2 - 39 - 6 + 3 - 4\",\n \"5\\n1 - 83 - 13 + 14 - 5\",\n \"5\\n2 - 57 - 13 + 17 - 5\",\n \"5\\n1 - 6 - 24 + 14 - 6\",\n \"5\\n2 - 119 - 8 + 19 - 3\",\n \"5\\n1 - 6 - 13 + 14 - 6\",\n \"5\\n2 - 159 - 9 + 21 - 5\",\n \"5\\n2 - 171 - 9 + 19 - 5\",\n \"5\\n1 - 3 - 13 + 18 - 6\",\n \"5\\n1 - 5 - 13 + 18 - 11\",\n \"5\\n2 - 80 - 1 + 14 - 5\",\n \"5\\n2 - 167 - 13 + 9 - 5\",\n \"5\\n3 - 119 - 13 + 30 - 5\",\n \"5\\n2 - 78 - 28 + 14 - 4\",\n \"5\\n1 - 119 - 2 + 19 - 9\",\n \"5\\n2 - 6 - 23 + 5 - 6\",\n \"5\\n1 - 90 - 13 + 14 - 5\",\n \"5\\n0 - 39 - 13 + 0 - 4\",\n \"5\\n1 - 6 - 24 + 22 - 6\",\n \"5\\n2 - 49 - 13 + 39 - 10\",\n \"5\\n1 - 3 - 20 + 18 - 6\",\n \"5\\n2 - 73 - 1 + 14 - 3\",\n \"5\\n0 - 81 - 13 + 24 - 1\",\n \"5\\n2 - 119 - 9 + 11 - 5\",\n \"5\\n0 - 6 - 21 + 32 - 6\",\n \"5\\n2 - 131 - 1 + 14 - 5\",\n \"5\\n1 - 167 - 13 + 9 - 5\",\n \"5\\n2 - 78 - 14 + 14 - 4\",\n \"5\\n2 - 54 - 6 + 3 - 2\",\n \"5\\n1 - 157 - 13 + 14 - 5\",\n \"5\\n0 - 76 - 13 + 0 - 4\",\n \"5\\n1 - 3 - 20 + 18 - 10\",\n \"5\\n0 - 81 - 11 + 24 - 1\",\n \"5\\n0 - 6 - 17 + 32 - 6\"\n ],\n \"output\": [\n \"5\",\n \"7\",\n \"13\",\n \"6\\n\",\n \"-5\\n\",\n \"-12\\n\",\n \"-11\\n\",\n \"-46\\n\",\n \"-23\\n\",\n \"-10\\n\",\n \"8\\n\",\n \"27\\n\",\n \"-17\\n\",\n \"-85\\n\",\n \"-4\\n\",\n \"13\\n\",\n \"17\\n\",\n \"7\\n\",\n \"26\\n\",\n \"-80\\n\",\n \"0\\n\",\n \"16\\n\",\n \"-81\\n\",\n \"18\\n\",\n \"-77\\n\",\n \"-16\\n\",\n \"20\\n\",\n \"-9\\n\",\n \"10\\n\",\n \"22\\n\",\n \"9\\n\",\n \"-8\\n\",\n \"-13\\n\",\n \"-15\\n\",\n \"-39\\n\",\n \"-86\\n\",\n \"-2\\n\",\n \"14\\n\",\n \"5\\n\",\n \"37\\n\",\n \"-98\\n\",\n \"19\\n\",\n \"-95\\n\",\n \"23\\n\",\n \"12\\n\",\n \"-18\\n\",\n \"-118\\n\",\n \"-91\\n\",\n \"4\\n\",\n \"-84\\n\",\n \"-96\\n\",\n \"32\\n\",\n \"11\\n\",\n \"-19\\n\",\n \"-25\\n\",\n \"-7\\n\",\n \"31\\n\",\n \"-31\\n\",\n \"-14\\n\",\n \"-93\\n\",\n \"33\\n\",\n \"-42\\n\",\n \"3\\n\",\n \"-6\\n\",\n \"2\\n\",\n \"-52\\n\",\n \"-90\\n\",\n \"-69\\n\",\n \"-89\\n\",\n \"-24\\n\",\n \"-50\\n\",\n \"-20\\n\",\n \"39\\n\",\n \"-87\\n\",\n \"28\\n\",\n \"-122\\n\",\n \"-136\\n\",\n \"35\\n\",\n \"38\\n\",\n \"-58\\n\",\n \"-138\\n\",\n \"-68\\n\",\n \"-30\\n\",\n \"-88\\n\",\n \"30\\n\",\n \"-57\\n\",\n \"-22\\n\",\n \"47\\n\",\n \"15\\n\",\n \"42\\n\",\n \"-53\\n\",\n \"-43\\n\",\n \"-92\\n\",\n \"53\\n\",\n \"-109\\n\",\n \"-139\\n\",\n \"-44\\n\",\n \"-41\\n\",\n \"-124\\n\",\n \"-59\\n\",\n \"46\\n\",\n \"-45\\n\",\n \"49\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nJoisino has a formula consisting of N terms: A_1 op_1 A_2 ... op_{N-1} A_N. Here, A_i is an integer, and op_i is an binary operator either `+` or `-`. Because Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula. Opening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer. It is allowed to insert any number of parentheses at a position. Your task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\n\nConstraints\n\n* 1≦N≦10^5\n* 1≦A_i≦10^9\n* op_i is either `+` or `-`.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\nA_1 op_1 A_2 ... op_{N-1} A_N\n\n\nOutput\n\nPrint the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.\n\nExamples\n\nInput\n\n3\n5 - 1 - 3\n\n\nOutput\n\n7\n\n\nInput\n\n5\n1 - 2 + 3 - 4 + 5\n\n\nOutput\n\n5\n\n\nInput\n\n5\n1 - 20 - 13 + 14 - 5\n\n\nOutput\n\n13\n\n### Input:\n5\n1 - 2 + 3 - 4 + 5\n### Output:\n5\n\n### Input:\n3\n5 - 1 - 3\n### Output:\n7\n\n### Code:\n#!/usr/bin/env python3\n\n\ndef solve(n):\n\n s = input()\n sum_a = 0\n sum_n = 0\n sum_np = 0\n min_sum_np = 10 ** 15\n\n j = s.find('-')\n if j < 0:\n return sum(list(map(int, s.split(' + '))))\n\n sum_a = sum(list(map(int, s[:j - 1].split(' + '))))\n j += 2\n s += ' '\n len_s = len(s)\n sign = -1\n w = ''\n while j < len_s:\n ch = s[j]\n j += 1\n if ch == ' ':\n if len(w):\n a = int(w)\n sum_a += a\n w = ''\n if sign < 0:\n sum_n += a\n sum_np = 0\n else:\n sum_np += a\n elif ch == '+':\n sign = 1\n elif ch == '-':\n min_sum_np = min(min_sum_np, sum_n + sum_np)\n sign = -1\n else:\n w += ch\n\n min_sum_np = min(min_sum_np, sum_n + sum_np)\n return sum_a - 2 * min_sum_np\n\n\ndef main():\n n = input()\n n = int(n)\n\n print(solve(n))\n\n\nif __name__ == '__main__':\n main()\n\n"}}},{"rowIdx":692,"cells":{"id":{"kind":"string","value":"p04017 AtCoder Regular Contest 060 - Tak and Hotels_3260"},"description":{"kind":"string","value":"N hotels are located on a straight line. The coordinate of the i-th hotel (1 \\leq i \\leq N) is x_i.\n\nTak the traveler has the following two personal principles:\n\n* He never travels a distance of more than L in a single day.\n* He never sleeps in the open. That is, he must stay at a hotel at the end of a day.\n\n\n\nYou are given Q queries. The j-th (1 \\leq j \\leq Q) query is described by two distinct integers a_j and b_j. For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles. It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.\n\nConstraints\n\n* 2 \\leq N \\leq 10^5\n* 1 \\leq L \\leq 10^9\n* 1 \\leq Q \\leq 10^5\n* 1 \\leq x_i < x_2 < ... < x_N \\leq 10^9\n* x_{i+1} - x_i \\leq L\n* 1 \\leq a_j,b_j \\leq N\n* a_j \\neq b_j\n* N,\\,L,\\,Q,\\,x_i,\\,a_j,\\,b_j are integers.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\nx_1 x_2 ... x_N\nL\nQ\na_1 b_1\na_2 b_2\n:\na_Q b_Q\n\n\nOutput\n\nPrint Q lines. The j-th line (1 \\leq j \\leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.\n\nExample\n\nInput\n\n9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5\n\n\nOutput\n\n4\n2\n1\n2"},"code":{"kind":"string","value":"import bisect\n\nN = int(input())\nx = list(map(int, input().split()))\nL = int(input())\n\ndest = []\ndest_1 = [0] * N\nfor i in range(N):\n dest_1[i] = bisect.bisect_left(x, x[i] + L + 0.5) - 1\ndest.append(dest_1)\nfor i in range(1, len(bin(N - 1)) - 1):\n dest_prev = dest[i - 1]\n dest_i = [0] * N\n for j in range(N):\n dest_i[j] = dest_prev[dest_prev[j]]\n dest.append(dest_i)\n\nQ = int(input())\nfor _ in range(Q):\n a, b = map(int, input().split())\n a -= 1\n b -= 1\n if a > b:\n a, b = b, a\n k = len(dest) - 1\n ans = 0\n while True:\n d = dest[k][a]\n if d >= b:\n if k > 0:\n k -= 1\n else:\n ans += 1\n break\n else:\n ans += 2 ** k\n a = d\n print(ans)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"9\\n1 3 6 13 15 18 19 29 31\\n10\\n4\\n1 8\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 15 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 6 6 13 23 18 19 29 31\\n10\\n3\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 5\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 9\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 3\\n9 7\\n8 7\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n8 7\",\n \"9\\n1 6 6 13 23 18 27 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n3\\n1 9\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 58\\n10\\n2\\n1 2\\n7 5\\n6 7\\n8 5\",\n \"9\\n1 7 6 13 23 18 19 29 31\\n18\\n3\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 3\\n1 5\\n9 7\\n8 1\",\n \"9\\n1 3 6 13 15 13 19 29 31\\n10\\n2\\n2 8\\n9 3\\n1 7\\n8 5\",\n \"9\\n1 3 6 13 15 18 19 29 40\\n10\\n3\\n1 6\\n7 3\\n6 3\\n8 5\",\n \"9\\n1 3 6 13 15 18 19 29 40\\n10\\n3\\n2 6\\n7 3\\n6 3\\n8 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n2\\n1 9\\n7 6\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 15 18 19 29 31\\n10\\n4\\n1 8\\n7 3\\n6 7\\n8 3\",\n \"9\\n1 3 5 15 23 18 19 29 31\\n10\\n1\\n1 8\\n7 3\\n9 7\\n8 5\",\n \"9\\n1 7 6 13 23 18 19 29 31\\n10\\n3\\n1 8\\n7 3\\n6 1\\n8 10\",\n \"9\\n1 8 6 13 23 18 19 22 31\\n10\\n3\\n1 8\\n7 3\\n6 7\\n5 10\",\n \"9\\n1 1 6 13 15 13 19 29 31\\n10\\n2\\n2 8\\n9 3\\n1 7\\n8 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n1\\n1 9\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n17\\n2\\n1 8\\n1 3\\n2 7\\n8 7\",\n \"9\\n0 3 1 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n6 7\",\n \"9\\n1 7 6 13 23 18 19 29 31\\n10\\n3\\n2 8\\n7 3\\n6 1\\n8 10\",\n \"9\\n1 7 6 13 23 18 19 29 31\\n18\\n3\\n1 2\\n1 3\\n6 7\\n8 10\",\n \"9\\n1 6 6 24 15 15 19 29 31\\n10\\n2\\n2 8\\n8 3\\n1 2\\n5 5\",\n \"9\\n1 6 6 24 7 15 19 29 31\\n10\\n3\\n2 8\\n8 3\\n1 2\\n5 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n4\\n1 8\\n1 5\\n9 7\\n8 7\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 4\\n7 3\\n1 2\\n5 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n3\\n1 9\\n2 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n4\\n1 9\\n7 6\\n6 7\\n8 5\",\n \"9\\n1 3 10 13 15 18 19 29 40\\n10\\n3\\n2 6\\n7 2\\n6 3\\n8 5\",\n \"9\\n1 3 6 13 15 18 19 29 31\\n10\\n3\\n1 8\\n7 5\\n6 7\\n8 3\",\n \"9\\n1 4 6 20 15 18 22 60 40\\n10\\n1\\n1 6\\n5 4\\n6 4\\n1 1\",\n \"9\\n2 5 6 13 23 34 29 39 48\\n18\\n3\\n1 2\\n2 6\\n6 7\\n1 10\",\n \"9\\n0 3 4 13 5 18 17 27 55\\n21\\n1\\n1 4\\n1 8\\n9 4\\n22 10\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n1\\n1 4\\n7 3\\n1 2\\n5 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n4\\n1 9\\n7 6\\n6 7\\n8 1\",\n \"9\\n1 3 4 13 7 18 36 29 55\\n12\\n2\\n1 6\\n1 7\\n9 4\\n15 11\",\n \"9\\n1 2 7 13 14 23 19 29 31\\n10\\n4\\n1 8\\n7 3\\n3 7\\n8 5\",\n \"9\\n2 5 6 13 23 18 27 29 31\\n18\\n3\\n1 2\\n2 5\\n2 7\\n1 10\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n16\\n3\\n1 9\\n7 6\\n6 7\\n8 1\",\n \"9\\n1 3 6 13 23 18 23 31 31\\n10\\n3\\n1 9\\n6 1\\n6 7\\n22 11\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n9 7\\n8 5\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 15 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n9 7\\n8 5\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 7\\n8 5\",\n \"9\\n1 6 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 5 15 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n9 7\\n8 5\",\n \"9\\n1 3 7 13 15 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n9 7\\n8 7\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n2 7\\n8 5\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 2\\n8 5\",\n \"9\\n1 8 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 58\\n10\\n2\\n1 8\\n7 5\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n1 3\\n9 7\\n8 7\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n6 7\\n8 10\",\n \"9\\n1 8 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n14 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n6 7\\n16 10\",\n \"9\\n1 8 6 13 23 18 19 29 42\\n10\\n2\\n1 8\\n7 3\\n6 7\\n14 10\",\n \"9\\n1 3 6 13 23 18 19 29 30\\n10\\n2\\n1 9\\n7 2\\n6 7\\n16 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n6 7\",\n \"9\\n1 3 4 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n6 7\",\n \"9\\n1 3 6 13 15 18 19 29 31\\n10\\n2\\n1 6\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n2 7\\n8 5\",\n \"9\\n1 3 6 13 15 13 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 7\\n8 5\",\n \"9\\n1 7 6 13 23 18 19 29 31\\n10\\n3\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 7 13 15 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n3 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 5\\n6 11\\n8 5\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 2\\n5 5\",\n \"9\\n1 8 6 13 23 18 19 22 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n10 7\\n8 10\",\n \"9\\n1 3 6 13 13 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n6 7\\n16 10\",\n \"9\\n1 8 6 13 23 18 19 29 42\\n10\\n2\\n1 8\\n7 3\\n0 7\\n14 10\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n8 1\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n12\\n2\\n1 8\\n2 5\\n9 7\\n6 7\",\n \"9\\n1 3 4 13 23 18 19 29 31\\n12\\n2\\n1 8\\n1 5\\n9 7\\n8 7\",\n \"9\\n1 3 6 13 15 18 19 29 40\\n10\\n2\\n1 6\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 15 13 19 29 31\\n10\\n2\\n2 8\\n7 3\\n1 7\\n8 5\",\n \"9\\n1 6 6 13 23 18 27 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 19\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n3\\n1 9\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 8 6 13 23 18 19 22 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n5 10\",\n \"9\\n1 3 0 13 23 18 19 29 58\\n10\\n2\\n1 2\\n7 5\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n10 2\\n8 10\",\n \"9\\n1 3 6 13 13 18 19 29 31\\n10\\n2\\n1 9\\n7 2\\n12 7\\n16 10\",\n \"9\\n1 8 6 13 23 18 19 29 42\\n10\\n2\\n1 8\\n7 3\\n0 2\\n14 10\",\n \"9\\n1 3 6 13 15 18 19 29 40\\n10\\n2\\n1 6\\n7 3\\n6 3\\n8 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n3\\n1 9\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 6 13 23 19 19 29 31\\n10\\n2\\n1 9\\n7 3\\n6 7\\n8 5\",\n \"9\\n1 3 10 13 15 18 19 29 40\\n10\\n3\\n2 6\\n7 3\\n6 3\\n8 5\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 10\\n8 5\",\n \"9\\n2 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 7\\n8 10\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 7\\n8 1\",\n \"9\\n1 3 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n9 10\\n8 7\",\n \"9\\n1 3 6 13 15 15 19 29 31\\n10\\n2\\n1 8\\n4 3\\n2 7\\n8 5\",\n \"9\\n1 3 6 6 15 15 19 29 31\\n10\\n2\\n1 8\\n7 3\\n1 2\\n8 5\",\n \"9\\n1 8 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n7 3\\n6 14\\n8 10\",\n \"9\\n1 1 6 13 23 18 19 29 31\\n10\\n2\\n1 8\\n1 3\\n9 7\\n8 7\"\n ],\n \"output\": [\n \"4\\n2\\n1\\n2\",\n \"4\\n2\\n\",\n \"4\\n2\\n1\\n\",\n \"4\\n1\\n\",\n \"5\\n2\\n\",\n \"3\\n1\\n\",\n \"3\\n2\\n\",\n \"5\\n3\\n\",\n \"5\\n2\\n1\\n\",\n \"1\\n1\\n\",\n \"2\\n1\\n1\\n\",\n \"1\\n2\\n\",\n \"3\\n4\\n\",\n \"3\\n2\\n2\\n\",\n \"2\\n2\\n2\\n\",\n \"5\\n1\\n\",\n \"4\\n2\\n1\\n3\\n\",\n \"4\\n\",\n \"4\\n2\\n3\\n\",\n \"3\\n2\\n1\\n\",\n \"4\\n4\\n\",\n \"5\\n\",\n \"2\\n1\\n\",\n \"4\\n3\\n\",\n \"3\\n2\\n3\\n\",\n \"1\\n1\\n1\\n\",\n \"3\\n3\\n\",\n \"3\\n3\\n1\\n\",\n \"3\\n2\\n1\\n1\\n\",\n \"2\\n2\\n\",\n \"5\\n1\\n1\\n\",\n \"5\\n1\\n1\\n1\\n\",\n \"2\\n2\\n1\\n\",\n \"4\\n1\\n1\\n\",\n \"3\\n\",\n \"1\\n2\\n1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"5\\n1\\n1\\n4\\n\",\n \"2\\n3\\n\",\n \"4\\n2\\n2\\n2\\n\",\n \"1\\n1\\n2\\n\",\n \"3\\n1\\n1\\n\",\n \"4\\n3\\n1\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n1\\n\",\n \"4\\n1\\n\",\n \"5\\n2\\n\",\n \"4\\n2\\n\",\n \"5\\n2\\n\",\n \"4\\n2\\n\",\n \"5\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n1\\n\",\n \"4\\n2\\n\",\n \"4\\n1\\n\",\n \"4\\n2\\n\",\n \"3\\n2\\n\",\n \"5\\n2\\n\",\n \"5\\n2\\n\",\n \"4\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"3\\n2\\n\",\n \"5\\n3\\n\",\n \"5\\n2\\n1\\n\",\n \"3\\n2\\n\",\n \"1\\n1\\n\",\n \"5\\n2\\n\",\n \"5\\n2\\n\",\n \"4\\n2\\n\",\n \"3\\n2\\n\",\n \"5\\n2\\n1\\n\",\n \"5\\n2\\n\",\n \"2\\n1\\n1\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n1\\n\",\n \"4\\n2\\n\",\n \"4\\n2\\n\",\n \"4\\n1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"5","name":"ATCODER"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nN hotels are located on a straight line. The coordinate of the i-th hotel (1 \\leq i \\leq N) is x_i.\n\nTak the traveler has the following two personal principles:\n\n* He never travels a distance of more than L in a single day.\n* He never sleeps in the open. That is, he must stay at a hotel at the end of a day.\n\n\n\nYou are given Q queries. The j-th (1 \\leq j \\leq Q) query is described by two distinct integers a_j and b_j. For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles. It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.\n\nConstraints\n\n* 2 \\leq N \\leq 10^5\n* 1 \\leq L \\leq 10^9\n* 1 \\leq Q \\leq 10^5\n* 1 \\leq x_i < x_2 < ... < x_N \\leq 10^9\n* x_{i+1} - x_i \\leq L\n* 1 \\leq a_j,b_j \\leq N\n* a_j \\neq b_j\n* N,\\,L,\\,Q,\\,x_i,\\,a_j,\\,b_j are integers.\n\nInput\n\nThe input is given from Standard Input in the following format:\n\n\nN\nx_1 x_2 ... x_N\nL\nQ\na_1 b_1\na_2 b_2\n:\na_Q b_Q\n\n\nOutput\n\nPrint Q lines. The j-th line (1 \\leq j \\leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.\n\nExample\n\nInput\n\n9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5\n\n\nOutput\n\n4\n2\n1\n2\n\n### Input:\n9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5\n### Output:\n4\n2\n1\n2\n\n### Input:\n9\n1 3 6 13 15 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 5\n### Output:\n4\n2\n\n\n### Code:\nimport bisect\n\nN = int(input())\nx = list(map(int, input().split()))\nL = int(input())\n\ndest = []\ndest_1 = [0] * N\nfor i in range(N):\n dest_1[i] = bisect.bisect_left(x, x[i] + L + 0.5) - 1\ndest.append(dest_1)\nfor i in range(1, len(bin(N - 1)) - 1):\n dest_prev = dest[i - 1]\n dest_i = [0] * N\n for j in range(N):\n dest_i[j] = dest_prev[dest_prev[j]]\n dest.append(dest_i)\n\nQ = int(input())\nfor _ in range(Q):\n a, b = map(int, input().split())\n a -= 1\n b -= 1\n if a > b:\n a, b = b, a\n k = len(dest) - 1\n ans = 0\n while True:\n d = dest[k][a]\n if d >= b:\n if k > 0:\n k -= 1\n else:\n ans += 1\n break\n else:\n ans += 2 ** k\n a = d\n print(ans)\n"}}},{"rowIdx":693,"cells":{"id":{"kind":"string","value":"p00101 Aizu PR_3264"},"description":{"kind":"string","value":"An English booklet has been created for publicizing Aizu to the world. When you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says \"Hoshino\" not \"Hoshina\".\n\nYour task is to write a program which replace all the words \"Hoshino\" with \"Hoshina\". You can assume that the number of characters in a text is less than or equal to 1000.\n\n\n\nInput\n\nThe input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.\n\nOutput\n\nFor each dataset, print the converted texts in a line.\n\nExample\n\nInput\n\n3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n\n\nOutput\n\nHoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa."},"code":{"kind":"string","value":"[print(input().replace(\"Hoshino\",\"Hoshina\")) for i in range(int(input()))]\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3\\nHoshino\\nHashino\\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\",\n \"3\\nHoshimo\\nHashino\\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\",\n \"3\\nHoshimo\\nHashino\\nMasayuki Hoshino was the grandspn of Ieyasu Tokugawa.\",\n \"3\\nHoshimo\\nHashino\\nMasayuki Hoshino was the grandspn of ueyasI Tokugawa.\",\n \"3\\nHoshimo\\nHashino\\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\",\n \"3\\nHoshimo\\nHashoni\\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\",\n \"3\\nHoshimo\\nHashoni\\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\",\n \"3\\nHmshioo\\nHashoni\\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\",\n \"3\\nHmshioo\\nHashoni\\nMasayuki omihsoH was the grandspn of uezasI Tokugawa.\",\n \"3\\nHmshioo\\nHashoni\\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn of uezasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn fo uezasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn fo ufzasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\",\n \"3\\nHmshjoo\\ninohsaH\\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\",\n \"3\\nHmshjoo\\ninohsaH\\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH Tokugawa.\",\n \"3\\nHmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\",\n \"3\\nImshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\",\n \"3\\nImshjoo\\nHashoni\\nikuy`saM onihsoH taw the grandspn fo ufzasH .awagukoT\",\n \"3\\nImshjoo\\nHashoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\",\n \"3\\nImshjoo\\nhasHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\",\n \"3\\nImshjoo\\nhatHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\",\n \"3\\nImshjoo\\nhatHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazG .awagukoT\",\n \"3\\nImshjoo\\nhatHoni\\nMas`yuki onihsoH taw the grandspn fo ufsazG .awagukoT\",\n \"3\\nImshjoo\\nhatHoni\\nMas`yuki onihsoH taw the grandspn fo ufsazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`yuki onohsiH taw the grandspn fo ufsazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`yukj onohsiH taw the grandspn fo ufsazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH taw the grandspn fo ufsazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo ufsazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaguTok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugok\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugpk\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH vat the grandspn fo uesazG .awaTugpk\",\n \"3\\nImshjoo\\nhatHoni\\nMas`ykuj onohsiH vat eht grandspn fo uesazG .awaTugpk\",\n \"3\\nImshjoo\\nhatHoni\\nMasaykuj onohsiH vat the grandspn fo uesazG .awaTugpk\",\n \"3\\nImshjoo\\nhatHoni\\nMasaykuj onohsiH vat the gr`ndspn fo uesazG .awaTugpk\",\n \"3\\nImshjoo\\nhatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\",\n \"3\\nImshioo\\nhatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\",\n \"3\\nImshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\",\n \"3\\nImshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo ufsazG .awaTugpk\",\n \"3\\nImshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspo fo ufsazG .awaTugpk\",\n \"3\\nImshioo\\niatHoni\\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\",\n \"3\\nImsiioo\\niatHoni\\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\",\n \"3\\nImsiioo\\niatHoni\\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\",\n \"3\\nImsiino\\niatHoni\\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\",\n \"3\\nImsiino\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\",\n \"3\\nImsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\",\n \"3\\nImsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTugpk\",\n \"3\\nImsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\",\n \"3\\nImsiinp\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\",\n \"3\\nImsiinp\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\",\n \"3\\npniismI\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\",\n \"3\\npniismI\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\",\n \"3\\npniismI\\ninoHtai\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\",\n \"3\\nImsiinp\\ninoHtai\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\",\n \"3\\nImsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo fn uftazG kpugTawa.\",\n \"3\\nImsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo nf uftazG kpugTawa.\",\n \"3\\nImsiinp\\ninoHtai\\njukyasaM onohsiI vta huf gr`ncspo nf uftazG kpugTawa.\",\n \"3\\nImsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\",\n \"3\\nImsiinp\\ntnoHiai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\",\n \"3\\nImsiinp\\ntnoHiai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\",\n \"3\\nImsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\",\n \"3\\nImsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr`ncspo fn uftaGz .awaTgupk\",\n \"3\\nImsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn uftaGz .awaTgupk\",\n \"3\\nImsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI wta htf gr_ncspo fn ugtaGz .awaTgupk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgupk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgvpk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpk\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo nf ugtaGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo nf ugatGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaTgvpl\",\n \"3\\npniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg gr_ncspo me ugatGz .awaSgvpl\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg me ugatGz .awaSgvpl\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpl\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg nf ugatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg fn ugatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `tw htg ppscn_rg fn ugatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `uw htg ppscn_rg fn ugatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nitkyasaM onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohsiI `vw htg ppscn_rg fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohsiI `vw htg gr_ncspp fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohsiI v`w htg gr_ncspp fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz .awaSgvpm\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz mpvgSawa.\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\",\n \"3\\npniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp nf zGtagv mpvgSawa.\",\n \"3\\npniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\",\n \"3\\npniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGatgv mpvgSawa.\",\n \"3\\npniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp nf zGatgv mpvgSawa.\"\n ],\n \"output\": [\n \"Hoshina\\nHashino\\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\",\n \"Hoshimo\\nHashino\\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\\n\",\n \"Hoshimo\\nHashino\\nMasayuki Hoshina was the grandspn of Ieyasu Tokugawa.\\n\",\n \"Hoshimo\\nHashino\\nMasayuki Hoshina was the grandspn of ueyasI Tokugawa.\\n\",\n \"Hoshimo\\nHashino\\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\\n\",\n \"Hoshimo\\nHashoni\\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\\n\",\n \"Hoshimo\\nHashoni\\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\\n\",\n \"Hmshioo\\nHashoni\\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\\n\",\n \"Hmshioo\\nHashoni\\nMasayuki omihsoH was the grandspn of uezasI Tokugawa.\\n\",\n \"Hmshioo\\nHashoni\\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn of uezasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn fo uezasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nMas`yuki omihsoH saw the grandspn fo ufzasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\\n\",\n \"Hmshjoo\\ninohsaH\\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\\n\",\n \"Hmshjoo\\ninohsaH\\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH Tokugawa.\\n\",\n \"Hmshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\\n\",\n \"Imshjoo\\nHashoni\\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\\n\",\n \"Imshjoo\\nHashoni\\nikuy`saM onihsoH taw the grandspn fo ufzasH .awagukoT\\n\",\n \"Imshjoo\\nHashoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\\n\",\n \"Imshjoo\\nhasHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\\n\",\n \"Imshjoo\\nhatHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\\n\",\n \"Imshjoo\\nhatHoni\\nikuy`saM onihsoH taw the grandspn fo ufsazG .awagukoT\\n\",\n \"Imshjoo\\nhatHoni\\nMas`yuki onihsoH taw the grandspn fo ufsazG .awagukoT\\n\",\n \"Imshjoo\\nhatHoni\\nMas`yuki onihsoH taw the grandspn fo ufsazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`yuki onohsiH taw the grandspn fo ufsazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`yukj onohsiH taw the grandspn fo ufsazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH taw the grandspn fo ufsazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo ufsazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaguTok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugok\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugpk\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH vat the grandspn fo uesazG .awaTugpk\\n\",\n \"Imshjoo\\nhatHoni\\nMas`ykuj onohsiH vat eht grandspn fo uesazG .awaTugpk\\n\",\n \"Imshjoo\\nhatHoni\\nMasaykuj onohsiH vat the grandspn fo uesazG .awaTugpk\\n\",\n \"Imshjoo\\nhatHoni\\nMasaykuj onohsiH vat the gr`ndspn fo uesazG .awaTugpk\\n\",\n \"Imshjoo\\nhatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\\n\",\n \"Imshioo\\nhatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\\n\",\n \"Imshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\\n\",\n \"Imshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspn fo ufsazG .awaTugpk\\n\",\n \"Imshioo\\niatHoni\\nMasaykuj onohsiH vat thf gr`ndspo fo ufsazG .awaTugpk\\n\",\n \"Imshioo\\niatHoni\\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\\n\",\n \"Imsiioo\\niatHoni\\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\\n\",\n \"Imsiioo\\niatHoni\\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\\n\",\n \"Imsiino\\niatHoni\\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\\n\",\n \"Imsiino\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\\n\",\n \"Imsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\\n\",\n \"Imsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTugpk\\n\",\n \"Imsiinp\\niatHoni\\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\\n\",\n \"Imsiinp\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\\n\",\n \"Imsiinp\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\\n\",\n \"pniismI\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\\n\",\n \"pniismI\\niatHoni\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\\n\",\n \"pniismI\\ninoHtai\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\\n\",\n \"Imsiinp\\ninoHtai\\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\\n\",\n \"Imsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo fn uftazG kpugTawa.\\n\",\n \"Imsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo nf uftazG kpugTawa.\\n\",\n \"Imsiinp\\ninoHtai\\njukyasaM onohsiI vta huf gr`ncspo nf uftazG kpugTawa.\\n\",\n \"Imsiinp\\ninoHtai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\\n\",\n \"Imsiinp\\ntnoHiai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\\n\",\n \"Imsiinp\\ntnoHiai\\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\\n\",\n \"Imsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\\n\",\n \"Imsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr`ncspo fn uftaGz .awaTgupk\\n\",\n \"Imsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn uftaGz .awaTgupk\\n\",\n \"Imsiinp\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI wta htf gr_ncspo fn ugtaGz .awaTgupk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgupk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgvpk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpk\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo nf ugtaGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo nf ugatGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\niukyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaTgvpl\\n\",\n \"pniismI\\ntnoHiai\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg gr_ncspo me ugatGz .awaSgvpl\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg me ugatGz .awaSgvpl\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpl\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg nf ugatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg opscn_rg fn ugatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `tw htg ppscn_rg fn ugatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `uw htg ppscn_rg fn ugatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nitkyasaM onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohsiI `vw htg ppscn_rg fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohsiI `vw htg gr_ncspp fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohsiI v`w htg gr_ncspp fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz .awaSgvpm\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz mpvgSawa.\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\\n\",\n \"pniismI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp nf zGtagv mpvgSawa.\\n\",\n \"pniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\\n\",\n \"pniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp fn zGatgv mpvgSawa.\\n\",\n \"pniisnI\\ntioHian\\nMasaykti onohisI v`w htg gr_ncspp nf zGatgv mpvgSawa.\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nAn English booklet has been created for publicizing Aizu to the world. When you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says \"Hoshino\" not \"Hoshina\".\n\nYour task is to write a program which replace all the words \"Hoshino\" with \"Hoshina\". You can assume that the number of characters in a text is less than or equal to 1000.\n\n\n\nInput\n\nThe input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.\n\nOutput\n\nFor each dataset, print the converted texts in a line.\n\nExample\n\nInput\n\n3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n\n\nOutput\n\nHoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\n\n### Input:\n3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n### Output:\nHoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\n\n### Input:\n3\nHoshimo\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.\n### Output:\nHoshimo\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\n\n\n### Code:\n[print(input().replace(\"Hoshino\",\"Hoshina\")) for i in range(int(input()))]\n"}}},{"rowIdx":694,"cells":{"id":{"kind":"string","value":"p00234 Aizu Buried Treasure_3267"},"description":{"kind":"string","value":"Aizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost.\n\nThe state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation:\n\n1. A cell filled with soil. There is a fixed cost for each cell to dig.\n2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen.\n\n\n\nOnly left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up.\n\nYou must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded.\n\nCreate a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output \"NA\".\n\n\n\n\n\nInput\n\nA sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format.\n\n\nW H\nf m o\nc1,1 c2,1 ... cW,1\nc1,2 c2,2 ... cW,2\n...\nc1, H c2, H ... cW, H\n\n\nThe horizontal size W of the formation and the vertical size H (3 ≤ W, H ≤ 10) are given in the first line. The second line is the integer f (1 ≤ f ≤ 10000) that represents your excavation cost, the integer m (3 ≤ m ≤ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≤ m) is given.\n\nThe following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format:\nIf the value is negative, the cell is full of soil and the value represents the cost.\nIf the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen.\nHowever, there are no more than 50 cells in which oxygen has accumulated.\n\nThe number of datasets does not exceed 50.\n\nOutput\n\nPrint the minimum cost or NA on one line for each dataset.\n\nExample\n\nInput\n\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0\n\n\nOutput\n\n60\n80\nNA\n50\n390"},"code":{"kind":"string","value":"import sys\nsys.setrecursionlimit(1000000)\nINF = 10 ** 20\n\ndef update_state(state, newx):\n tmp = list(state)\n tmp[newx] = 1\n return tuple(tmp)\n\ndef get_co(x, y):\n dc = do = 0\n score = mp[y][x]\n if score < 0:\n dc = -score\n else:\n do = score\n return dc, do\n\ndef minimum_cost(x, y, state, ox, goal, dic, w, m):\n if (x, y, state, ox) in dic:\n return dic[(x, y, state, ox)]\n if y == goal:\n return 0\n if ox <= 1:\n return INF\n \n ret = INF\n \n if x >= 1:\n if state[x - 1] == 0:\n dc, do = get_co(x - 1, y)\n ret = min(ret, minimum_cost(x - 1, y, update_state(state, x - 1), min(ox + do - 1, m), goal, dic, w, m) + dc)\n else:\n ret = min(ret, minimum_cost(x - 1, y, state, ox - 1, goal, dic, w, m))\n \n if x < w - 1:\n if state[x + 1] == 0:\n dc, do = get_co(x + 1, y)\n ret = min(ret, minimum_cost(x + 1, y, update_state(state, x + 1), min(ox + do - 1, m), goal, dic, w, m) + dc)\n else:\n ret = min(ret, minimum_cost(x + 1, y, state, ox - 1, goal, dic, w, m))\n \n \n dc, do = get_co(x, y + 1)\n ret = min(ret, minimum_cost(x, y + 1, tuple((1 if i == x else 0 for i in range(w))), min(ox + do - 1, m), goal, dic, w, m) + dc)\n dic[(x, y, state, ox)] = ret\n return ret\n\nwhile True:\n w, h = map(int, input().split())\n if w == 0:\n break\n f, m, o = map(int, input().split())\n mp = [list(map(int, input().split())) for _ in range(h)]\n if o <= 1:\n print(\"NA\")\n continue\n dic = {}\n ans = INF\n for i in range(w):\n dc, do = get_co(i, 0)\n state = tuple(1 if i == j else 0 for j in range(w))\n ans = min(ans, minimum_cost(i, 0, state, min(o + do - 1, m), h - 1, dic, w, m) + dc)\n if ans > f:\n print(\"NA\")\n else:\n print(ans)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n110 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 0 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n110 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -14\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -18 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-117 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-127 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -144 8\\n-250 -130 -330 -120\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n6 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-8 -79 -20\\n3 3\\n110 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-122 -40 -50 -8\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n111 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -15\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -7\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -11\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -18 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 3\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -30 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -24 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n111 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -15\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-117 -20 -100\\n3 3\\n100 10 5\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -9\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-18 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-127 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -80 8\\n-224 -130 -330 -120\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-174 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -38\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -31\\n-7 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -25 -100\\n-100 -20 -100\\n-117 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-147 -20 -100\\n-20 -20 -20\\n-20 -124 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -48 -50 -20\\n-250 -5 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-117 -20 -195\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-127 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -144 12\\n-250 -130 -330 -18\\n-56 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -24 -100\\n-100 -20 -63\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-146 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-33 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n111 3 3\\n-100 -20 -30\\n-100 -20 2\\n-46 -20 -15\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -165\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-117 -20 -195\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -38 -30\\n-100 -20 2\\n-127 -20 -20\\n4 5\\n883 5 4\\n0 -380 -250 -312\\n-90 2 -144 12\\n-250 -130 -330 -18\\n-56 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -24 -100\\n-100 -20 -63\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-146 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-33 -20 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-100\\n-100 -20 -100\\n-120 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -7\\n3 3\\n101 19 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -172 -11\\n3 3\\n100 1 3\\n-100 0 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -107\\n-90 2 -80 8\\n-250 -130 -330 -166\\n-120 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n6 3\\n100 10 7\\n-100 -20 -100\\n-125 -29 -20\\n-78 -60 -20\\n3 3\\n110 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-8 -29 -20\\n3 3\\n110 3 3\\n-100 -8 0\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -6\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -24 -100\\n-100 -20 -63\\n-130 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-146 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-33 -20 -100\\n-20 -33 -20\\n-20 -79 -20\\n3 3\\n111 3 3\\n-100 -20 -30\\n-100 -20 2\\n-46 -20 -15\\n4 5\\n1500 5 4\\n-10 -380 -250 -162\\n-90 2 -80 8\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -10 -32 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -25 -100\\n-100 -20 -100\\n-117 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -32\\n-100 -60 -20\\n3 3\\n100 19 3\\n-147 -3 -100\\n-20 -20 -20\\n-20 -124 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -80 8\\n-274 -168 -330 -120\\n-120 -48 -50 -20\\n-250 -5 -10 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -25 -100\\n-49 -20 -100\\n-227 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -40 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-147 -3 -100\\n-20 -20 -20\\n-20 -124 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-72 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -312\\n-90 2 -80 8\\n-207 -168 -330 -120\\n-120 -48 -50 -20\\n-250 -5 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -25 -100\\n-100 -22 -100\\n-117 -20 -15\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-147 -3 -100\\n-20 -20 -20\\n-20 -124 -14\\n3 3\\n100 3 3\\n-100 -20 -30\\n-72 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -226 -312\\n-90 2 -80 8\\n-207 -168 -330 -120\\n-120 -48 -50 -20\\n-250 -5 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-117 -2 -195\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 19 3\\n-172 -20 -100\\n-20 -20 -20\\n-10 -100 -20\\n3 3\\n110 3 3\\n-100 -38 -30\\n-100 -20 2\\n-127 -20 -20\\n4 5\\n883 5 4\\n1 -380 -250 -312\\n-90 2 -144 12\\n-467 -130 -330 -29\\n-56 -40 -50 -20\\n-250 -10 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -25 -100\\n-100 -20 -35\\n-117 -29 -15\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-122 -60 -20\\n3 3\\n110 19 3\\n-289 -3 -100\\n-20 -20 -20\\n-20 -124 -20\\n3 3\\n000 3 3\\n-78 -20 -30\\n-72 -20 2\\n-100 -20 -20\\n4 5\\n89 5 4\\n-10 -380 -250 -253\\n-90 2 -80 8\\n-207 -107 -330 -120\\n-120 -48 -50 -20\\n-250 -5 -20 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n110 10 10\\n-100 -20 -100\\n-100 -20 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -100 -20\\n3 3\\n100 3 3\\n-100 -20 -30\\n-100 -20 2\\n-100 -20 -20\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 8\\n-250 -130 -330 -106\\n-120 -40 -50 -20\\n-250 -8 -13 -150\\n0 0\",\n \"3 3\\n100 10 10\\n-100 -20 -100\\n-100 -20 -100\\n-100 -20 -100\\n3 3\\n100 10 10\\n-100 -20 -100\\n-100 -4 -20\\n-100 -60 -20\\n3 3\\n100 10 3\\n-100 -20 -100\\n-20 -20 -20\\n-20 -79 -20\\n3 3\\n110 3 3\\n-100 -20 -30\\n-22 -20 2\\n-100 -20 -14\\n4 5\\n1500 5 4\\n-10 -380 -250 -250\\n-90 2 -80 1\\n-250 -130 -330 -120\\n-120 -40 -50 -12\\n-250 -4 -32 -150\\n0 0\"\n ],\n \"output\": [\n \"60\\n80\\nNA\\n50\\n390\",\n \"60\\n80\\nNA\\n50\\n376\\n\",\n \"60\\n80\\nNA\\n50\\n388\\n\",\n \"60\\n80\\nNA\\n50\\n394\\n\",\n \"60\\n80\\nNA\\n50\\n390\\n\",\n \"60\\n80\\nNA\\n50\\nNA\\n\",\n \"60\\n80\\nNA\\n44\\n394\\n\",\n \"58\\n80\\nNA\\n50\\n376\\n\",\n \"60\\n80\\nNA\\n50\\n454\\n\",\n \"60\\n40\\nNA\\n50\\n388\\n\",\n \"60\\n80\\nNA\\n50\\n378\\n\",\n \"60\\n80\\nNA\\n45\\n394\\n\",\n \"60\\n67\\nNA\\n50\\n390\\n\",\n \"58\\n80\\nNA\\n50\\n386\\n\",\n \"64\\n80\\nNA\\n45\\n394\\n\",\n \"60\\n69\\nNA\\n50\\n390\\n\",\n \"60\\n98\\nNA\\n50\\n388\\n\",\n \"65\\n80\\nNA\\n50\\n390\\n\",\n \"60\\n80\\nNA\\n50\\n352\\n\",\n \"64\\n80\\nNA\\n45\\n439\\n\",\n \"60\\n80\\nNA\\n50\\n342\\n\",\n \"64\\n80\\nNA\\n64\\n439\\n\",\n \"60\\n80\\nNA\\n50\\n270\\n\",\n \"65\\n80\\nNA\\nNA\\n390\\n\",\n \"60\\n80\\nNA\\n50\\n258\\n\",\n \"74\\n80\\nNA\\nNA\\n390\\n\",\n \"74\\n76\\nNA\\nNA\\n390\\n\",\n \"60\\n80\\nNA\\n50\\n383\\n\",\n \"60\\n70\\nNA\\n50\\n388\\n\",\n \"60\\n80\\nNA\\n50\\n384\\n\",\n \"60\\n80\\nNA\\n50\\n386\\n\",\n \"60\\n87\\nNA\\n50\\n390\\n\",\n \"60\\n80\\nNA\\nNA\\n390\\n\",\n \"60\\nNA\\nNA\\n50\\n390\\n\",\n \"60\\n80\\nNA\\n54\\n388\\n\",\n \"60\\n80\\nNA\\n50\\n280\\n\",\n \"60\\n71\\nNA\\n50\\n390\\n\",\n \"NA\\n80\\nNA\\n50\\n390\\n\",\n \"53\\n80\\nNA\\n50\\n390\\n\",\n \"50\\n80\\nNA\\n50\\n454\\n\",\n \"64\\n80\\nNA\\nNA\\n394\\n\",\n \"60\\n40\\nNA\\n50\\n397\\n\",\n \"64\\n80\\nNA\\n45\\n399\\n\",\n \"60\\n67\\nNA\\n50\\n436\\n\",\n \"64\\n80\\nNA\\n56\\n439\\n\",\n \"60\\n67\\nNA\\n50\\n409\\n\",\n \"65\\n80\\nNA\\n50\\n380\\n\",\n \"60\\n96\\nNA\\n50\\n342\\n\",\n \"64\\n80\\nNA\\n57\\n439\\n\",\n \"60\\n80\\nNA\\n50\\n222\\n\",\n \"65\\n80\\nNA\\nNA\\n260\\n\",\n \"65\\n80\\nNA\\nNA\\n377\\n\",\n \"65\\n76\\nNA\\nNA\\n390\\n\",\n \"60\\n70\\nNA\\n50\\n314\\n\",\n \"60\\n80\\nNA\\n50\\n437\\n\",\n \"60\\n80\\nNA\\n44\\n554\\n\",\n \"52\\n80\\nNA\\n50\\n386\\n\",\n \"47\\n80\\nNA\\n50\\n376\\n\",\n \"60\\n80\\nNA\\nNA\\n388\\n\",\n \"60\\n80\\nNA\\nNA\\n380\\n\",\n \"58\\n80\\nNA\\n50\\n280\\n\",\n \"60\\n100\\nNA\\n54\\n388\\n\",\n \"60\\n40\\nNA\\n50\\n384\\n\",\n \"NA\\n80\\nNA\\nNA\\n390\\n\",\n \"60\\n80\\nNA\\n50\\n294\\n\",\n \"69\\n80\\nNA\\n45\\n394\\n\",\n \"60\\n80\\n40\\nNA\\n390\\n\",\n \"60\\n100\\nNA\\n50\\n388\\n\",\n \"60\\n69\\nNA\\n50\\n352\\n\",\n \"60\\n67\\nNA\\nNA\\n436\\n\",\n \"60\\n67\\nNA\\n50\\n280\\n\",\n \"60\\n60\\nNA\\n50\\n409\\n\",\n \"60\\n80\\nNA\\n50\\n277\\n\",\n \"65\\nNA\\nNA\\n50\\n390\\n\",\n \"65\\n80\\nNA\\n50\\n352\\n\",\n \"60\\n68\\nNA\\n50\\n270\\n\",\n \"43\\n80\\nNA\\n50\\n258\\n\",\n \"60\\n80\\nNA\\n50\\n345\\n\",\n \"60\\n70\\nNA\\nNA\\n314\\n\",\n \"60\\n80\\nNA\\n50\\n382\\n\",\n \"60\\n86\\nNA\\n50\\n390\\n\",\n \"47\\n80\\nNA\\n50\\n375\\n\",\n \"60\\n80\\nNA\\n55\\n388\\n\",\n \"60\\n40\\nNA\\n45\\n384\\n\",\n \"60\\n65\\nNA\\n50\\n390\\n\",\n \"NA\\n80\\nNA\\nNA\\n396\\n\",\n \"58\\n80\\nNA\\n50\\n390\\n\",\n \"69\\n80\\nNA\\n45\\nNA\\n\",\n \"60\\n100\\n40\\nNA\\n390\\n\",\n \"64\\n80\\nNA\\n45\\n389\\n\",\n \"60\\n69\\nNA\\n50\\n357\\n\",\n \"60\\n67\\nNA\\nNA\\n363\\n\",\n \"60\\n40\\nNA\\n20\\n388\\n\",\n \"64\\n80\\nNA\\n45\\n376\\n\",\n \"65\\n92\\nNA\\n50\\n380\\n\",\n \"65\\n100\\nNA\\n50\\n390\\n\",\n \"67\\n80\\nNA\\n50\\n390\\n\",\n \"42\\n80\\nNA\\n50\\n270\\n\",\n \"74\\n80\\nNA\\nNA\\nNA\\n\",\n \"60\\n80\\nNA\\n50\\n369\\n\",\n \"60\\n64\\nNA\\n44\\n554\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nAizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost.\n\nThe state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation:\n\n1. A cell filled with soil. There is a fixed cost for each cell to dig.\n2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen.\n\n\n\nOnly left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up.\n\nYou must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded.\n\nCreate a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output \"NA\".\n\n\n\n\n\nInput\n\nA sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format.\n\n\nW H\nf m o\nc1,1 c2,1 ... cW,1\nc1,2 c2,2 ... cW,2\n...\nc1, H c2, H ... cW, H\n\n\nThe horizontal size W of the formation and the vertical size H (3 ≤ W, H ≤ 10) are given in the first line. The second line is the integer f (1 ≤ f ≤ 10000) that represents your excavation cost, the integer m (3 ≤ m ≤ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≤ m) is given.\n\nThe following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format:\nIf the value is negative, the cell is full of soil and the value represents the cost.\nIf the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen.\nHowever, there are no more than 50 cells in which oxygen has accumulated.\n\nThe number of datasets does not exceed 50.\n\nOutput\n\nPrint the minimum cost or NA on one line for each dataset.\n\nExample\n\nInput\n\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0\n\n\nOutput\n\n60\n80\nNA\n50\n390\n\n### Input:\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0\n### Output:\n60\n80\nNA\n50\n390\n\n### Input:\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0\n### Output:\n60\n80\nNA\n50\n376\n\n\n### Code:\nimport sys\nsys.setrecursionlimit(1000000)\nINF = 10 ** 20\n\ndef update_state(state, newx):\n tmp = list(state)\n tmp[newx] = 1\n return tuple(tmp)\n\ndef get_co(x, y):\n dc = do = 0\n score = mp[y][x]\n if score < 0:\n dc = -score\n else:\n do = score\n return dc, do\n\ndef minimum_cost(x, y, state, ox, goal, dic, w, m):\n if (x, y, state, ox) in dic:\n return dic[(x, y, state, ox)]\n if y == goal:\n return 0\n if ox <= 1:\n return INF\n \n ret = INF\n \n if x >= 1:\n if state[x - 1] == 0:\n dc, do = get_co(x - 1, y)\n ret = min(ret, minimum_cost(x - 1, y, update_state(state, x - 1), min(ox + do - 1, m), goal, dic, w, m) + dc)\n else:\n ret = min(ret, minimum_cost(x - 1, y, state, ox - 1, goal, dic, w, m))\n \n if x < w - 1:\n if state[x + 1] == 0:\n dc, do = get_co(x + 1, y)\n ret = min(ret, minimum_cost(x + 1, y, update_state(state, x + 1), min(ox + do - 1, m), goal, dic, w, m) + dc)\n else:\n ret = min(ret, minimum_cost(x + 1, y, state, ox - 1, goal, dic, w, m))\n \n \n dc, do = get_co(x, y + 1)\n ret = min(ret, minimum_cost(x, y + 1, tuple((1 if i == x else 0 for i in range(w))), min(ox + do - 1, m), goal, dic, w, m) + dc)\n dic[(x, y, state, ox)] = ret\n return ret\n\nwhile True:\n w, h = map(int, input().split())\n if w == 0:\n break\n f, m, o = map(int, input().split())\n mp = [list(map(int, input().split())) for _ in range(h)]\n if o <= 1:\n print(\"NA\")\n continue\n dic = {}\n ans = INF\n for i in range(w):\n dc, do = get_co(i, 0)\n state = tuple(1 if i == j else 0 for j in range(w))\n ans = min(ans, minimum_cost(i, 0, state, min(o + do - 1, m), h - 1, dic, w, m) + dc)\n if ans > f:\n print(\"NA\")\n else:\n print(ans)\n"}}},{"rowIdx":695,"cells":{"id":{"kind":"string","value":"p00396 Playing With Stones_3270"},"description":{"kind":"string","value":"Playing with Stones\n\nKoshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:\n\n1. Before starting the game, they define some small areas and place \"one or more black stones and one or more white stones\" in each of the areas.\n2. Koshiro and Ukiko alternately select an area and perform one of the following operations.\n(a) Remove a white stone from the area\n(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area.\n(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game.\n\n3. If either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.\n\n\n\nThey played the game several times, with Koshiro’s first move and Ukiko’s second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.\n\nGiven the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.\n\n\n\nInput\n\nThe input is given in the following format.\n\n\n$N$\n$w_1$ $b_1$\n$w_2$ $b_2$\n:\n$w_N$ $b_N$\n\n\nThe first line provides the number of areas $N$ ($1 \\leq N \\leq 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 \\leq w_i, b_i \\leq 100$) in the $i$-th area.\n\nOutput\n\nOutput 0 if Koshiro wins and 1 if Ukiko wins.\n\nExamples\n\nInput\n\n4\n24 99\n15 68\n12 90\n95 79\n\n\nOutput\n\n0\n\n\nInput\n\n3\n2 46\n94 8\n46 57\n\n\nOutput\n\n1"},"code":{"kind":"string","value":"#!usr/bin/env python3\nfrom collections import defaultdict,deque\nfrom heapq import heappush, heappop\nfrom itertools import permutations\nimport sys\nimport math\nimport bisect\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef I(): return int(sys.stdin.readline())\ndef LS():return [list(x) for x in sys.stdin.readline().split()]\ndef S():\n res = list(sys.stdin.readline())\n if res[-1] == \"\\n\":\n return res[:-1]\n return res\ndef IR(n):\n return [I() for i in range(n)]\ndef LIR(n):\n return [LI() for i in range(n)]\ndef SR(n):\n return [S() for i in range(n)]\ndef LSR(n):\n return [LS() for i in range(n)]\n\nsys.setrecursionlimit(1000000)\nmod = 1000000007\n\ndef solve():\n g = defaultdict(lambda : None)\n g[(0,0)] = 0\n def grundy(w,b):\n if g[(w,b)] != None:\n return g[(w,b)]\n s = set()\n if w:\n s.add(grundy(w-1,b))\n if b:\n s.add(grundy(w+1,b-1))\n for i in range(1,min(w,b)+1):\n s.add(grundy(w,b-i))\n i = 0\n while i in s:\n i += 1\n g[(w,b)] = i\n return i\n\n n = I()\n ans = 0\n for _ in range(n):\n w,b = LI()\n ans ^= grundy(w,b)\n print(0 if ans else 1)\n return\n\n#Solve\nif __name__ == \"__main__\":\n solve()\n\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4\\n24 99\\n15 68\\n12 90\\n95 79\",\n \"3\\n2 46\\n94 8\\n46 57\",\n \"4\\n24 99\\n15 68\\n12 90\\n95 66\",\n \"3\\n0 46\\n94 8\\n46 57\",\n \"4\\n24 99\\n15 44\\n12 90\\n95 66\",\n \"3\\n0 46\\n9 8\\n46 57\",\n \"4\\n18 99\\n15 44\\n12 90\\n95 66\",\n \"3\\n1 46\\n9 8\\n46 57\",\n \"4\\n18 99\\n15 44\\n3 90\\n95 66\",\n \"3\\n1 63\\n9 8\\n46 57\",\n \"4\\n18 99\\n15 44\\n3 90\\n95 104\",\n \"3\\n1 63\\n9 8\\n46 21\",\n \"4\\n18 99\\n15 15\\n3 90\\n95 104\",\n \"3\\n2 63\\n9 8\\n46 21\",\n \"3\\n2 63\\n9 8\\n46 15\",\n \"3\\n2 63\\n9 8\\n24 15\",\n \"3\\n2 32\\n9 8\\n24 15\",\n \"3\\n2 32\\n9 8\\n24 17\",\n \"3\\n2 32\\n9 11\\n24 17\",\n \"3\\n2 32\\n9 11\\n24 4\",\n \"3\\n2 32\\n9 16\\n24 4\",\n \"3\\n3 32\\n9 16\\n24 4\",\n \"3\\n3 32\\n9 16\\n35 4\",\n \"3\\n3 15\\n9 16\\n35 4\",\n \"3\\n0 15\\n9 16\\n35 4\",\n \"3\\n1 15\\n9 16\\n35 4\",\n \"3\\n2 15\\n9 16\\n35 4\",\n \"3\\n1 15\\n9 32\\n35 4\",\n \"3\\n1 15\\n9 38\\n35 4\",\n \"3\\n1 13\\n9 38\\n35 4\",\n \"3\\n1 13\\n9 38\\n35 1\",\n \"3\\n1 13\\n9 38\\n35 0\",\n \"3\\n1 13\\n9 38\\n46 0\",\n \"3\\n1 13\\n9 38\\n46 1\",\n \"3\\n1 13\\n9 58\\n46 1\",\n \"3\\n0 13\\n9 58\\n46 1\",\n \"3\\n0 5\\n9 58\\n46 1\",\n \"3\\n0 5\\n9 23\\n46 1\",\n \"3\\n0 5\\n9 23\\n66 1\",\n \"3\\n0 5\\n9 19\\n66 1\",\n \"3\\n0 5\\n9 19\\n17 1\",\n \"3\\n1 5\\n9 19\\n17 1\",\n \"3\\n1 5\\n16 19\\n17 1\",\n \"3\\n1 8\\n16 19\\n17 1\",\n \"3\\n1 2\\n16 19\\n17 1\",\n \"3\\n2 2\\n16 19\\n17 1\",\n \"3\\n2 2\\n12 19\\n17 1\",\n \"3\\n2 2\\n12 34\\n17 1\",\n \"3\\n2 2\\n19 34\\n17 1\",\n \"3\\n2 2\\n19 34\\n17 0\",\n \"3\\n2 2\\n19 32\\n17 0\",\n \"3\\n2 2\\n5 32\\n17 0\",\n \"3\\n3 2\\n5 32\\n17 0\",\n \"3\\n3 2\\n5 13\\n17 0\",\n \"3\\n1 2\\n5 13\\n17 0\",\n \"3\\n1 2\\n2 13\\n17 0\",\n \"3\\n1 2\\n2 21\\n17 0\",\n \"3\\n1 2\\n2 21\\n3 0\",\n \"3\\n1 1\\n2 21\\n3 0\",\n \"3\\n1 1\\n2 21\\n5 0\",\n \"4\\n24 99\\n15 68\\n12 155\\n95 79\",\n \"3\\n2 46\\n94 12\\n46 57\",\n \"4\\n24 99\\n15 68\\n0 90\\n95 79\",\n \"3\\n2 46\\n94 5\\n46 57\",\n \"4\\n24 99\\n15 68\\n0 90\\n95 33\",\n \"3\\n2 46\\n94 5\\n56 57\",\n \"4\\n24 99\\n24 68\\n0 90\\n95 33\",\n \"3\\n0 46\\n94 5\\n56 57\",\n \"3\\n0 46\\n94 5\\n56 105\",\n \"3\\n0 46\\n94 5\\n27 105\",\n \"3\\n0 46\\n94 5\\n25 105\",\n \"3\\n0 46\\n15 5\\n25 105\",\n \"4\\n24 99\\n15 97\\n12 90\\n95 79\",\n \"3\\n2 46\\n94 8\\n5 57\",\n \"4\\n24 99\\n15 68\\n0 90\\n95 87\",\n \"3\\n2 26\\n94 5\\n46 57\",\n \"4\\n24 99\\n15 68\\n0 78\\n95 33\",\n \"3\\n2 46\\n94 5\\n56 110\",\n \"4\\n24 99\\n24 68\\n0 90\\n95 64\",\n \"3\\n0 46\\n94 5\\n56 41\",\n \"3\\n0 46\\n94 3\\n27 105\",\n \"3\\n0 46\\n60 5\\n25 105\",\n \"3\\n0 46\\n15 5\\n30 105\",\n \"4\\n24 99\\n15 97\\n12 149\\n95 79\",\n \"3\\n2 72\\n94 8\\n5 57\",\n \"4\\n24 99\\n15 34\\n0 90\\n95 87\",\n \"3\\n2 26\\n94 5\\n69 57\",\n \"3\\n2 90\\n94 5\\n56 110\",\n \"4\\n24 99\\n24 68\\n0 90\\n95 31\",\n \"3\\n0 46\\n94 5\\n27 41\",\n \"3\\n0 46\\n23 5\\n25 105\",\n \"3\\n0 46\\n15 1\\n30 105\",\n \"4\\n39 99\\n15 97\\n12 149\\n95 79\",\n \"3\\n2 72\\n94 8\\n8 57\",\n \"3\\n2 26\\n78 5\\n69 57\",\n \"3\\n2 90\\n94 5\\n56 100\",\n \"4\\n24 99\\n24 127\\n0 90\\n95 31\",\n \"3\\n0 46\\n54 5\\n27 41\",\n \"3\\n0 46\\n23 5\\n28 105\",\n \"3\\n0 46\\n8 1\\n30 105\",\n \"3\\n2 72\\n94 13\\n8 57\",\n \"3\\n2 26\\n78 5\\n132 57\"\n ],\n \"output\": [\n \"0\",\n \"1\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nPlaying with Stones\n\nKoshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:\n\n1. Before starting the game, they define some small areas and place \"one or more black stones and one or more white stones\" in each of the areas.\n2. Koshiro and Ukiko alternately select an area and perform one of the following operations.\n(a) Remove a white stone from the area\n(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area.\n(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game.\n\n3. If either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.\n\n\n\nThey played the game several times, with Koshiro’s first move and Ukiko’s second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.\n\nGiven the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.\n\n\n\nInput\n\nThe input is given in the following format.\n\n\n$N$\n$w_1$ $b_1$\n$w_2$ $b_2$\n:\n$w_N$ $b_N$\n\n\nThe first line provides the number of areas $N$ ($1 \\leq N \\leq 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 \\leq w_i, b_i \\leq 100$) in the $i$-th area.\n\nOutput\n\nOutput 0 if Koshiro wins and 1 if Ukiko wins.\n\nExamples\n\nInput\n\n4\n24 99\n15 68\n12 90\n95 79\n\n\nOutput\n\n0\n\n\nInput\n\n3\n2 46\n94 8\n46 57\n\n\nOutput\n\n1\n\n### Input:\n4\n24 99\n15 68\n12 90\n95 79\n### Output:\n0\n\n### Input:\n3\n2 46\n94 8\n46 57\n### Output:\n1\n\n### Code:\n#!usr/bin/env python3\nfrom collections import defaultdict,deque\nfrom heapq import heappush, heappop\nfrom itertools import permutations\nimport sys\nimport math\nimport bisect\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef I(): return int(sys.stdin.readline())\ndef LS():return [list(x) for x in sys.stdin.readline().split()]\ndef S():\n res = list(sys.stdin.readline())\n if res[-1] == \"\\n\":\n return res[:-1]\n return res\ndef IR(n):\n return [I() for i in range(n)]\ndef LIR(n):\n return [LI() for i in range(n)]\ndef SR(n):\n return [S() for i in range(n)]\ndef LSR(n):\n return [LS() for i in range(n)]\n\nsys.setrecursionlimit(1000000)\nmod = 1000000007\n\ndef solve():\n g = defaultdict(lambda : None)\n g[(0,0)] = 0\n def grundy(w,b):\n if g[(w,b)] != None:\n return g[(w,b)]\n s = set()\n if w:\n s.add(grundy(w-1,b))\n if b:\n s.add(grundy(w+1,b-1))\n for i in range(1,min(w,b)+1):\n s.add(grundy(w,b-i))\n i = 0\n while i in s:\n i += 1\n g[(w,b)] = i\n return i\n\n n = I()\n ans = 0\n for _ in range(n):\n w,b = LI()\n ans ^= grundy(w,b)\n print(0 if ans else 1)\n return\n\n#Solve\nif __name__ == \"__main__\":\n solve()\n\n"}}},{"rowIdx":696,"cells":{"id":{"kind":"string","value":"p00749 Off Balance_3274"},"description":{"kind":"string","value":"You are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building.\n\nSubmitted designs will look like a screenshot of a well known game as shown below.\n\n\n\nThis is because the center specifies that the building should be constructed by stacking regular units called pieces, each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions.\n\n* All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position.\n* All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse.\n* The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces.\n* The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below.\n\n\n\n\nIt will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows.\n\nAssume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy-coordinates of its left-bottom corner. The unit length is the edge length of a block.\n\nAmong the blocks of the piece that touch another piece or the ground on their bottom faces, let xL be the leftmost x-coordinate of the leftmost block, and let xR be the rightmost x-coordinate of the rightmost block. Let the x-coordinate of its accumulated center of mass of the piece be M, where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P, in addition to P itself. Then the piece is stable, if and only if xL < M < xR. Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable.\n\nNote that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable.\n\n | | \n---|---|---\n\nAlso note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.\n\nWrite a program that judges stability of each design based on the above quick check rules.\n\nInput\n\nThe input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset, which represents a front view of a building, is formatted as follows.\n\n> w h\n> p0(h-1)p1(h-1)...p(w-1)(h-1)\n> ...\n> p01p11...p(w-1)1\n> p00p10...p(w-1)0\n>\n\nThe integers w and h separated by a space are the numbers of columns and rows of the layout, respectively. You may assume 1 ≤ w ≤ 10 and 1 ≤ h ≤ 60. The next h lines specify the placement of the pieces. The character pxy indicates the status of a block at (x,y), either ``.`', meaning empty, or one digit character between ``1`' and ``9`', inclusive, meaning a block of a piece. (As mentioned earlier, we denote a location of a block by xy-coordinates of its left-bottom corner.)\n\nWhen two blocks with the same number touch each other by any of their top, bottom, left or right face, those blocks are of the same piece. (Note that there might be two different pieces that are denoted by the same number.) The bottom of a block at (x,0) touches the ground.\n\nYou may assume that the pieces in each dataset are stacked in a tree-like form.\n\nOutput\n\nFor each dataset, output a line containing a word `STABLE` when the design is stable with respect to the above quick check rules. Otherwise, output `UNSTABLE`. The output should be written with uppercase letters, and should not contain any other extra characters.\n\nSample Input\n\n\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n\n\nOutput for the Sample Input\n\n\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n\n\n\n\n\nExample\n\nInput\n\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n\n\nOutput\n\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE"},"code":{"kind":"string","value":"while True:\n w, h = map(int, input().split())\n if w == 0:\n break\n\n mp = [[0] + list(input()) + [0] for _ in range(h)]\n mp.insert(0, [0] * (w + 2))\n mp.append([0] * (w + 2))\n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y][x] == \".\":\n mp[y][x] = 0\n else:\n mp[y][x] = int(mp[y][x])\n\n last_id = 10\n vec = ((0, 1), (0, -1), (1, 0), (-1, 0))\n \n def update(last_id, target, x, y):\n if mp[y][x] != target:\n return\n mp[y][x] = last_id\n for dx, dy in vec:\n update(last_id, target, x + dx, y + dy)\n \n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if 1 <= mp[y][x] <= 9:\n update(last_id, mp[y][x], x, y)\n last_id += 1\n\n node_num = last_id - 10\n\n edges = [set() for _ in range(node_num)]\n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y - 1][x] != mp[y][x] and mp[y - 1][x] != 0 and mp[y][x] != 0:\n edges[mp[y][x] - 10].add(mp[y - 1][x] - 10)\n\n for x in range(1, w + 1):\n if mp[h][x] != 0:\n root = mp[h][x] - 10\n break\n \n center = [0] * node_num\n ground = [None] * node_num\n \n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y][x] != 0:\n target = mp[y][x] - 10\n center[target] += (x + 0.5) / 4\n if mp[y + 1][x] in (0, target + 10):\n continue\n if ground[target] == None:\n ground[target] = [x, x + 1]\n else:\n ground[target][0] = min(ground[target][0], x)\n ground[target][1] = max(ground[target][1], x + 1)\n\n for x in range(1, w + 1):\n if mp[h][x] == root + 10:\n if ground[root] == None:\n ground[root] = [x, x + 1]\n else:\n ground[root][0] = min(ground[root][0], x)\n ground[root][1] = max(ground[root][1], x + 1)\n\n total_center = [None] * node_num\n def get_total_center(node):\n mom = center[node]\n wei = 1\n for to in edges[node]:\n to_wei, to_pos = get_total_center(to)\n mom += to_wei * to_pos\n wei += to_wei\n\n total_center[node] = mom / wei\n return wei, total_center[node]\n \n get_total_center(root)\n\n for gr, cen in zip(ground, total_center):\n l, r = gr\n if not (l < cen < r):\n print(\"UNSTABLE\")\n break\n else:\n print(\"STABLE\")\n\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n..33\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n.1..\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n33..\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n..33\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n33..\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n..33\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n1.0304765877571223\\n0 0\",\n \"4 5\\n..33\\n33..\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n1..1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n..33\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n1.5938270010912552\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n./..1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n3944\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.-..1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n.11.\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n32\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..01\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n.1..\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..01\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n20\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..01\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n33..\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n..33\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n1.5938270010912552\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n/2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n.1..\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..01\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2/\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n.1..\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.20\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n./..1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n32\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.//.1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n....1\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.-..1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n32\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..33\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1..1\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n3188\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1.1.\\n11..0\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.//.1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.3.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n...-1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.-..1\\n.1..1\\n.1.1.\\n12..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n32\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.-/.1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n32\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1.1.\\n11..0\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..12\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.//.1\\n.1..1\\n-1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.3.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n...-1\\n1..1.\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n....1\\n.1..1\\n.1.1.\\n11..1\\n.2222\\n..111\\n...1-\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.2.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n23\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\",\n \"4 5\\n..33\\n..32\\n2222\\n..1.\\n.111\\n5 7\\n.//.1\\n.1..1\\n-1.1.\\n11..1\\n.2222\\n..111\\n...1.\\n3 6\\n.3.\\n233\\n23.\\n22.\\n.11\\n.11\\n4 3\\n2222\\n..11\\n..11\\n4 5\\n.3..\\n33..\\n322.\\n2211\\n.11.\\n3 3\\n222\\n2.1\\n111\\n3 4\\n11.\\n11.\\n.3.\\n222\\n3 4\\n.11\\n.11\\n.2.\\n222\\n2 7\\n11\\n.1\\n21\\n22\\n26\\n.3\\n33\\n2 3\\n1.\\n11\\n.1\\n0 0\"\n ],\n \"output\": [\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\n\",\n \"UNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"UNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\",\n \"STABLE\\nUNSTABLE\\nSTABLE\\nUNSTABLE\\nSTABLE\\nSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\nUNSTABLE\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nYou are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building.\n\nSubmitted designs will look like a screenshot of a well known game as shown below.\n\n\n\nThis is because the center specifies that the building should be constructed by stacking regular units called pieces, each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions.\n\n* All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position.\n* All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse.\n* The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces.\n* The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below.\n\n\n\n\nIt will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows.\n\nAssume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy-coordinates of its left-bottom corner. The unit length is the edge length of a block.\n\nAmong the blocks of the piece that touch another piece or the ground on their bottom faces, let xL be the leftmost x-coordinate of the leftmost block, and let xR be the rightmost x-coordinate of the rightmost block. Let the x-coordinate of its accumulated center of mass of the piece be M, where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P, in addition to P itself. Then the piece is stable, if and only if xL < M < xR. Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable.\n\nNote that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable.\n\n | | \n---|---|---\n\nAlso note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.\n\nWrite a program that judges stability of each design based on the above quick check rules.\n\nInput\n\nThe input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset, which represents a front view of a building, is formatted as follows.\n\n> w h\n> p0(h-1)p1(h-1)...p(w-1)(h-1)\n> ...\n> p01p11...p(w-1)1\n> p00p10...p(w-1)0\n>\n\nThe integers w and h separated by a space are the numbers of columns and rows of the layout, respectively. You may assume 1 ≤ w ≤ 10 and 1 ≤ h ≤ 60. The next h lines specify the placement of the pieces. The character pxy indicates the status of a block at (x,y), either ``.`', meaning empty, or one digit character between ``1`' and ``9`', inclusive, meaning a block of a piece. (As mentioned earlier, we denote a location of a block by xy-coordinates of its left-bottom corner.)\n\nWhen two blocks with the same number touch each other by any of their top, bottom, left or right face, those blocks are of the same piece. (Note that there might be two different pieces that are denoted by the same number.) The bottom of a block at (x,0) touches the ground.\n\nYou may assume that the pieces in each dataset are stacked in a tree-like form.\n\nOutput\n\nFor each dataset, output a line containing a word `STABLE` when the design is stable with respect to the above quick check rules. Otherwise, output `UNSTABLE`. The output should be written with uppercase letters, and should not contain any other extra characters.\n\nSample Input\n\n\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n\n\nOutput for the Sample Input\n\n\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n\n\n\n\n\nExample\n\nInput\n\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n\n\nOutput\n\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n### Input:\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n### Output:\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n### Input:\n4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0\n### Output:\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n\n\n### Code:\nwhile True:\n w, h = map(int, input().split())\n if w == 0:\n break\n\n mp = [[0] + list(input()) + [0] for _ in range(h)]\n mp.insert(0, [0] * (w + 2))\n mp.append([0] * (w + 2))\n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y][x] == \".\":\n mp[y][x] = 0\n else:\n mp[y][x] = int(mp[y][x])\n\n last_id = 10\n vec = ((0, 1), (0, -1), (1, 0), (-1, 0))\n \n def update(last_id, target, x, y):\n if mp[y][x] != target:\n return\n mp[y][x] = last_id\n for dx, dy in vec:\n update(last_id, target, x + dx, y + dy)\n \n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if 1 <= mp[y][x] <= 9:\n update(last_id, mp[y][x], x, y)\n last_id += 1\n\n node_num = last_id - 10\n\n edges = [set() for _ in range(node_num)]\n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y - 1][x] != mp[y][x] and mp[y - 1][x] != 0 and mp[y][x] != 0:\n edges[mp[y][x] - 10].add(mp[y - 1][x] - 10)\n\n for x in range(1, w + 1):\n if mp[h][x] != 0:\n root = mp[h][x] - 10\n break\n \n center = [0] * node_num\n ground = [None] * node_num\n \n for y in range(1, h + 1):\n for x in range(1, w + 1):\n if mp[y][x] != 0:\n target = mp[y][x] - 10\n center[target] += (x + 0.5) / 4\n if mp[y + 1][x] in (0, target + 10):\n continue\n if ground[target] == None:\n ground[target] = [x, x + 1]\n else:\n ground[target][0] = min(ground[target][0], x)\n ground[target][1] = max(ground[target][1], x + 1)\n\n for x in range(1, w + 1):\n if mp[h][x] == root + 10:\n if ground[root] == None:\n ground[root] = [x, x + 1]\n else:\n ground[root][0] = min(ground[root][0], x)\n ground[root][1] = max(ground[root][1], x + 1)\n\n total_center = [None] * node_num\n def get_total_center(node):\n mom = center[node]\n wei = 1\n for to in edges[node]:\n to_wei, to_pos = get_total_center(to)\n mom += to_wei * to_pos\n wei += to_wei\n\n total_center[node] = mom / wei\n return wei, total_center[node]\n \n get_total_center(root)\n\n for gr, cen in zip(ground, total_center):\n l, r = gr\n if not (l < cen < r):\n print(\"UNSTABLE\")\n break\n else:\n print(\"STABLE\")\n\n"}}},{"rowIdx":697,"cells":{"id":{"kind":"string","value":"p00887 Awkward Lights_3277"},"description":{"kind":"string","value":"You are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.\n\nEach floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x1, y1) of a grid of rooms and the room at (x2, y2) is given by |x1 - x2| + |y1 - y2|. For example, if the position of the toggle switch of the room at (2, 2) of a 4 × 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1, 1), (1, 3), (2, 4), (3, 1), (3, 3), and (4, 2) as well as at (2, 2) are reversed as shown in Figure D.1, where black and white squares represent the ON/OFF states of the lights.\n\n\n\nFigure D.1: An example behavior of the lighting system\n\nYour mission is to write a program that answer whether all the lights on a floor can be turned off.\n\n\n\nInput\n\nThe input is a sequence of datasets. Each dataset is formatted as follows.\n\nm n d\nS11 S12 S13 ... S1m\nS21 S22 S23 ... S2m\n...\nSn1 Sn2 Sn3 ... Snm\n\n\nThe first line of a dataset contains three integers. m and n (1 ≤ m ≤ 25, 1 ≤ n ≤ 25) are the numbers of columns and rows of the grid, respectively. d (1 ≤ d ≤ m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each Sij (1 ≤ i ≤ n, 1 ≤ j ≤ m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.\n\nThe end of the input is indicated by a line containing three zeros.\n\nOutput\n\nFor each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case, print it in one line for each input dataset.\n\nExample\n\nInput\n\n1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n\n\nOutput\n\n1\n1\n0\n1\n0\n0\n1\n1\n0\n1"},"code":{"kind":"string","value":"import sys,queue,math,copy,itertools\nLI = lambda : [int(x) for x in sys.stdin.readline().split()]\n\nwhile True:\n M,N,D = LI()\n if N == 0 : break\n\n S = []\n for _ in range(N):\n S.extend(LI())\n\n x = []\n for i in range(N):\n for j in range(M):\n y = [0 for _ in range(N*M)]\n for p in range(-D,D+1):\n q1 = j + (D - abs(p))\n q2 = j - (D - abs(p))\n if 0 <= i + p < N and 0 <= q1 < M:\n y[(i+p) * M + q1] = 1\n if 0 <= i+ p < N and 0 <= q2 < M:\n y[(i+p) * M + q2] = 1\n y[i * M + j] = 1\n x.append(y)\n x.append(S)\n\n z = []\n for i in range(N*M):\n b = 0\n for j in range(N*M+1):\n b <<= 1\n b += x[j][i]\n z.append(b)\n\n\n c = [True for _ in range(N*M)]\n b = 1 << (N * M)\n for i in range(N*M):\n for j in range(N*M):\n if z[j] & b and c[j]:\n for k in range(N*M):\n if k == j or z[k] & b == 0: continue\n z[k] ^= z[j]\n c[j] = False\n break\n b >>= 1\n\n if z.count(1):\n print (0)\n else:\n print (1)\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"1 1 1\\n1\\n2 2 1\\n1 1\\n1 1\\n3 2 1\\n1 0 1\\n0 1 0\\n3 3 1\\n1 0 1\\n0 1 0\\n1 0 1\\n4 4 2\\n1 1 0 1\\n0 0 0 1\\n1 0 1 1\\n1 0 0 0\\n5 5 1\\n1 1 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n0 1 0 1 0\\n1 0 1 0 1\\n5 5 2\\n0 0 0 0 0\\n0 0 0 0 0\\n0 0 1 0 0\\n0 0 0 0 0\\n0 0 0 0 0\\n11 11 3\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 1 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n11 11 3\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 0 0 0 0 0 0\\n0 0 0 0 0 1 1 0 0 0 0\\n0 0 0 0 0 0 0 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\"1\\n1\\n0\\n1\\n0\\n0\\n1\\n\",\n \"1\\n1\\n0\\n1\\n0\\n0\\n0\\n0\\n\",\n \"1\\n1\\n0\\n1\\n0\\n0\\n1\\n\",\n \"1\\n1\\n0\\n1\\n0\\n0\\n0\\n0\\n\",\n \"1\\n1\\n0\\n1\\n0\\n0\\n1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nYou are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.\n\nEach floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x1, y1) of a grid of rooms and the room at (x2, y2) is given by |x1 - x2| + |y1 - y2|. For example, if the position of the toggle switch of the room at (2, 2) of a 4 × 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1, 1), (1, 3), (2, 4), (3, 1), (3, 3), and (4, 2) as well as at (2, 2) are reversed as shown in Figure D.1, where black and white squares represent the ON/OFF states of the lights.\n\n\n\nFigure D.1: An example behavior of the lighting system\n\nYour mission is to write a program that answer whether all the lights on a floor can be turned off.\n\n\n\nInput\n\nThe input is a sequence of datasets. Each dataset is formatted as follows.\n\nm n d\nS11 S12 S13 ... S1m\nS21 S22 S23 ... S2m\n...\nSn1 Sn2 Sn3 ... Snm\n\n\nThe first line of a dataset contains three integers. m and n (1 ≤ m ≤ 25, 1 ≤ n ≤ 25) are the numbers of columns and rows of the grid, respectively. d (1 ≤ d ≤ m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each Sij (1 ≤ i ≤ n, 1 ≤ j ≤ m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.\n\nThe end of the input is indicated by a line containing three zeros.\n\nOutput\n\nFor each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case, print it in one line for each input dataset.\n\nExample\n\nInput\n\n1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n\n\nOutput\n\n1\n1\n0\n1\n0\n0\n1\n1\n0\n1\n\n### Input:\n1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n### Output:\n1\n1\n0\n1\n0\n0\n1\n1\n0\n1\n\n### Input:\n1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 -1 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0\n### Output:\n1\n1\n0\n1\n0\n0\n1\n1\n0\n1\n\n\n### Code:\nimport sys,queue,math,copy,itertools\nLI = lambda : [int(x) for x in sys.stdin.readline().split()]\n\nwhile True:\n M,N,D = LI()\n if N == 0 : break\n\n S = []\n for _ in range(N):\n S.extend(LI())\n\n x = []\n for i in range(N):\n for j in range(M):\n y = [0 for _ in range(N*M)]\n for p in range(-D,D+1):\n q1 = j + (D - abs(p))\n q2 = j - (D - abs(p))\n if 0 <= i + p < N and 0 <= q1 < M:\n y[(i+p) * M + q1] = 1\n if 0 <= i+ p < N and 0 <= q2 < M:\n y[(i+p) * M + q2] = 1\n y[i * M + j] = 1\n x.append(y)\n x.append(S)\n\n z = []\n for i in range(N*M):\n b = 0\n for j in range(N*M+1):\n b <<= 1\n b += x[j][i]\n z.append(b)\n\n\n c = [True for _ in range(N*M)]\n b = 1 << (N * M)\n for i in range(N*M):\n for j in range(N*M):\n if z[j] & b and c[j]:\n for k in range(N*M):\n if k == j or z[k] & b == 0: continue\n z[k] ^= z[j]\n c[j] = False\n break\n b >>= 1\n\n if z.count(1):\n print (0)\n else:\n print (1)\n"}}},{"rowIdx":698,"cells":{"id":{"kind":"string","value":"p01018 Warping Girl_3280"},"description":{"kind":"string","value":"Problem\n\nAizu Magic School is a school where people who can use magic gather. Haruka, one of the students of that school, can use the magic of warp on the magic team.\n\nFrom her house to the school, there is a straight road of length L. There are also magic circles on this road.\nShe uses this road every day to go to school, so she wants to get to school in the shortest possible time.\n\nSo as a programmer, you decided to teach her the minimum amount of time it would take to get to school.\n\nHaruka can walk forward by a distance of 1 in 1 minute (* cannot go back). Also, by casting magic at the position Pi where the magic circle of the warp is written, you can move in Ti minutes to the place just Di from Pi. Even if there is a magic circle at the destination, it will be continuous. You can use warp magic.\n\nThe location of her house is 0 and the location of her school is L.\n\nConstraints\n\nThe input meets the following conditions.\n\n* All numbers given are integers\n* 1 ≤ L ≤ 109\n* 0 ≤ n ≤ min (103, L) (min represents the smaller of A and B)\n* 0 ≤ Pi ≤ L -1\n* 0 ≤ Di ≤ L --Pi\n* 0 ≤ Ti ≤ 103\n* Pi ≠ Pj\n\nInput\n\n\nL n\nP1 D1 T1\nP2 D2 T2\n..\n..\nPn Dn Tn\n\n\nThe first line is given the length of the road L, the number of magic circles n. Next, the state of n magic circles is given. Pi is the position where the i-th magic circle is, and Di is the i-th magic circle. Distance to warp from, Ti represents the time it takes to warp using the i-th magic circle.\n\nOutput\n\nOutput the minimum time to get to school in one line.\n\nExamples\n\nInput\n\n10 3\n2 2 1\n4 2 1\n8 1 1\n\n\nOutput\n\n8\n\n\nInput\n\n10 2\n2 3 1\n3 5 1\n\n\nOutput\n\n6\n\n\nInput\n\n1 0\n\n\nOutput\n\n1"},"code":{"kind":"string","value":"INF = 10 ** 20\nl, n = map(int, input().split())\nlst = [list(map(int, input().split())) for _ in range(n)] + [[l, 0, INF]]\nlst.sort()\nscore = {}\nfor p, _, _ in lst:\n score[p] = p\nfor i in range(n + 1):\n p, d, t = lst[i]\n for j in range(i + 1, n + 1):\n to_p, _, _ = lst[j]\n if to_p >= p + d:\n score[to_p] = min(score[to_p], score[p] + t + to_p - p - d, score[p] + to_p - p)\n else:\n score[to_p] = min(score[to_p], score[p] + to_p - p)\nprint(score[l])\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"10 2\\n2 3 1\\n3 5 1\",\n \"1 0\",\n \"10 3\\n2 2 1\\n4 2 1\\n8 1 1\",\n \"10 2\\n2 3 1\\n1 5 1\",\n \"10 2\\n2 3 1\\n1 5 0\",\n \"10 0\\n2 3 1\\n1 5 1\",\n \"18 0\\n2 3 1\\n1 5 1\",\n \"0 0\\n2 -1 1\\n0 1 1\",\n \"1 0\\n2 0 2\\n1 2 1\",\n \"2 1\\n1 0 7\\n4 -1 0\",\n \"10 3\\n2 0 1\\n4 2 1\\n8 1 1\",\n \"34 0\\n2 3 1\\n1 5 1\",\n \"8 0\\n2 0 1\\n0 3 1\",\n \"10 2\\n2 6 1\\n1 5 -1\",\n \"30 0\\n2 0 1\\n-1 2 1\",\n \"20 2\\n2 6 1\\n1 5 -1\",\n \"20 2\\n2 6 1\\n1 5 0\",\n \"23 0\\n2 2 1\\n-1 1 1\",\n \"7 0\\n2 1 1\\n-1 0 1\",\n \"27 0\\n3 1 1\\n0 1 1\",\n \"43 0\\n1 2 2\\n0 1 1\",\n \"16 0\\n2 -2 1\\n2 2 1\",\n \"19 1\\n0 1 1\\n-2 0 1\",\n \"31 1\\n2 2 2\\n0 3 1\",\n \"4 1\\n0 2 1\\n-2 0 1\",\n \"16 1\\n2 2 -1\\n0 3 1\",\n \"25 0\\n3 3 1\\n1 5 1\",\n \"35 0\\n2 0 2\\n0 5 1\",\n \"23 1\\n1 2 1\\n0 1 1\",\n \"12 0\\n1 1 7\\n5 0 0\",\n \"30 1\\n2 1 0\\n0 1 -1\",\n \"24 0\\n1 1 0\\n0 1 -1\",\n \"21 0\\n2 3 1\\n0 5 1\",\n \"10 3\\n2 3 1\\n1 5 1\",\n \"18 0\\n2 0 1\\n1 5 1\",\n \"18 0\\n2 0 1\\n1 2 1\",\n \"18 0\\n2 0 1\\n0 2 1\",\n \"18 0\\n2 0 1\\n0 1 1\",\n \"18 0\\n2 0 1\\n1 1 1\",\n \"18 0\\n2 0 1\\n0 3 1\",\n \"18 0\\n2 -1 1\\n0 3 1\",\n \"18 0\\n2 -1 1\\n0 1 1\",\n \"0 0\\n2 -1 1\\n0 2 1\",\n \"0 0\\n2 -1 1\\n1 2 1\",\n \"0 0\\n2 0 1\\n1 2 1\",\n \"0 0\\n2 0 2\\n1 2 1\",\n \"1 0\\n2 0 2\\n1 2 0\",\n \"1 0\\n0 0 2\\n1 2 0\",\n \"1 0\\n0 0 2\\n2 2 0\",\n \"1 0\\n0 0 2\\n2 3 0\",\n \"1 1\\n0 0 2\\n2 3 0\",\n \"1 1\\n1 0 2\\n2 3 0\",\n \"1 1\\n1 0 4\\n2 3 0\",\n \"1 1\\n1 0 4\\n2 0 0\",\n \"1 1\\n1 0 4\\n4 0 0\",\n \"1 1\\n1 0 4\\n4 -1 0\",\n \"1 1\\n1 0 7\\n4 -1 0\",\n \"10 2\\n2 3 2\\n3 5 1\",\n \"10 2\\n2 3 1\\n0 5 1\",\n \"10 2\\n2 6 1\\n1 5 0\",\n \"10 0\\n2 2 1\\n1 5 1\",\n \"18 0\\n2 0 2\\n1 5 1\",\n \"18 0\\n2 0 1\\n2 2 1\",\n \"18 0\\n2 0 1\\n-1 2 1\",\n \"18 0\\n2 1 1\\n0 1 1\",\n \"18 1\\n2 0 1\\n1 1 1\",\n \"18 0\\n4 0 1\\n0 1 1\",\n \"0 0\\n1 -1 1\\n0 1 1\",\n \"0 0\\n2 -1 1\\n0 2 2\",\n \"0 0\\n2 0 0\\n1 2 1\",\n \"0 0\\n2 0 2\\n1 2 0\",\n \"0 0\\n4 0 2\\n1 2 1\",\n \"2 0\\n2 0 2\\n1 2 0\",\n \"2 0\\n0 0 2\\n2 2 0\",\n \"1 0\\n0 1 2\\n2 2 0\",\n \"1 0\\n0 0 2\\n4 3 0\",\n \"1 1\\n0 0 2\\n4 3 0\",\n \"1 1\\n1 0 4\\n2 3 -1\",\n \"1 1\\n1 0 4\\n2 0 -1\",\n \"1 1\\n1 0 4\\n0 0 0\",\n \"1 1\\n1 0 4\\n0 -1 0\",\n \"1 0\\n1 0 7\\n4 -1 0\",\n \"2 1\\n1 0 7\\n4 0 0\",\n \"10 3\\n2 3 2\\n3 5 1\",\n \"10 0\\n2 2 1\\n1 6 1\",\n \"34 0\\n3 3 1\\n1 5 1\",\n \"18 0\\n2 0 2\\n0 5 1\",\n \"18 0\\n2 0 1\\n2 2 0\",\n \"18 1\\n2 1 1\\n0 1 1\",\n \"18 1\\n2 0 2\\n1 1 1\",\n \"8 0\\n2 1 1\\n0 3 1\",\n \"18 0\\n4 0 2\\n0 1 1\",\n \"0 0\\n1 -1 1\\n-1 1 1\",\n \"0 0\\n2 0 1\\n0 2 1\",\n \"0 0\\n2 0 0\\n1 3 1\",\n \"1 0\\n4 0 2\\n1 2 0\",\n \"0 0\\n4 0 3\\n1 2 1\",\n \"2 0\\n2 0 2\\n0 2 0\",\n \"2 0\\n0 0 2\\n2 2 1\",\n \"1 0\\n0 0 2\\n3 2 0\",\n \"1 0\\n0 0 2\\n4 4 0\",\n \"1 1\\n0 0 2\\n7 3 0\",\n \"1 1\\n1 0 0\\n2 3 -1\"\n ],\n \"output\": [\n \"6\",\n \"1\",\n \"8\",\n \"6\\n\",\n \"5\\n\",\n \"10\\n\",\n \"18\\n\",\n \"0\\n\",\n \"1\\n\",\n \"2\\n\",\n \"9\\n\",\n \"34\\n\",\n \"8\\n\",\n \"4\\n\",\n \"30\\n\",\n \"14\\n\",\n \"15\\n\",\n \"23\\n\",\n \"7\\n\",\n \"27\\n\",\n \"43\\n\",\n \"16\\n\",\n \"19\\n\",\n \"31\\n\",\n \"3\\n\",\n \"13\\n\",\n \"25\\n\",\n \"35\\n\",\n \"22\\n\",\n \"12\\n\",\n \"29\\n\",\n \"24\\n\",\n \"21\\n\",\n \"6\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"6\\n\",\n \"6\\n\",\n \"5\\n\",\n \"10\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"2\\n\",\n \"2\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"2\\n\",\n \"6\\n\",\n \"10\\n\",\n \"34\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"18\\n\",\n \"8\\n\",\n \"18\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"2\\n\",\n \"2\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nProblem\n\nAizu Magic School is a school where people who can use magic gather. Haruka, one of the students of that school, can use the magic of warp on the magic team.\n\nFrom her house to the school, there is a straight road of length L. There are also magic circles on this road.\nShe uses this road every day to go to school, so she wants to get to school in the shortest possible time.\n\nSo as a programmer, you decided to teach her the minimum amount of time it would take to get to school.\n\nHaruka can walk forward by a distance of 1 in 1 minute (* cannot go back). Also, by casting magic at the position Pi where the magic circle of the warp is written, you can move in Ti minutes to the place just Di from Pi. Even if there is a magic circle at the destination, it will be continuous. You can use warp magic.\n\nThe location of her house is 0 and the location of her school is L.\n\nConstraints\n\nThe input meets the following conditions.\n\n* All numbers given are integers\n* 1 ≤ L ≤ 109\n* 0 ≤ n ≤ min (103, L) (min represents the smaller of A and B)\n* 0 ≤ Pi ≤ L -1\n* 0 ≤ Di ≤ L --Pi\n* 0 ≤ Ti ≤ 103\n* Pi ≠ Pj\n\nInput\n\n\nL n\nP1 D1 T1\nP2 D2 T2\n..\n..\nPn Dn Tn\n\n\nThe first line is given the length of the road L, the number of magic circles n. Next, the state of n magic circles is given. Pi is the position where the i-th magic circle is, and Di is the i-th magic circle. Distance to warp from, Ti represents the time it takes to warp using the i-th magic circle.\n\nOutput\n\nOutput the minimum time to get to school in one line.\n\nExamples\n\nInput\n\n10 3\n2 2 1\n4 2 1\n8 1 1\n\n\nOutput\n\n8\n\n\nInput\n\n10 2\n2 3 1\n3 5 1\n\n\nOutput\n\n6\n\n\nInput\n\n1 0\n\n\nOutput\n\n1\n\n### Input:\n10 2\n2 3 1\n3 5 1\n### Output:\n6\n\n### Input:\n1 0\n### Output:\n1\n\n### Code:\nINF = 10 ** 20\nl, n = map(int, input().split())\nlst = [list(map(int, input().split())) for _ in range(n)] + [[l, 0, INF]]\nlst.sort()\nscore = {}\nfor p, _, _ in lst:\n score[p] = p\nfor i in range(n + 1):\n p, d, t = lst[i]\n for j in range(i + 1, n + 1):\n to_p, _, _ = lst[j]\n if to_p >= p + d:\n score[to_p] = min(score[to_p], score[p] + t + to_p - p - d, score[p] + to_p - p)\n else:\n score[to_p] = min(score[to_p], score[p] + to_p - p)\nprint(score[l])\n"}}},{"rowIdx":699,"cells":{"id":{"kind":"string","value":"p01290 Queen's Case_3284"},"description":{"kind":"string","value":"A small country called Maltius was governed by a queen. The queen was known as an oppressive ruler. People in the country suffered from heavy taxes and forced labor. So some young people decided to form a revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into the entrance.\n\nYour task is to write a program to determine whether the queen can escape or will be caught by the army.\n\nHere is detailed description.\n\n* The palace can be considered as grid squares.\n* The queen and the army move alternately. The queen moves first.\n* At each of their turns, they either move to an adjacent cell or stay at the same cell.\n* Each of them must follow the optimal strategy.\n* If the queen and the army are at the same cell, the queen will be caught by the army immediately.\n* If the queen is at any of exit cells alone after the army’s turn, the queen can escape from the army.\n* There may be cases in which the queen cannot escape but won’t be caught by the army forever, under their optimal strategies.\n\nHint\n\nOn the first sample input, the queen can move to exit cells, but either way the queen will be caught at the next army’s turn. So the optimal strategy for the queen is staying at the same cell. Then the army can move to exit cells as well, but again either way the army will miss the queen from the other exit. So the optimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won’t be caught.\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 ≤ W ≤ 30) and H (1 ≤ H ≤ 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. \"Q\" indicates the queen, \"A\" the army,\"E\" an exit,\"#\" a wall and \".\" a floor.\n\nThe map contains exactly one \"Q\", exactly one \"A\" and at least one \"E\". You can assume both the queen and the army can reach all the exits.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\n\nOutput\n\nFor each dataset, output \"Queen can escape.\", \"Army can catch Queen.\" or \"Queen can not escape and Army can not catch Queen.\" in a line.\n\nExamples\n\nInput\n\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n####.\n..E..\n.####\n....Q\n0 0\n\n\nOutput\n\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n\nInput\n\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0\n\n\nOutput\n\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen."},"code":{"kind":"string","value":"from collections import deque, defaultdict\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndd = ((-1, 0), (0, -1), (1, 0), (0, 1), (0, 0))\ndef solve():\n W, H = map(int, readline().split())\n if W == H == 0:\n return False\n S = [readline().strip() for i in range(H)]\n px = py = qx = qy = 0\n rs = []\n pp = []\n MP = [[0]*W for i in range(H)]\n for i in range(H):\n for j, c in enumerate(S[i]):\n if c == \"Q\":\n px = j; py = i\n elif c == \"A\":\n qx = j; qy = i\n elif c == \"E\":\n MP[i][j] = 1\n rs.append((j, i))\n elif c == \"#\":\n MP[i][j] = 2\n if c != \"#\":\n pp.append((j, i))\n mp = {}\n L = 0\n for ax, ay in pp:\n for bx, by in pp:\n mp[ax, ay, bx, by, 0] = L\n L += 1\n mp[ax, ay, bx, by, 1] = L\n L += 1\n\n que1 = deque()\n ss = [-1]*L\n cc = [0]*L\n\n que = deque([(px, py, qx, qy, 0)])\n used = [0]*L\n used[mp[px, py, qx, qy, 0]] = 1\n RG = [[] for i in range(L)]\n deg = [0]*L\n while que:\n ax, ay, bx, by, t = key = que.popleft()\n k0 = mp[key]\n if ax == bx and ay == by:\n que1.append(k0)\n ss[k0] = 1\n continue\n if t == 0 and MP[ay][ax] == 1:\n que1.append(k0)\n ss[k0] = 0\n continue\n if t == 1:\n for dx, dy in dd:\n nx = bx + dx; ny = by + dy\n if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:\n continue\n k1 = mp[ax, ay, nx, ny, t^1]\n deg[k0] += 1\n RG[k1].append(k0)\n if not used[k1]:\n used[k1] = 1\n que.append((ax, ay, nx, ny, t^1))\n else:\n for dx, dy in dd:\n nx = ax + dx; ny = ay + dy\n if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:\n continue\n k1 = mp[nx, ny, bx, by, t^1]\n deg[k0] += 1\n RG[k1].append(k0)\n if not used[k1]:\n used[k1] = 1\n que.append((nx, ny, bx, by, t^1))\n\n while que1:\n v = que1.popleft()\n s = ss[v]; t = v % 2\n if t == 0:\n for w in RG[v]:\n if ss[w] != -1:\n continue\n if s == 1:\n que1.append(w)\n ss[w] = 1\n else:\n deg[w] -= 1\n if deg[w] == 0:\n que1.append(w)\n ss[w] = 0\n else:\n for w in RG[v]:\n if ss[w] != -1:\n continue\n if s == 0:\n que1.append(w)\n ss[w] = 0\n else:\n deg[w] -= 1\n if deg[w] == 0:\n que1.append(w)\n ss[w] = 1\n k0 = mp[px, py, qx, qy, 0]\n if ss[k0] == -1:\n write(\"Queen can not escape and Army can not catch Queen.\\n\")\n elif ss[k0] == 0:\n write(\"Queen can escape.\\n\")\n else:\n write(\"Army can catch Queen.\\n\")\n return True\nwhile solve():\n ...\n"},"test_samples":{"kind":"string","value":"{\n \"input\": [\n \"2 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n####.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n##A#Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 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5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nAE\\n3 1\\nEAQ\\n3 1\\nAQD\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nQ.E.A\\n5 5\\nA/...\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"1 2\\nQE\\nAE\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA../.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 1\\nQAE\\n3 1\\nAQD\\n5 5\\n..E..\\n.###.\\nQ##$A\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n3 1\\nQAE\\n3 1\\nDQA\\n5 5\\n....E\\n.###.\\nA##\\\"Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nAE\\n3 1\\nEAQ\\n3 1\\nAQD\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nQ.E.A\\n5 5\\nA//..\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"1 2\\nQE\\nAE\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\nE....\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA../.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nAEQ\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n5 1\\n..EQA\\n5 5\\nA....\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n3 1\\nEAQ\\n3 1\\nDQA\\n5 5\\n....E\\n.###.\\nA##\\\"Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"1 2\\nQE\\nAE\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\nE....\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA../.\\n.\\nE....\\n.####\\nQ....\\n0 0\",\n \"2 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nAEQ\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n10 1\\n..EQA\\n5 5\\nA....\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nAEQ\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n10 1\\n..EQA\\n5 5\\nA....\\n.\\n.E...\\n.####\\nQ....\\n0 0\",\n \"4 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nAEQ\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n10 1\\n..EQA\\n5 5\\nA....\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"4 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nQEA\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n10 1\\n..EQA\\n5 5\\nA....\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"4 2\\nQE\\nAD\\n2 1\\nQAE\\n3 1\\nQEA\\n10 5\\n..E..\\n.###.\\nA#$#Q\\n.###.\\n..E..\\n10 1\\n..EQA\\n5 5\\n....A\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"4 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"4 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA\\\"##Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n##A#Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n##A#Q\\n.#.##\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n....E\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 1\\nQAE\\n6 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA..-.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n11 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n10 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\n..E..\\n.####\\n..Q..\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n10 5\\n..E..\\n.#$#.\\nA###Q\\n.###.\\n..E..\\n5 1\\nQ.E.A\\n5 5\\nA....\\n.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nEQA\\n5 5\\n..E..\\n.###.\\nA\\\"##Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"3 2\\nEQ\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n##A#Q\\n.#.##\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nAE\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 1\\nQAE\\n5 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA..-.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n3 1\\nQAE\\n3 1\\nAQD\\n5 5\\n..E..\\n.###.\\nA##\\\"Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA/...\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 1\\nEAQ\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA.--.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nEQA\\n10 5\\n..E-.\\n###..\\nA###Q\\n###..\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"3 2\\nQE\\nAE\\n3 1\\nQAF\\n3 1\\nAQD\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n.-.E.\\n6 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n@###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA.-..\\n.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n##A#Q\\n.#.##\\n..E..\\n5 1\\n..EAQ\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n6 1\\nAQE\\n10 5\\n..E..\\n.##\\\".\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n10 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nQ.E.A\\n5 5\\nA.-..\\n.\\n.E...\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nAE\\n3 1\\nQAE\\n2 1\\nAQD\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE./..\\n.####\\n....Q\\n0 0\",\n \"1 2\\nQD\\nAE\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\nE....\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA../.\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"2 2\\nEQ\\nEA\\n3 1\\nEAQ\\n3 1\\nDQA\\n6 5\\n....E\\n.###.\\nA##\\\"Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\nE....\\n.####\\n....Q\\n0 0\",\n \"7 2\\nQE\\nEA\\n3 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n.\\n..E..\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nEA\\n2 1\\nQAE\\n3 1\\nAQE\\n5 5\\n..E..\\n.###.\\n\\\"#A#Q\\n.#.##\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA....\\n-\\n....E\\n.####\\n....Q\\n0 0\",\n \"2 2\\nQE\\nAE\\n3 1\\nEAQ\\n6 1\\nAQE\\n5 5\\n..E..\\n.###.\\nA###Q\\n.###.\\n..E..\\n5 1\\nA.E.Q\\n5 5\\nA..-.\\n.\\nE....\\n.####\\n....Q\\n0 0\"\n ],\n \"output\": [\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Army can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nQueen can escape.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nQueen can escape.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\n\",\n \"Queen can escape.\\nQueen can escape.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nQueen can escape.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Army can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Army can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Army can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Army can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can escape.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\",\n \"Queen can escape.\\nArmy can catch Queen.\\nQueen can escape.\\nQueen can not escape and Army can not catch Queen.\\nArmy can catch Queen.\\nArmy can catch Queen.\\n\"\n ]\n}"},"source":{"kind":"class label","value":"6","name":"AIZU"},"prompt":{"kind":"string","value":"Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.\n\n### Description:\nA small country called Maltius was governed by a queen. The queen was known as an oppressive ruler. People in the country suffered from heavy taxes and forced labor. So some young people decided to form a revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into the entrance.\n\nYour task is to write a program to determine whether the queen can escape or will be caught by the army.\n\nHere is detailed description.\n\n* The palace can be considered as grid squares.\n* The queen and the army move alternately. The queen moves first.\n* At each of their turns, they either move to an adjacent cell or stay at the same cell.\n* Each of them must follow the optimal strategy.\n* If the queen and the army are at the same cell, the queen will be caught by the army immediately.\n* If the queen is at any of exit cells alone after the army’s turn, the queen can escape from the army.\n* There may be cases in which the queen cannot escape but won’t be caught by the army forever, under their optimal strategies.\n\nHint\n\nOn the first sample input, the queen can move to exit cells, but either way the queen will be caught at the next army’s turn. So the optimal strategy for the queen is staying at the same cell. Then the army can move to exit cells as well, but again either way the army will miss the queen from the other exit. So the optimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won’t be caught.\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 ≤ W ≤ 30) and H (1 ≤ H ≤ 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. \"Q\" indicates the queen, \"A\" the army,\"E\" an exit,\"#\" a wall and \".\" a floor.\n\nThe map contains exactly one \"Q\", exactly one \"A\" and at least one \"E\". You can assume both the queen and the army can reach all the exits.\n\nThe last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.\n\nOutput\n\nFor each dataset, output \"Queen can escape.\", \"Army can catch Queen.\" or \"Queen can not escape and Army can not catch Queen.\" in a line.\n\nExamples\n\nInput\n\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n####.\n..E..\n.####\n....Q\n0 0\n\n\nOutput\n\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n\nInput\n\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0\n\n\nOutput\n\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n### Input:\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0\n### Output:\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n### Input:\n2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n####.\n..E..\n.####\n....Q\n0 0\n### Output:\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n\n### Code:\nfrom collections import deque, defaultdict\nimport sys\nreadline = sys.stdin.readline\nwrite = sys.stdout.write\ndd = ((-1, 0), (0, -1), (1, 0), (0, 1), (0, 0))\ndef solve():\n W, H = map(int, readline().split())\n if W == H == 0:\n return False\n S = [readline().strip() for i in range(H)]\n px = py = qx = qy = 0\n rs = []\n pp = []\n MP = [[0]*W for i in range(H)]\n for i in range(H):\n for j, c in enumerate(S[i]):\n if c == \"Q\":\n px = j; py = i\n elif c == \"A\":\n qx = j; qy = i\n elif c == \"E\":\n MP[i][j] = 1\n rs.append((j, i))\n elif c == \"#\":\n MP[i][j] = 2\n if c != \"#\":\n pp.append((j, i))\n mp = {}\n L = 0\n for ax, ay in pp:\n for bx, by in pp:\n mp[ax, ay, bx, by, 0] = L\n L += 1\n mp[ax, ay, bx, by, 1] = L\n L += 1\n\n que1 = deque()\n ss = [-1]*L\n cc = [0]*L\n\n que = deque([(px, py, qx, qy, 0)])\n used = [0]*L\n used[mp[px, py, qx, qy, 0]] = 1\n RG = [[] for i in range(L)]\n deg = [0]*L\n while que:\n ax, ay, bx, by, t = key = que.popleft()\n k0 = mp[key]\n if ax == bx and ay == by:\n que1.append(k0)\n ss[k0] = 1\n continue\n if t == 0 and MP[ay][ax] == 1:\n que1.append(k0)\n ss[k0] = 0\n continue\n if t == 1:\n for dx, dy in dd:\n nx = bx + dx; ny = by + dy\n if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:\n continue\n k1 = mp[ax, ay, nx, ny, t^1]\n deg[k0] += 1\n RG[k1].append(k0)\n if not used[k1]:\n used[k1] = 1\n que.append((ax, ay, nx, ny, t^1))\n else:\n for dx, dy in dd:\n nx = ax + dx; ny = ay + dy\n if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:\n continue\n k1 = mp[nx, ny, bx, by, t^1]\n deg[k0] += 1\n RG[k1].append(k0)\n if not used[k1]:\n used[k1] = 1\n que.append((nx, ny, bx, by, t^1))\n\n while que1:\n v = que1.popleft()\n s = ss[v]; t = v % 2\n if t == 0:\n for w in RG[v]:\n if ss[w] != -1:\n continue\n if s == 1:\n que1.append(w)\n ss[w] = 1\n else:\n deg[w] -= 1\n if deg[w] == 0:\n que1.append(w)\n ss[w] = 0\n else:\n for w in RG[v]:\n if ss[w] != -1:\n continue\n if s == 0:\n que1.append(w)\n ss[w] = 0\n else:\n deg[w] -= 1\n if deg[w] == 0:\n que1.append(w)\n ss[w] = 1\n k0 = mp[px, py, qx, qy, 0]\n if ss[k0] == -1:\n write(\"Queen can not escape and Army can not catch Queen.\\n\")\n elif ss[k0] == 0:\n write(\"Queen can escape.\\n\")\n else:\n write(\"Army can catch Queen.\\n\")\n return True\nwhile solve():\n ...\n"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":6,"numItemsPerPage":100,"numTotalItems":8139,"offset":600,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTcyNjY4MjQ5OSwic3ViIjoiL2RhdGFzZXRzL2lhbXRhcnVuL2NvZGVfY29udGVzdF9weXRob24zX2FscGFjYSIsImV4cCI6MTcyNjY4NjA5OSwiaXNzIjoiaHR0cHM6Ly9odWdnaW5nZmFjZS5jbyJ9.7fz_Nmbqu0-PP2FzLB4beMfL4aPzOqQBEHhCJnCJDlm72IT7OTPWx5zuC-ihkVFhlZCbxOdX4EE83fNhejBnAQ","displayUrls":true},"discussionsStats":{"closed":0,"open":0,"total":0},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false}">
id
stringlengths 14
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| description
stringlengths 29
13k
| code
stringlengths 10
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| test_samples
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class label 3
classes | prompt
stringlengths 391
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|
|---|---|---|---|---|---|
505_B. Mr. Kitayuta's Colorful Graph_2838 | Mr. Kitayuta has just bought an undirected graph consisting of n vertices and m edges. The vertices of the graph are numbered from 1 to n. Each edge, namely edge i, has a color ci, connecting vertex ai and bi.
Mr. Kitayuta wants you to process the following q queries.
In the i-th query, he gives you two integers — ui and vi.
Find the number of the colors that satisfy the following condition: the edges of that color connect vertex ui and vertex vi directly or indirectly.
Input
The first line of the input contains space-separated two integers — n and m (2 ≤ n ≤ 100, 1 ≤ m ≤ 100), denoting the number of the vertices and the number of the edges, respectively.
The next m lines contain space-separated three integers — ai, bi (1 ≤ ai < bi ≤ n) and ci (1 ≤ ci ≤ m). Note that there can be multiple edges between two vertices. However, there are no multiple edges of the same color between two vertices, that is, if i ≠ j, (ai, bi, ci) ≠ (aj, bj, cj).
The next line contains a integer — q (1 ≤ q ≤ 100), denoting the number of the queries.
Then follows q lines, containing space-separated two integers — ui and vi (1 ≤ ui, vi ≤ n). It is guaranteed that ui ≠ vi.
Output
For each query, print the answer in a separate line.
Examples
Input
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3
3
1 2
3 4
1 4
Output
2
1
0
Input
5 7
1 5 1
2 5 1
3 5 1
4 5 1
1 2 2
2 3 2
3 4 2
5
1 5
5 1
2 5
1 5
1 4
Output
1
1
1
1
2
Note
Let's consider the first sample.
<image> The figure above shows the first sample.
* Vertex 1 and vertex 2 are connected by color 1 and 2.
* Vertex 3 and vertex 4 are connected by color 3.
* Vertex 1 and vertex 4 are not connected by any single color. | def build_graph():
line1 = input().strip().split()
n = int(line1[0])
m = int(line1[1])
graph = {}
for _ in range(m):
line = input().strip().split()
u = int(line[0])
v = int(line[1])
c = int(line[2])
if c not in graph:
graph[c] = {j: [] for j in range(1, n+1)}
graph[c][u].append(v)
graph[c][v].append(u)
return graph
def no_of_paths(u, v, graph):
x = 0
for c in graph:
parent = {}
parent = dfs_visit(v, graph[c], parent)
if u in parent:
x += 1
return x
def dfs_visit(i, adj_list, parent):
for j in adj_list[i]:
if j not in parent:
parent[j] = i
dfs_visit(j, adj_list, parent)
return parent
if __name__ == "__main__":
graph = build_graph()
for _ in range(int(input())):
line = input().strip().split()
print(no_of_paths(int(line[0]), int(line[1]), graph)) | {
"input": [
"5 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 1\n1 2 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"2 1\n1 2 1\n1\n1 2\n",
"2 3\n1 2 3\n1 2 2\n1 2 1\n1\n1 2\n",
"2 5\n1 2 1\n1 2 2\n1 2 3\n1 2 4\n1 2 5\n1\n1 2\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 1\n1 1 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"6 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"6 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 2\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 2\n",
"2 3\n1 2 3\n1 2 2\n2 2 1\n1\n1 2\n",
"5 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 4 1\n1 2 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n1 2 1\n1 1 2\n2 3 1\n2 3 3\n2 1 3\n3\n1 2\n3 4\n1 4\n",
"6 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 2\n5 1\n2 5\n1 5\n1 6\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 3\n2 5\n1 4\n",
"4 5\n1 4 1\n1 2 2\n2 3 1\n2 1 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n2 4 1\n2\n1 2\n3 4\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n2 4 1\n1\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n4 3 2\n3 4 2\n5\n1 5\n5 2\n2 3\n2 5\n1 4\n",
"8 7\n1 5 2\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n5 5 1\n4 5 2\n1 1 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 2\n1 1 3\n2 3 1\n1 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n1 2 1\n1 1 2\n2 3 1\n2 3 3\n2 1 3\n3\n1 2\n3 1\n1 4\n",
"6 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 6 2\n3 4 2\n5\n1 2\n5 1\n2 5\n1 5\n1 6\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n4 3 3\n2 4 1\n3\n1 2\n3 4\n1 4\n",
"4 5\n1 4 1\n1 2 2\n2 3 1\n2 1 3\n3 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n2 1 1\n2 5 1\n3 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n4\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n2 1 1\n2\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n5 5 1\n4 5 2\n1 1 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n2 4\n",
"4 5\n2 2 1\n2 1 2\n2 3 1\n2 3 3\n4 4 1\n1\n1 2\n3 4\n1 4\n",
"4 5\n1 2 2\n1 1 3\n1 3 1\n1 3 3\n2 4 3\n3\n1 2\n3 4\n2 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 5 3\n3 3 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 2 2\n1 2 1\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 3\n2 3\n1 4\n",
"5 7\n1 5 2\n2 5 1\n3 5 2\n4 5 1\n1 3 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 4\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 1\n1 1 3\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n5 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 2\n1 1 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n1 2 2\n1 1 3\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 2\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 3 1\n1 1 3\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 2\n5 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 2\n1 1 2\n2 3 1\n4 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n2 4 1\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n3 5 3\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 2\n",
"5 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"5 7\n2 1 1\n2 5 1\n3 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"5 5\n1 3 1\n1 1 3\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 2\n5 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n4 5\n1 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 2\n2 3\n2 5\n1 4\n",
"5 7\n1 5 2\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"5 7\n2 1 1\n2 5 1\n3 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 2\n1 4\n",
"5 5\n1 3 1\n1 1 3\n2 3 1\n4 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"8 7\n1 5 2\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"5 5\n1 3 1\n1 1 3\n2 3 2\n4 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"4 5\n1 3 1\n1 1 3\n2 3 2\n4 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"7 5\n1 3 1\n1 1 3\n2 3 2\n4 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n3 5\n1 5\n1 4\n",
"4 5\n1 2 2\n1 1 3\n1 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n4 5\n1 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 5 2\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n3 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 4\n5 1\n2 5\n1 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 2 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 3\n2 5\n1 4\n",
"5 7\n1 1 1\n2 5 2\n5 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n3 5\n1 5\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n1 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 2\n2 3\n2 5\n1 4\n",
"5 7\n1 5 2\n2 5 1\n3 5 1\n4 5 1\n1 2 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"4 5\n2 2 1\n1 1 2\n2 3 1\n2 3 3\n4 4 1\n1\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n3 3 2\n3 4 2\n5\n1 5\n5 2\n2 3\n2 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 4 1\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n3 5\n1 5\n1 4\n",
"4 5\n1 2 2\n1 1 3\n1 3 1\n1 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 5 2\n3 3 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"4 5\n1 2 1\n1 1 2\n2 4 1\n2 3 3\n2 1 3\n3\n1 2\n3 1\n1 4\n",
"5 7\n1 1 1\n2 1 1\n1 5 1\n4 2 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 3\n2 3\n1 4\n",
"5 7\n1 5 2\n2 5 1\n3 5 1\n4 5 1\n1 3 1\n2 3 1\n3 4 2\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 1 2\n2 1 1\n1 5 1\n4 5 2\n1 2 2\n3 3 2\n3 4 2\n5\n1 5\n5 2\n2 3\n2 5\n1 4\n",
"5 7\n1 1 1\n2 5 1\n1 5 1\n4 5 2\n1 2 2\n2 5 3\n3 3 4\n5\n1 5\n5 1\n2 5\n2 5\n1 4\n",
"5 7\n1 5 2\n2 5 1\n3 5 2\n4 5 1\n1 3 1\n2 3 1\n3 4 2\n5\n1 5\n5 2\n2 5\n2 5\n1 4\n",
"4 5\n1 2 1\n1 2 2\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n2 4\n",
"4 5\n1 2 1\n1 1 2\n2 3 1\n2 3 3\n2 3 3\n3\n1 2\n3 4\n1 4\n",
"5 7\n1 1 1\n2 5 1\n3 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 3\n5 1\n2 5\n1 5\n1 4\n",
"4 5\n1 2 1\n1 2 3\n2 3 1\n2 3 3\n2 4 3\n3\n1 2\n3 4\n1 4\n",
"7 7\n1 1 1\n2 5 1\n5 5 1\n4 5 2\n1 2 2\n2 3 2\n3 4 2\n5\n1 5\n5 1\n2 5\n1 5\n1 4\n",
"6 7\n1 5 1\n2 5 1\n3 5 1\n4 5 1\n1 2 2\n2 3 2\n5 4 2\n5\n1 2\n5 1\n2 5\n1 5\n1 4\n"
],
"output": [
"1\n1\n1\n1\n2\n",
"2\n1\n0\n",
"1\n",
"3\n",
"5\n",
"0\n0\n1\n0\n1\n",
"1\n1\n0\n",
"1\n1\n2\n1\n1\n",
"1\n1\n1\n1\n2\n",
"2\n2\n2\n2\n1\n",
"2\n1\n1\n1\n2\n",
"0\n1\n0\n",
"2\n2\n2\n2\n2\n",
"2\n",
"1\n1\n1\n1\n1\n",
"1\n1\n1\n",
"2\n0\n0\n",
"2\n1\n1\n1\n0\n",
"2\n2\n1\n2\n1\n",
"2\n0\n2\n",
"0\n1\n",
"0\n",
"1\n1\n0\n1\n0\n",
"2\n2\n1\n1\n1\n",
"0\n0\n2\n0\n0\n",
"1\n0\n0\n",
"2\n2\n0\n",
"2\n1\n1\n1\n1\n",
"0\n2\n0\n",
"2\n1\n1\n",
"2\n2\n2\n2\n",
"1\n0\n",
"0\n0\n2\n0\n1\n",
"1\n",
"1\n0\n1\n",
"1\n1\n2\n2\n0\n",
"1\n1\n1\n1\n0\n",
"2\n2\n1\n1\n2\n",
"1\n0\n1\n0\n1\n",
"1\n1\n0\n",
"1\n1\n2\n1\n1\n",
"1\n1\n0\n",
"1\n1\n0\n",
"2\n2\n2\n2\n1\n",
"2\n2\n2\n2\n1\n",
"2\n2\n2\n2\n2\n",
"1\n1\n2\n1\n1\n",
"1\n1\n0\n",
"1\n1\n1\n1\n1\n",
"1\n1\n0\n",
"0\n1\n0\n",
"1\n1\n1\n1\n2\n",
"1\n1\n1\n1\n1\n",
"2\n2\n2\n2\n1\n",
"1\n1\n0\n",
"1\n1\n1\n1\n1\n",
"2\n2\n1\n2\n1\n",
"2\n2\n1\n2\n1\n",
"2\n2\n2\n2\n1\n",
"1\n1\n0\n",
"2\n2\n1\n2\n1\n",
"0\n1\n0\n",
"0\n1\n0\n",
"0\n1\n0\n",
"0\n0\n1\n0\n1\n",
"1\n1\n0\n",
"2\n2\n1\n2\n1\n",
"2\n2\n2\n2\n1\n",
"1\n1\n1\n1\n1\n",
"1\n1\n2\n1\n1\n",
"1\n1\n1\n1\n1\n",
"1\n1\n1\n1\n1\n",
"2\n2\n1\n2\n1\n",
"2\n2\n1\n1\n1\n",
"0\n",
"1\n1\n0\n1\n0\n",
"0\n0\n1\n0\n1\n",
"1\n0\n0\n",
"2\n2\n2\n2\n1\n",
"2\n1\n1\n",
"1\n1\n1\n1\n1\n",
"2\n2\n1\n1\n1\n",
"1\n1\n0\n1\n0\n",
"1\n1\n2\n2\n0\n",
"2\n1\n1\n1\n2\n",
"2\n1\n1\n",
"1\n0\n0\n",
"1\n1\n2\n1\n1\n",
"2\n1\n1\n",
"1\n1\n2\n1\n1\n",
"2\n1\n1\n1\n1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Mr. Kitayuta has just bought an undirected graph consisting of n vertices and m edges. The vertices of the graph are numbered from 1 to n. Each edge, namely edge i, has a color ci, connecting vertex ai and bi.
Mr. Kitayuta wants you to process the following q queries.
In the i-th query, he gives you two integers — ui and vi.
Find the number of the colors that satisfy the following condition: the edges of that color connect vertex ui and vertex vi directly or indirectly.
Input
The first line of the input contains space-separated two integers — n and m (2 ≤ n ≤ 100, 1 ≤ m ≤ 100), denoting the number of the vertices and the number of the edges, respectively.
The next m lines contain space-separated three integers — ai, bi (1 ≤ ai < bi ≤ n) and ci (1 ≤ ci ≤ m). Note that there can be multiple edges between two vertices. However, there are no multiple edges of the same color between two vertices, that is, if i ≠ j, (ai, bi, ci) ≠ (aj, bj, cj).
The next line contains a integer — q (1 ≤ q ≤ 100), denoting the number of the queries.
Then follows q lines, containing space-separated two integers — ui and vi (1 ≤ ui, vi ≤ n). It is guaranteed that ui ≠ vi.
Output
For each query, print the answer in a separate line.
Examples
Input
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3
3
1 2
3 4
1 4
Output
2
1
0
Input
5 7
1 5 1
2 5 1
3 5 1
4 5 1
1 2 2
2 3 2
3 4 2
5
1 5
5 1
2 5
1 5
1 4
Output
1
1
1
1
2
Note
Let's consider the first sample.
<image> The figure above shows the first sample.
* Vertex 1 and vertex 2 are connected by color 1 and 2.
* Vertex 3 and vertex 4 are connected by color 3.
* Vertex 1 and vertex 4 are not connected by any single color.
### Input:
5 7
1 5 1
2 5 1
3 5 1
4 5 1
1 2 2
2 3 2
3 4 2
5
1 5
5 1
2 5
1 5
1 4
### Output:
1
1
1
1
2
### Input:
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3
3
1 2
3 4
1 4
### Output:
2
1
0
### Code:
def build_graph():
line1 = input().strip().split()
n = int(line1[0])
m = int(line1[1])
graph = {}
for _ in range(m):
line = input().strip().split()
u = int(line[0])
v = int(line[1])
c = int(line[2])
if c not in graph:
graph[c] = {j: [] for j in range(1, n+1)}
graph[c][u].append(v)
graph[c][v].append(u)
return graph
def no_of_paths(u, v, graph):
x = 0
for c in graph:
parent = {}
parent = dfs_visit(v, graph[c], parent)
if u in parent:
x += 1
return x
def dfs_visit(i, adj_list, parent):
for j in adj_list[i]:
if j not in parent:
parent[j] = i
dfs_visit(j, adj_list, parent)
return parent
if __name__ == "__main__":
graph = build_graph()
for _ in range(int(input())):
line = input().strip().split()
print(no_of_paths(int(line[0]), int(line[1]), graph)) |
554_C. Kyoya and Colored Balls_2844 | Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen.
Input
The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.
Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).
The total number of balls doesn't exceed 1000.
Output
A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.
Examples
Input
3
2
2
1
Output
3
Input
4
1
2
3
4
Output
1680
Note
In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:
1 2 1 2 3
1 1 2 2 3
2 1 1 2 3
| from sys import stdin
c = [[0]*1002 for _ in range(0,1002)]
MOD = int(1e9+7)
for i in range(0,1002):
c[i][0] = c[i][i] = 1
for j in range(0,i):
c[i][j] = (c[i-1][j-1] + c[i-1][j])%MOD
r = map(int,stdin.read().split())
n = next(r)
ans = 1
sum = 0
for _ in range(0,n):
x = next(r)
ans = (ans * c[sum+x-1][sum])%MOD
sum += x
print(ans) | {
"input": [
"3\n2\n2\n1\n",
"4\n1\n2\n3\n4\n",
"25\n35\n43\n38\n33\n47\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n22\n26\n24\n17\n18\n21\n22\n21\n23\n17\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"3\n343\n317\n337\n",
"1\n5\n",
"10\n100\n100\n100\n100\n100\n100\n100\n100\n100\n100\n",
"1\n1\n",
"13\n67\n75\n76\n80\n69\n86\n75\n86\n81\n84\n73\n72\n76\n",
"5\n10\n10\n10\n10\n10\n",
"11\n291\n381\n126\n39\n19\n20\n3\n1\n20\n45\n2\n",
"25\n35\n43\n38\n33\n36\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n21\n23\n17\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"1\n3\n",
"5\n10\n5\n10\n10\n10\n",
"11\n291\n381\n126\n39\n19\n20\n3\n1\n20\n43\n2\n",
"4\n1\n4\n3\n4\n",
"25\n35\n43\n38\n33\n27\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n17\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"5\n10\n5\n10\n19\n10\n",
"11\n291\n394\n126\n39\n19\n20\n3\n1\n20\n43\n2\n",
"25\n35\n43\n38\n33\n27\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n17\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"5\n15\n5\n10\n19\n10\n",
"11\n291\n394\n126\n39\n19\n20\n3\n2\n20\n43\n2\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"5\n15\n2\n10\n19\n10\n",
"11\n291\n394\n52\n39\n19\n20\n3\n2\n20\n43\n2\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n39\n19\n20\n3\n2\n20\n43\n3\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n64\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n39\n19\n20\n3\n2\n31\n43\n3\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n64\n11\n33\n",
"47\n20\n21\n16\n18\n24\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n73\n19\n20\n3\n2\n31\n43\n3\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n73\n19\n26\n3\n2\n31\n43\n3\n",
"25\n69\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n25\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n42\n19\n26\n3\n2\n31\n43\n3\n",
"25\n69\n43\n38\n63\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n30\n20\n25\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n42\n19\n26\n3\n2\n31\n68\n3\n",
"25\n69\n43\n38\n63\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n8\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n38\n20\n19\n26\n30\n20\n25\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n42\n19\n26\n3\n3\n31\n68\n3\n",
"25\n69\n43\n38\n63\n27\n44\n40\n37\n41\n42\n33\n14\n49\n42\n62\n39\n40\n35\n43\n31\n19\n8\n77\n11\n33\n",
"11\n291\n394\n52\n42\n19\n26\n3\n3\n31\n119\n3\n",
"25\n69\n43\n38\n38\n27\n44\n40\n37\n41\n42\n33\n14\n49\n42\n62\n39\n40\n35\n43\n31\n19\n8\n77\n11\n33\n",
"11\n291\n394\n52\n42\n19\n26\n3\n3\n16\n119\n3\n",
"25\n69\n43\n38\n38\n27\n44\n40\n37\n41\n42\n33\n14\n58\n42\n62\n39\n40\n35\n43\n31\n19\n8\n77\n11\n33\n",
"11\n291\n394\n52\n42\n26\n26\n3\n3\n16\n119\n3\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n22\n26\n24\n17\n18\n21\n22\n21\n23\n17\n15\n24\n13\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"3\n188\n317\n337\n",
"5\n10\n10\n17\n10\n10\n",
"11\n291\n291\n126\n39\n19\n20\n3\n1\n20\n45\n2\n",
"3\n2\n2\n2\n",
"4\n2\n2\n3\n4\n",
"25\n35\n43\n38\n33\n36\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n49\n35\n43\n31\n42\n46\n42\n34\n33\n",
"5\n10\n5\n10\n2\n10\n",
"11\n291\n381\n126\n39\n19\n20\n3\n1\n20\n43\n1\n",
"4\n2\n4\n3\n4\n",
"25\n7\n43\n38\n33\n27\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n42\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n11\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n17\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"5\n10\n5\n20\n19\n10\n",
"11\n291\n394\n126\n54\n19\n20\n3\n1\n20\n43\n2\n",
"25\n35\n75\n38\n33\n27\n44\n40\n36\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n17\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n30\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"5\n15\n5\n10\n19\n14\n",
"11\n214\n394\n126\n39\n19\n20\n3\n2\n20\n43\n2\n",
"25\n35\n43\n38\n33\n43\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n46\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n34\n20\n19\n26\n25\n20\n17\n17\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n39\n19\n16\n3\n2\n20\n43\n2\n",
"25\n35\n43\n38\n33\n27\n27\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n42\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n18\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n25\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n39\n19\n20\n3\n4\n20\n43\n3\n",
"25\n35\n43\n38\n33\n4\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n64\n34\n33\n",
"47\n20\n21\n16\n18\n24\n20\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n30\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n39\n19\n20\n3\n2\n43\n43\n3\n",
"25\n35\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n36\n62\n39\n40\n35\n43\n31\n19\n6\n64\n11\n33\n",
"47\n20\n21\n16\n18\n24\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n20\n24\n19\n9\n21\n20\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n73\n19\n14\n3\n2\n31\n43\n3\n",
"25\n35\n43\n38\n33\n27\n80\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n36\n19\n26\n25\n20\n17\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n73\n19\n26\n3\n4\n31\n43\n3\n",
"25\n69\n43\n38\n33\n27\n44\n40\n37\n41\n42\n33\n30\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n1\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n25\n20\n25\n7\n17\n41\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n457\n52\n42\n19\n26\n3\n2\n31\n43\n3\n",
"25\n69\n43\n38\n63\n27\n44\n40\n37\n41\n42\n33\n16\n49\n42\n62\n39\n40\n35\n43\n31\n19\n6\n77\n11\n33\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n9\n21\n20\n19\n26\n30\n20\n25\n7\n17\n26\n32\n20\n21\n48\n51\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n394\n52\n42\n19\n26\n3\n2\n8\n68\n3\n",
"47\n20\n21\n16\n18\n2\n7\n25\n13\n20\n20\n26\n24\n17\n18\n21\n22\n19\n23\n9\n15\n24\n19\n5\n38\n20\n19\n26\n30\n20\n25\n7\n17\n26\n32\n20\n21\n48\n28\n24\n21\n21\n17\n28\n20\n20\n31\n19\n",
"11\n291\n82\n52\n42\n19\n26\n3\n3\n31\n68\n3\n",
"25\n69\n43\n38\n63\n27\n44\n40\n37\n41\n42\n33\n14\n49\n42\n62\n39\n40\n35\n43\n31\n19\n8\n64\n11\n33\n",
"11\n291\n394\n52\n42\n11\n26\n3\n3\n31\n119\n3\n",
"25\n69\n43\n38\n38\n27\n44\n40\n37\n41\n70\n33\n14\n49\n42\n62\n39\n40\n35\n43\n31\n19\n8\n77\n11\n33\n",
"11\n291\n394\n52\n42\n30\n26\n3\n3\n16\n119\n3\n",
"1\n4\n",
"1\n2\n"
],
"output": [
"3\n",
"1680\n",
"362689152\n",
"295545118\n",
"691446102\n",
"1\n",
"12520708\n",
"1\n",
"232242896\n",
"425711769\n",
"902382672\n",
"683385905\n",
"874969659\n",
"1\n",
"418394244\n",
"133409084\n",
"13860\n",
"960840482\n",
"777222528\n",
"704582418\n",
"762530917\n",
"447995088\n",
"436630400\n",
"277332034\n",
"757104390\n",
"297569513\n",
"512670764\n",
"337657833\n",
"157057612\n",
"66678052\n",
"723498274\n",
"497992827\n",
"125583648\n",
"126998154\n",
"795265363\n",
"151250638\n",
"695576313\n",
"71028079\n",
"115424347\n",
"588344159\n",
"944364428\n",
"960926976\n",
"742867140\n",
"654505129\n",
"610729591\n",
"566478672\n",
"729515917\n",
"511882986\n",
"173840134\n",
"539856535\n",
"620013562\n",
"257936337\n",
"741359563\n",
"654952422\n",
"728192535\n",
"255552417\n",
"314954011\n",
"607706537\n",
"705078768\n",
"664062671\n",
"15\n",
"5400\n",
"807245750\n",
"670344246\n",
"46751493\n",
"61600\n",
"997824461\n",
"977947431\n",
"930377845\n",
"347669631\n",
"785395614\n",
"627302562\n",
"585017380\n",
"400475244\n",
"614705642\n",
"89604172\n",
"569301761\n",
"414231253\n",
"638382221\n",
"345839683\n",
"934280941\n",
"328940714\n",
"403670881\n",
"460872653\n",
"73100902\n",
"110668519\n",
"386012099\n",
"923085909\n",
"195591746\n",
"672123031\n",
"149753111\n",
"605457812\n",
"41476019\n",
"805880511\n",
"294275718\n",
"415341452\n",
"584182163\n",
"167316265\n",
"627529073\n",
"514489760\n",
"891327513\n",
"1\n",
"1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen.
Input
The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.
Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).
The total number of balls doesn't exceed 1000.
Output
A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.
Examples
Input
3
2
2
1
Output
3
Input
4
1
2
3
4
Output
1680
Note
In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:
1 2 1 2 3
1 1 2 2 3
2 1 1 2 3
### Input:
3
2
2
1
### Output:
3
### Input:
4
1
2
3
4
### Output:
1680
### Code:
from sys import stdin
c = [[0]*1002 for _ in range(0,1002)]
MOD = int(1e9+7)
for i in range(0,1002):
c[i][0] = c[i][i] = 1
for j in range(0,i):
c[i][j] = (c[i-1][j-1] + c[i-1][j])%MOD
r = map(int,stdin.read().split())
n = next(r)
ans = 1
sum = 0
for _ in range(0,n):
x = next(r)
ans = (ans * c[sum+x-1][sum])%MOD
sum += x
print(ans) |
580_B. Kefa and Company_2848 | Kefa wants to celebrate his first big salary by going to restaurant. However, he needs company.
Kefa has n friends, each friend will agree to go to the restaurant if Kefa asks. Each friend is characterized by the amount of money he has and the friendship factor in respect to Kefa. The parrot doesn't want any friend to feel poor compared to somebody else in the company (Kefa doesn't count). A friend feels poor if in the company there is someone who has at least d units of money more than he does. Also, Kefa wants the total friendship factor of the members of the company to be maximum. Help him invite an optimal company!
Input
The first line of the input contains two space-separated integers, n and d (1 ≤ n ≤ 105, <image>) — the number of Kefa's friends and the minimum difference between the amount of money in order to feel poor, respectively.
Next n lines contain the descriptions of Kefa's friends, the (i + 1)-th line contains the description of the i-th friend of type mi, si (0 ≤ mi, si ≤ 109) — the amount of money and the friendship factor, respectively.
Output
Print the maximum total friendship factir that can be reached.
Examples
Input
4 5
75 5
0 100
150 20
75 1
Output
100
Input
5 100
0 7
11 32
99 10
46 8
87 54
Output
111
Note
In the first sample test the most profitable strategy is to form a company from only the second friend. At all other variants the total degree of friendship will be worse.
In the second sample test we can take all the friends. | n, d = map(int, input().split())
v = []
for i in range(0, n):
a, b = map(int, input().split())
v.append((a, b))
v = sorted(v)
lo = 0
totalFriendship = v[0][1]
bestFriendship = totalFriendship
for i in range(1, n):
while v[i][0] - v[lo][0] >= d:
totalFriendship -= v[lo][1]
lo += 1
totalFriendship += v[i][1]
bestFriendship = max(bestFriendship, totalFriendship)
print(bestFriendship)
| {
"input": [
"5 100\n0 7\n11 32\n99 10\n46 8\n87 54\n",
"4 5\n75 5\n0 100\n150 20\n75 1\n",
"5 9\n0 98\n2 1000000000\n8 1000000000\n5 999999999\n3 989898989\n",
"4 1\n2 4\n2 2\n3 3\n3 3\n",
"3 1\n801 10101\n802 134509124\n801 1\n",
"5 6\n5 11\n10 11\n11 11\n12 11\n100 1\n",
"7 6\n5 11\n9 11\n10 11\n11 11\n12 11\n13 11\n100 1\n",
"3 3\n4 15\n0 17\n9 11\n",
"15 1234\n2738 322313356\n1160 970909702\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 650181776\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 9\n2 10\n8 5\n18 12\n1 1\n",
"8 5\n3 227589091\n12 131068951\n8 492784630\n20 918918112\n11 6972428\n20 585402296\n12 220234661\n1 225083234\n",
"5 10\n8 90\n1009 1000000\n9 121\n10 298\n0 109092\n",
"4 2\n1 1\n2 100\n3 100\n4 1\n",
"4 2\n10909234 9\n10909236 8\n10909237 10\n10909235 98\n",
"1 1000000000\n15 12\n",
"5 9\n0 98\n2 1000000000\n8 1000000000\n5 999999999\n3 1489916668\n",
"4 1\n2 4\n2 2\n1 3\n3 3\n",
"3 1\n801 10100\n802 134509124\n801 1\n",
"3 3\n4 15\n0 17\n6 11\n",
"15 1234\n2738 365370390\n1160 970909702\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 650181776\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 9\n2 10\n8 5\n18 13\n1 1\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n20 918918112\n11 6972428\n20 585402296\n12 220234661\n1 225083234\n",
"5 10\n8 90\n1009 1000000\n14 121\n10 298\n0 109092\n",
"1 1000000000\n15 20\n",
"5 100\n0 7\n11 32\n99 10\n46 2\n87 54\n",
"4 5\n75 5\n0 100\n179 20\n75 1\n",
"5 10\n8 90\n1009 1001000\n14 121\n10 298\n0 109092\n",
"5 100\n0 7\n11 32\n168 10\n46 2\n87 54\n",
"4 5\n75 5\n0 110\n179 20\n75 1\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n20 25503219\n11 6972428\n20 585402296\n12 114701518\n1 225083234\n",
"5 100\n0 9\n11 32\n168 10\n46 2\n87 54\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n29 25503219\n11 8756474\n20 585402296\n12 114701518\n1 225083234\n",
"15 1234\n2738 365370390\n1091 680412079\n3762 902749351\n3126 324754476\n5847 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 9\n0 98\n2 1000000000\n8 1000000000\n5 999999999\n3 15331851\n",
"4 1\n2 6\n2 2\n3 3\n3 3\n",
"3 1\n801 10101\n802 246867226\n801 1\n",
"3 3\n4 5\n0 17\n9 11\n",
"15 1234\n2738 322313356\n1160 970909702\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 650181776\n1025 982858164\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 9\n2 3\n8 5\n18 12\n1 1\n",
"4 2\n10909234 9\n10909236 8\n10167263 10\n10909235 98\n",
"1 1000000000\n15 1\n",
"5 100\n0 7\n11 32\n99 10\n46 8\n87 13\n",
"5 9\n0 98\n2 1000000000\n8 0000000000\n5 999999999\n3 1489916668\n",
"3 1\n801 10100\n802 70503936\n801 1\n",
"15 1234\n2738 365370390\n1160 970909702\n2594 145443401\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 650181776\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 9\n2 10\n8 5\n18 25\n1 1\n",
"5 100\n0 7\n11 32\n168 10\n46 3\n87 54\n",
"15 1234\n2738 365370390\n1160 680412079\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n808 142176544\n3595 680519527\n1191 32199940\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n20 25503219\n11 6972428\n20 457192047\n12 114701518\n1 225083234\n",
"15 1234\n2738 365370390\n1160 680412079\n2594 902749351\n3126 347138217\n3151 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"4 1\n2 4\n2 2\n1 6\n3 3\n",
"3 1\n801 10100\n1454 134509124\n801 1\n",
"3 3\n8 15\n0 17\n6 11\n",
"15 1234\n2738 365370390\n1160 970909702\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 3\n2 10\n8 5\n18 13\n1 1\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n20 918918112\n11 6972428\n20 585402296\n12 114701518\n1 225083234\n",
"1 1000000000\n19 20\n",
"2 1\n2 4\n2 2\n1 6\n3 3\n",
"3 2\n801 10100\n1454 134509124\n801 1\n",
"15 1234\n2738 365370390\n1160 680412079\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"4 5\n75 5\n0 110\n179 20\n100 1\n",
"2 1\n2 4\n2 2\n1 6\n3 2\n",
"15 1234\n2738 365370390\n1160 680412079\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"8 5\n3 227589091\n12 131068951\n8 291000839\n20 25503219\n11 8756474\n20 585402296\n12 114701518\n1 225083234\n",
"2 1\n2 4\n2 2\n1 6\n4 2\n",
"15 1234\n2738 365370390\n1160 680412079\n3762 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"15 1234\n2738 365370390\n1091 680412079\n3762 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"8 5\n3 227589091\n12 89525763\n8 291000839\n29 25503219\n11 8756474\n20 585402296\n12 114701518\n1 225083234\n",
"8 5\n3 227589091\n12 89525763\n8 291000839\n29 25503219\n11 8756474\n20 585402296\n12 172711181\n1 225083234\n",
"15 1234\n2738 365370390\n953 680412079\n3762 902749351\n3126 324754476\n5847 177963947\n3424 396145897\n5578 737768323\n3755 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"8 5\n3 227589091\n12 19086443\n8 291000839\n29 25503219\n11 8756474\n20 585402296\n12 172711181\n1 225083234\n",
"8 5\n3 227589091\n12 19086443\n8 291000839\n29 25503219\n9 8756474\n20 585402296\n12 172711181\n1 225083234\n",
"8 5\n3 227589091\n12 19086443\n8 291000839\n58 25503219\n9 8756474\n20 585402296\n12 172711181\n1 225083234\n",
"8 5\n3 227589091\n12 18498253\n8 291000839\n58 25503219\n9 8756474\n20 585402296\n12 172711181\n1 225083234\n",
"8 5\n3 227589091\n12 18498253\n8 291000839\n58 25503219\n9 9933363\n20 585402296\n12 172711181\n1 225083234\n",
"8 5\n3 227589091\n5 131068951\n8 492784630\n20 918918112\n11 6972428\n20 585402296\n12 220234661\n1 225083234\n",
"5 10\n8 90\n1009 1000000\n9 121\n10 298\n-1 109092\n",
"4 5\n75 5\n0 100\n150 20\n75 2\n",
"4 1\n2 4\n2 2\n1 5\n3 3\n",
"3 3\n4 15\n0 25\n6 11\n",
"8 5\n3 227589091\n13 131068951\n8 291000839\n20 918918112\n11 6972428\n20 585402296\n12 220234661\n1 225083234\n",
"5 12\n8 90\n1009 1000000\n14 121\n10 298\n0 109092\n",
"1 1000100000\n15 20\n",
"5 100\n0 7\n11 32\n99 10\n8 2\n87 54\n",
"4 5\n75 5\n0 000\n179 20\n75 1\n",
"4 1\n2 4\n4 2\n1 6\n3 3\n",
"3 1\n801 10100\n1454 134509124\n1510 1\n",
"3 3\n8 15\n1 17\n6 11\n",
"15 1234\n2738 365370390\n1160 68890665\n2594 902749351\n3126 324754476\n3151 177963947\n3424 396145897\n5578 737768323\n3423 687640543\n381 848813098\n1058 197211286\n936 829986595\n1025 776492538\n3598 142176544\n3595 680519527\n1191 32199940\n",
"5 1\n5 3\n2 10\n9 5\n18 13\n1 1\n",
"8 5\n3 227589091\n1 131068951\n8 291000839\n20 918918112\n11 6972428\n20 585402296\n12 114701518\n1 225083234\n",
"5 10\n8 90\n1009 1001000\n11 121\n10 298\n0 109092\n",
"1 1000000000\n19 8\n",
"4 7\n75 5\n0 110\n179 20\n75 1\n",
"3 3\n801 10100\n1454 134509124\n801 1\n",
"5 100\n0 9\n11 32\n151 10\n46 2\n87 54\n",
"4 5\n75 1\n0 110\n179 20\n100 1\n"
],
"output": [
"111",
"100",
"3989899086",
"6",
"134509124",
"33",
"55",
"17",
"3634263641",
"12",
"1504320408",
"1000000",
"200",
"107",
"12",
"4489916765\n",
"6\n",
"134509124\n",
"26\n",
"3677320675\n",
"13\n",
"1504320408\n",
"1000000\n",
"20\n",
"105\n",
"100\n",
"1001000\n",
"95\n",
"110\n",
"610905515\n",
"97\n",
"585402296\n",
"3499356728\n",
"3015331948\n",
"8\n",
"246867226\n",
"17\n",
"3682173966\n",
"12\n",
"107\n",
"1\n",
"70\n",
"3489916765\n",
"70503936\n",
"3475808340\n",
"25\n",
"96\n",
"3535144131\n",
"543743736\n",
"3699704416\n",
"6\n",
"134509124\n",
"26\n",
"3677320675\n",
"13\n",
"1504320408\n",
"20\n",
"6\n",
"134509124\n",
"3677320675\n",
"110\n",
"6\n",
"3677320675\n",
"610905515\n",
"6\n",
"3677320675\n",
"3677320675\n",
"585402296\n",
"585402296\n",
"3499356728\n",
"585402296\n",
"585402296\n",
"585402296\n",
"585402296\n",
"585402296\n",
"1504320408\n",
"1000000\n",
"100\n",
"6\n",
"26\n",
"1504320408\n",
"1000000\n",
"20\n",
"105\n",
"20\n",
"6\n",
"134509124\n",
"26\n",
"3677320675\n",
"13\n",
"1504320408\n",
"1001000\n",
"8\n",
"110\n",
"134509124\n",
"97\n",
"110\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kefa wants to celebrate his first big salary by going to restaurant. However, he needs company.
Kefa has n friends, each friend will agree to go to the restaurant if Kefa asks. Each friend is characterized by the amount of money he has and the friendship factor in respect to Kefa. The parrot doesn't want any friend to feel poor compared to somebody else in the company (Kefa doesn't count). A friend feels poor if in the company there is someone who has at least d units of money more than he does. Also, Kefa wants the total friendship factor of the members of the company to be maximum. Help him invite an optimal company!
Input
The first line of the input contains two space-separated integers, n and d (1 ≤ n ≤ 105, <image>) — the number of Kefa's friends and the minimum difference between the amount of money in order to feel poor, respectively.
Next n lines contain the descriptions of Kefa's friends, the (i + 1)-th line contains the description of the i-th friend of type mi, si (0 ≤ mi, si ≤ 109) — the amount of money and the friendship factor, respectively.
Output
Print the maximum total friendship factir that can be reached.
Examples
Input
4 5
75 5
0 100
150 20
75 1
Output
100
Input
5 100
0 7
11 32
99 10
46 8
87 54
Output
111
Note
In the first sample test the most profitable strategy is to form a company from only the second friend. At all other variants the total degree of friendship will be worse.
In the second sample test we can take all the friends.
### Input:
5 100
0 7
11 32
99 10
46 8
87 54
### Output:
111
### Input:
4 5
75 5
0 100
150 20
75 1
### Output:
100
### Code:
n, d = map(int, input().split())
v = []
for i in range(0, n):
a, b = map(int, input().split())
v.append((a, b))
v = sorted(v)
lo = 0
totalFriendship = v[0][1]
bestFriendship = totalFriendship
for i in range(1, n):
while v[i][0] - v[lo][0] >= d:
totalFriendship -= v[lo][1]
lo += 1
totalFriendship += v[i][1]
bestFriendship = max(bestFriendship, totalFriendship)
print(bestFriendship)
|
602_A. Two Bases_2852 | After seeing the "ALL YOUR BASE ARE BELONG TO US" meme for the first time, numbers X and Y realised that they have different bases, which complicated their relations.
You're given a number X represented in base bx and a number Y represented in base by. Compare those two numbers.
Input
The first line of the input contains two space-separated integers n and bx (1 ≤ n ≤ 10, 2 ≤ bx ≤ 40), where n is the number of digits in the bx-based representation of X.
The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi < bx) — the digits of X. They are given in the order from the most significant digit to the least significant one.
The following two lines describe Y in the same way: the third line contains two space-separated integers m and by (1 ≤ m ≤ 10, 2 ≤ by ≤ 40, bx ≠ by), where m is the number of digits in the by-based representation of Y, and the fourth line contains m space-separated integers y1, y2, ..., ym (0 ≤ yi < by) — the digits of Y.
There will be no leading zeroes. Both X and Y will be positive. All digits of both numbers are given in the standard decimal numeral system.
Output
Output a single character (quotes for clarity):
* '<' if X < Y
* '>' if X > Y
* '=' if X = Y
Examples
Input
6 2
1 0 1 1 1 1
2 10
4 7
Output
=
Input
3 3
1 0 2
2 5
2 4
Output
<
Input
7 16
15 15 4 0 0 7 10
7 9
4 8 0 3 1 5 0
Output
>
Note
In the first sample, X = 1011112 = 4710 = Y.
In the second sample, X = 1023 = 215 and Y = 245 = 1123, thus X < Y.
In the third sample, <image> and Y = 48031509. We may notice that X starts with much larger digits and bx is much larger than by, so X is clearly larger than Y. | # print ("Input digits and base for number one")
n1, b1 = (int(x) for x in input().split())
# print ("Input all the digits")
d1 = list(int(x) for x in input().split())
d1.reverse()
# print ("Input digits and base for number two")
n2, b2 = (int(x) for x in input().split())
# print ("Input all the digits")
d2 = list(int(x) for x in input().split())
d2.reverse()
# Compute base ten representation of number one
answer1 = 0
power1 = 1
for digit in d1:
answer1 += digit*power1
power1 *= b1
# print(answer1)
# Compute base ten representation of number two
answer2 = 0
power2 = 1
for digit in d2:
answer2 += digit*power2
power2 *= b2
# print(answer2)
if answer1 < answer2:
print("<")
elif answer2 < answer1:
print(">")
else:
print("=")
| {
"input": [
"7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0\n",
"3 3\n1 0 2\n2 5\n2 4\n",
"6 2\n1 0 1 1 1 1\n2 10\n4 7\n",
"8 18\n1 1 4 15 7 4 9 3\n8 17\n1 10 2 10 3 11 14 10\n",
"4 7\n3 0 6 6\n3 11\n7 10 10\n",
"2 24\n20 9\n10 23\n21 10 15 11 6 8 20 16 14 11\n",
"10 40\n39 39 39 39 39 39 39 39 39 39\n10 39\n38 38 38 38 38 38 38 38 38 38\n",
"9 7\n2 0 3 2 6 6 1 4 3\n9 6\n4 4 1 1 4 5 5 0 2\n",
"9 39\n10 20 16 36 30 29 28 9 8\n9 38\n12 36 10 22 6 3 19 12 34\n",
"5 2\n1 0 0 0 1\n6 8\n1 4 7 2 0 0\n",
"2 6\n5 5\n2 34\n1 0\n",
"7 5\n4 0 4 1 3 0 4\n4 35\n1 18 7 34\n",
"2 35\n1 0\n2 6\n5 5\n",
"10 23\n5 21 4 15 12 7 10 7 16 21\n4 17\n3 11 1 14\n",
"5 37\n9 9 9 9 9\n6 27\n13 0 0 0 0 0\n",
"7 22\n1 13 9 16 7 13 3\n4 4\n3 0 2 1\n",
"1 36\n35\n4 5\n2 4 4 1\n",
"2 2\n1 0\n1 3\n1\n",
"3 5\n1 0 0\n3 3\n2 2 2\n",
"10 40\n1 1 14 5 6 3 3 11 3 25\n10 39\n1 11 24 33 25 34 38 29 27 33\n",
"6 7\n1 1 2 1 2 1\n6 6\n2 3 2 2 2 2\n",
"5 37\n29 29 5 7 27\n3 39\n13 1 10\n",
"6 4\n1 1 1 2 2 2\n7 3\n1 2 2 0 1 0 0\n",
"8 8\n4 0 4 3 4 1 5 6\n8 24\n19 8 15 6 10 7 2 18\n",
"6 29\n1 1 1 1 1 1\n10 21\n1 1 1 1 1 1 1 1 1 1\n",
"10 29\n15 22 0 5 11 12 17 22 4 27\n4 22\n9 2 8 14\n",
"7 39\n28 16 13 25 19 23 4\n7 38\n33 8 2 19 3 21 14\n",
"2 19\n4 8\n8 18\n7 8 6 8 4 11 9 1\n",
"2 40\n22 38\n5 39\n8 9 32 4 1\n",
"8 36\n23 5 27 1 10 7 26 27\n10 35\n28 33 9 22 10 28 26 4 27 29\n",
"10 40\n18 1 2 25 28 2 10 2 17 37\n10 39\n37 8 12 8 21 11 23 11 25 21\n",
"8 21\n5 19 0 14 13 13 10 5\n10 13\n1 0 0 6 11 10 8 2 8 1\n",
"2 4\n3 3\n2 15\n1 0\n",
"10 6\n3 5 4 2 4 2 3 5 4 2\n10 7\n3 2 1 1 3 1 0 3 4 5\n",
"1 22\n15\n10 14\n3 3 3 3 3 3 3 3 3 3\n",
"10 29\n10 19 8 27 1 24 13 15 13 26\n2 28\n20 14\n",
"5 5\n4 4 4 4 4\n4 6\n5 5 5 5\n",
"2 29\n11 11\n6 26\n11 11 11 11 11 11\n",
"10 3\n1 0 0 0 0 0 0 0 0 0\n8 13\n1 0 0 0 0 0 0 0\n",
"10 16\n15 15 4 0 0 0 0 7 10 9\n10 9\n4 8 0 3 1 5 4 8 1 0\n",
"9 37\n1 35 7 33 20 21 26 24 5\n10 40\n39 4 11 9 33 12 26 32 11 8\n",
"10 40\n39 39 39 39 39 39 39 39 39 39\n10 8\n7 7 7 7 7 7 7 7 7 7\n",
"6 26\n7 6 4 18 6 1\n6 25\n5 3 11 1 8 15\n",
"2 8\n1 0\n4 2\n1 0 0 0\n",
"4 22\n18 16 1 2\n10 26\n23 0 12 24 16 2 24 25 1 11\n",
"7 28\n1 10 7 0 13 14 11\n6 38\n8 11 27 5 14 35\n",
"3 3\n1 0 2\n2 5\n2 4\n",
"2 24\n4 18\n2 40\n29 24\n",
"3 39\n27 4 3\n8 38\n32 15 11 34 35 27 30 15\n",
"3 2\n1 1 1\n1 3\n1\n",
"9 3\n1 0 0 1 1 0 0 1 2\n6 4\n1 2 0 1 3 2\n",
"9 40\n39 39 39 39 39 39 39 39 39\n6 35\n34 34 34 34 34 34\n",
"7 26\n8 0 0 0 0 0 0\n9 9\n3 3 3 3 3 3 3 3 3\n",
"1 8\n5\n9 27\n23 23 23 23 23 23 23 23 23\n",
"7 31\n14 6 16 6 26 18 17\n7 24\n22 10 4 5 14 6 9\n",
"2 37\n25 2\n3 26\n13 13 12\n",
"1 40\n1\n2 5\n1 0\n",
"10 36\n1 13 13 23 31 35 5 32 18 21\n9 38\n32 1 20 14 12 37 13 15 23\n",
"10 38\n16 19 37 32 16 7 14 33 16 11\n10 39\n10 27 35 15 31 15 17 16 38 35\n",
"9 9\n2 2 3 6 3 6 3 8 4\n6 10\n4 7 7 0 3 8\n",
"9 34\n5 8 4 4 26 1 30 5 24\n10 27\n1 6 3 10 8 13 22 3 12 8\n",
"5 3\n1 0 0 0 0\n4 27\n1 0 0 0\n",
"6 19\n4 9 14 1 3 1\n8 10\n1 1 1 7 3 7 3 0\n",
"5 35\n22 18 28 29 11\n2 3\n2 0\n",
"1 30\n1\n1 31\n1\n",
"10 39\n34 2 24 34 11 6 33 12 22 21\n10 36\n25 35 17 24 30 0 1 32 14 35\n",
"2 7\n1 0\n2 3\n2 2\n",
"4 5\n1 4 2 0\n4 4\n3 2 2 3\n",
"3 5\n2 2 3\n3 6\n4 3 5\n",
"7 34\n21 22 28 16 30 4 27\n7 26\n5 13 21 10 8 12 10\n",
"1 3\n1\n1 2\n1\n",
"6 37\n22 15 14 10 1 8\n6 36\n18 5 28 10 1 17\n",
"3 11\n6 5 2\n8 10\n5 0 1 8 3 5 1 4\n",
"10 22\n3 3 3 3 3 3 3 3 3 3\n3 40\n19 19 19\n",
"10 39\n35 12 31 35 28 27 25 8 22 25\n10 40\n23 21 18 12 15 29 38 32 4 8\n",
"8 26\n6 6 17 25 24 8 8 25\n4 27\n24 7 5 24\n",
"10 16\n15 15 4 0 0 0 0 7 10 9\n7 9\n4 8 0 3 1 5 0\n",
"9 35\n34 3 20 29 27 30 2 8 5\n7 33\n17 3 22 31 1 11 6\n",
"2 8\n4 1\n1 7\n1\n",
"1 24\n6\n3 9\n1 1 1\n",
"2 10\n6 0\n10 26\n16 14 8 18 24 4 9 5 22 25\n",
"3 5\n1 1 3\n10 4\n3 3 2 3 0 0 0 3 1 1\n",
"7 15\n8 5 8 10 13 6 13\n8 13\n1 6 9 10 12 3 12 8\n",
"6 11\n10 6 1 0 2 2\n9 10\n4 3 4 1 1 6 3 4 1\n",
"7 2\n1 0 0 0 1 0 1\n9 6\n1 1 5 1 2 5 3 5 3\n",
"6 4\n3 3 2 2 0 2\n6 5\n1 1 1 1 0 3\n",
"2 9\n5 5\n4 3\n1 0 0 0\n",
"6 5\n4 4 4 3 1 3\n7 6\n4 2 2 2 5 0 4\n",
"4 4\n1 3 1 3\n9 3\n1 1 0 1 2 2 2 2 1\n",
"1 30\n9\n7 37\n20 11 18 14 0 36 27\n",
"2 12\n1 4\n8 16\n4 4 10 6 15 10 8 15\n",
"2 34\n1 32\n2 33\n2 0\n",
"4 20\n1 1 1 1\n5 22\n1 1 1 1 1\n",
"5 38\n1 31 2 21 21\n9 37\n8 36 32 30 13 9 24 2 35\n",
"7 29\n14 26 14 22 11 11 8\n6 28\n2 12 10 17 0 14\n",
"4 39\n13 25 23 35\n6 38\n19 36 20 4 12 33\n",
"2 8\n1 0\n2 3\n2 2\n",
"6 16\n4 9 13 4 2 8\n4 10\n3 5 2 4\n",
"1 2\n1\n1 40\n1\n",
"10 31\n6 27 17 22 14 16 25 9 13 26\n10 39\n6 1 3 26 12 32 28 19 9 19\n",
"2 40\n2 0\n5 13\n4 0 0 0 0\n",
"1 7\n2\n4 8\n3 2 3 2\n",
"5 38\n2 24 34 14 17\n8 34\n4 24 31 2 14 15 8 15\n",
"8 28\n3 1 10 19 10 14 21 15\n8 21\n14 0 18 13 2 1 18 6\n",
"1 10\n7\n3 9\n2 1 7\n",
"10 2\n1 1 1 1 1 1 1 1 1 1\n10 34\n14 14 14 14 14 14 14 14 14 14\n",
"10 21\n4 7 7 2 13 7 19 19 18 19\n3 31\n6 11 28\n",
"10 2\n1 0 1 0 1 0 1 0 1 0\n10 3\n2 2 2 2 2 2 2 2 2 2\n",
"7 3\n1 1 2 1 2 0 2\n2 2\n1 0\n",
"3 9\n2 5 4\n1 19\n15\n",
"2 5\n3 3\n5 2\n1 0 0 1 0\n",
"3 19\n9 18 16\n4 10\n4 3 5 4\n",
"2 5\n3 3\n6 6\n4 2 0 1 1 0\n",
"1 9\n2\n1 10\n2\n",
"7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0\n",
"10 39\n20 12 10 32 24 14 37 35 10 38\n9 40\n1 13 0 10 22 20 1 5 35\n",
"9 37\n2 6 1 9 19 6 11 28 35\n9 40\n1 6 14 37 1 8 31 4 9\n",
"6 16\n2 13 7 13 15 6\n10 22\n17 17 21 9 16 11 4 4 13 17\n",
"2 2\n1 0\n2 3\n1 0\n",
"2 2\n1 0\n1 3\n2\n",
"8 18\n1 1 4 15 7 4 9 3\n8 17\n0 10 2 10 3 11 14 10\n",
"2 24\n20 9\n10 23\n21 10 15 11 6 8 12 16 14 11\n",
"1 8\n2\n1 10\n2\n",
"4 7\n3 0 6 6\n3 11\n7 10 9\n",
"10 40\n39 39 39 14 39 39 39 39 39 39\n10 39\n38 38 38 38 38 38 38 38 38 38\n",
"9 7\n2 0 5 2 6 6 1 4 3\n9 6\n4 4 1 1 4 5 5 0 2\n",
"9 39\n10 21 16 36 30 29 28 9 8\n9 38\n12 36 10 22 6 3 19 12 34\n",
"5 2\n1 0 1 0 1\n6 8\n1 4 7 2 0 0\n",
"2 6\n5 5\n2 30\n1 0\n",
"7 5\n4 0 4 1 3 0 4\n4 35\n1 18 6 34\n",
"2 35\n1 1\n2 6\n5 5\n",
"5 37\n10 9 9 9 9\n6 27\n13 0 0 0 0 0\n",
"7 22\n0 13 9 16 7 13 3\n4 4\n3 0 2 1\n",
"3 5\n2 0 0\n3 3\n2 2 2\n",
"6 7\n1 1 2 1 2 1\n6 6\n2 3 2 2 2 1\n",
"5 37\n29 29 5 7 27\n3 39\n13 1 16\n",
"6 4\n1 1 1 2 2 2\n7 1\n1 2 2 0 1 0 0\n",
"8 8\n4 0 4 3 4 1 5 6\n8 24\n19 8 15 6 10 7 1 18\n",
"6 29\n1 1 1 1 1 1\n10 21\n1 1 1 1 1 1 1 1 0 1\n",
"10 29\n15 8 0 5 11 12 17 22 4 27\n4 22\n9 2 8 14\n",
"7 39\n28 16 13 25 19 28 4\n7 38\n33 8 2 19 3 21 14\n",
"1 19\n4 8\n8 18\n7 8 6 8 4 11 9 1\n",
"2 40\n22 38\n5 25\n8 9 32 4 1\n",
"8 36\n23 5 27 1 10 7 26 27\n10 35\n28 33 16 22 10 28 26 4 27 29\n",
"10 40\n18 1 2 25 28 2 10 2 17 8\n10 39\n37 8 12 8 21 11 23 11 25 21\n",
"8 21\n5 19 0 14 13 15 10 5\n10 13\n1 0 0 6 11 10 8 2 8 1\n",
"10 6\n3 5 4 2 4 2 3 5 4 2\n10 7\n3 1 1 1 3 1 0 3 4 5\n",
"1 22\n15\n10 14\n3 3 3 3 3 3 3 3 0 3\n",
"10 29\n18 19 8 27 1 24 13 15 13 26\n2 28\n20 14\n",
"2 29\n11 11\n6 26\n11 10 11 11 11 11\n",
"10 3\n1 0 0 1 0 0 0 0 0 0\n8 13\n1 0 0 0 0 0 0 0\n",
"10 16\n15 15 4 0 0 0 0 7 10 9\n10 9\n5 8 0 3 1 5 4 8 1 0\n",
"9 31\n1 35 7 33 20 21 26 24 5\n10 40\n39 4 11 9 33 12 26 32 11 8\n",
"10 40\n39 39 39 39 39 39 39 39 39 39\n10 8\n14 7 7 7 7 7 7 7 7 7\n",
"6 26\n7 6 4 18 11 1\n6 25\n5 3 11 1 8 15\n",
"4 22\n18 16 1 2\n10 26\n23 0 22 24 16 2 24 25 1 11\n",
"7 28\n1 10 7 0 13 14 11\n6 70\n8 11 27 5 14 35\n",
"3 3\n1 0 1\n2 5\n2 4\n",
"2 24\n4 18\n2 40\n29 1\n",
"7 26\n8 0 0 0 0 0 0\n9 9\n3 3 3 3 3 2 3 3 3\n",
"1 8\n5\n9 27\n23 23 23 23 23 23 36 23 23\n",
"7 31\n14 6 16 6 26 18 17\n7 24\n22 2 4 5 14 6 9\n",
"2 37\n25 2\n3 19\n13 13 12\n",
"1 40\n2\n2 5\n1 0\n",
"10 38\n16 19 37 32 16 7 14 33 5 11\n10 39\n10 27 35 15 31 15 17 16 38 35\n",
"9 9\n2 2 3 6 2 6 3 8 4\n6 10\n4 7 7 0 3 8\n",
"9 34\n5 8 4 4 26 1 30 5 24\n10 40\n1 6 3 10 8 13 22 3 12 8\n",
"6 19\n4 9 14 1 3 1\n8 10\n1 1 1 7 3 7 2 0\n",
"5 35\n22 21 28 29 11\n2 3\n2 0\n",
"10 39\n34 3 24 34 11 6 33 12 22 21\n10 36\n25 35 17 24 30 0 1 32 14 35\n",
"4 5\n1 4 2 0\n4 4\n3 2 3 3\n",
"3 5\n2 2 3\n3 6\n4 3 9\n",
"7 34\n21 22 28 16 30 4 10\n7 26\n5 13 21 10 8 12 10\n",
"6 37\n22 15 14 10 1 8\n6 36\n18 5 28 16 1 17\n",
"10 22\n3 3 3 3 3 3 3 3 3 4\n3 40\n19 19 19\n",
"10 39\n35 12 31 35 28 27 35 8 22 25\n10 40\n23 21 18 12 15 29 38 32 4 8\n",
"10 16\n15 15 4 0 0 0 0 7 10 9\n7 9\n4 8 1 3 1 5 0\n",
"9 35\n34 3 20 29 27 30 2 6 5\n7 33\n17 3 22 31 1 11 6\n",
"2 8\n4 0\n1 7\n1\n",
"1 24\n6\n3 9\n0 1 1\n",
"2 10\n6 0\n10 41\n16 14 8 18 24 4 9 5 22 25\n",
"3 5\n1 1 3\n10 8\n3 3 2 3 0 0 0 3 1 1\n",
"7 15\n8 5 8 10 13 6 13\n8 13\n1 6 0 10 12 3 12 8\n",
"6 11\n10 6 1 0 2 2\n9 10\n4 3 4 1 1 9 3 4 1\n",
"7 3\n1 0 0 0 1 0 1\n9 6\n1 1 5 1 2 5 3 5 3\n",
"6 7\n3 3 2 2 0 2\n6 5\n1 1 1 1 0 3\n",
"6 5\n4 4 4 3 1 3\n7 6\n4 2 2 2 5 0 8\n",
"4 4\n1 3 1 3\n9 3\n1 1 0 1 2 2 2 2 0\n",
"1 30\n9\n7 37\n20 11 18 14 0 26 27\n",
"2 12\n1 4\n8 16\n4 4 10 6 15 10 4 15\n",
"2 23\n1 32\n2 33\n2 0\n",
"4 20\n0 1 1 1\n5 22\n1 1 1 1 1\n",
"5 38\n1 31 2 21 21\n9 37\n8 36 32 30 13 9 24 3 35\n",
"7 29\n14 26 14 22 11 11 8\n6 28\n2 12 10 17 0 7\n",
"4 36\n13 25 23 35\n6 38\n19 36 20 4 12 33\n",
"2 8\n1 0\n2 3\n1 2\n",
"6 16\n4 9 13 4 2 8\n4 10\n3 6 2 4\n",
"1 7\n2\n4 7\n3 2 3 2\n",
"5 38\n0 24 34 14 17\n8 34\n4 24 31 2 14 15 8 15\n",
"1 8\n7\n3 9\n2 1 7\n",
"10 2\n1 1 1 1 1 1 1 1 1 1\n10 34\n14 14 14 25 14 14 14 14 14 14\n",
"10 21\n4 7 7 2 11 7 19 19 18 19\n3 31\n6 11 28\n",
"10 2\n1 0 1 0 1 0 1 0 1 0\n10 3\n2 4 2 2 2 2 2 2 2 2\n",
"3 17\n2 5 4\n1 19\n15\n",
"3 19\n9 18 16\n4 10\n4 3 5 6\n",
"7 16\n20 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0\n",
"9 37\n2 6 1 9 19 2 11 28 35\n9 40\n1 6 14 37 1 8 31 4 9\n",
"6 16\n2 13 7 13 15 6\n10 22\n17 17 21 3 16 11 4 4 13 17\n",
"2 4\n1 0\n2 3\n1 0\n",
"2 2\n1 0\n1 6\n2\n",
"7 16\n15 15 4 0 0 7 10\n7 9\n4 12 0 3 1 5 0\n",
"3 3\n1 0 2\n2 2\n2 4\n",
"6 2\n1 0 1 1 1 1\n2 10\n4 11\n",
"8 18\n1 1 4 15 7 4 9 3\n8 17\n0 10 1 10 3 11 14 10\n",
"4 2\n3 0 6 6\n3 11\n7 10 9\n"
],
"output": [
">",
"<",
"=",
"=",
">",
"<",
">",
">",
"=",
"<",
">",
"=",
"=",
">",
"<",
">",
"<",
">",
"<",
"=",
"=",
">",
"=",
"<",
"<",
">",
"=",
"<",
"<",
"<",
"<",
"=",
"=",
"<",
"<",
">",
">",
"<",
"<",
">",
"<",
">",
">",
"=",
"<",
"=",
"<",
"<",
"<",
">",
">",
">",
">",
"<",
">",
"<",
"<",
"=",
">",
">",
"=",
"<",
"=",
">",
"=",
">",
"<",
"=",
"<",
">",
"=",
">",
"<",
">",
">",
">",
">",
">",
">",
"<",
"<",
"<",
"=",
"<",
"<",
">",
">",
"<",
"<",
"<",
"<",
"=",
"<",
"<",
">",
"<",
"=",
">",
"=",
"<",
"<",
"<",
"<",
">",
"<",
"<",
">",
"<",
">",
">",
"=",
"<",
"<",
"=",
">",
">",
"=",
"<",
"<",
"=",
">\n",
"<\n",
"=\n",
">\n",
">\n",
">\n",
">\n",
"<\n",
">\n",
">\n",
">\n",
"<\n",
">\n",
">\n",
">\n",
">\n",
">\n",
"<\n",
"<\n",
">\n",
">\n",
"<\n",
"<\n",
"<\n",
"<\n",
">\n",
"<\n",
"<\n",
">\n",
"<\n",
"<\n",
">\n",
"<\n",
">\n",
">\n",
"<\n",
"<\n",
"<\n",
"<\n",
">\n",
"<\n",
">\n",
"<\n",
"<\n",
">\n",
">\n",
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">\n",
">\n",
">\n",
"<\n",
"<\n",
">\n",
">\n",
">\n",
">\n",
">\n",
">\n",
">\n",
"<\n",
"<\n",
"<\n",
">\n",
"<\n",
"<\n",
">\n",
"<\n",
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"<\n",
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"<\n",
">\n",
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">\n",
">\n",
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">\n",
"<\n",
">\n",
"<\n",
">\n",
"<\n",
"<\n",
">\n",
"=\n",
">\n",
">\n",
"<\n",
">\n",
"<\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
After seeing the "ALL YOUR BASE ARE BELONG TO US" meme for the first time, numbers X and Y realised that they have different bases, which complicated their relations.
You're given a number X represented in base bx and a number Y represented in base by. Compare those two numbers.
Input
The first line of the input contains two space-separated integers n and bx (1 ≤ n ≤ 10, 2 ≤ bx ≤ 40), where n is the number of digits in the bx-based representation of X.
The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi < bx) — the digits of X. They are given in the order from the most significant digit to the least significant one.
The following two lines describe Y in the same way: the third line contains two space-separated integers m and by (1 ≤ m ≤ 10, 2 ≤ by ≤ 40, bx ≠ by), where m is the number of digits in the by-based representation of Y, and the fourth line contains m space-separated integers y1, y2, ..., ym (0 ≤ yi < by) — the digits of Y.
There will be no leading zeroes. Both X and Y will be positive. All digits of both numbers are given in the standard decimal numeral system.
Output
Output a single character (quotes for clarity):
* '<' if X < Y
* '>' if X > Y
* '=' if X = Y
Examples
Input
6 2
1 0 1 1 1 1
2 10
4 7
Output
=
Input
3 3
1 0 2
2 5
2 4
Output
<
Input
7 16
15 15 4 0 0 7 10
7 9
4 8 0 3 1 5 0
Output
>
Note
In the first sample, X = 1011112 = 4710 = Y.
In the second sample, X = 1023 = 215 and Y = 245 = 1123, thus X < Y.
In the third sample, <image> and Y = 48031509. We may notice that X starts with much larger digits and bx is much larger than by, so X is clearly larger than Y.
### Input:
7 16
15 15 4 0 0 7 10
7 9
4 8 0 3 1 5 0
### Output:
>
### Input:
3 3
1 0 2
2 5
2 4
### Output:
<
### Code:
# print ("Input digits and base for number one")
n1, b1 = (int(x) for x in input().split())
# print ("Input all the digits")
d1 = list(int(x) for x in input().split())
d1.reverse()
# print ("Input digits and base for number two")
n2, b2 = (int(x) for x in input().split())
# print ("Input all the digits")
d2 = list(int(x) for x in input().split())
d2.reverse()
# Compute base ten representation of number one
answer1 = 0
power1 = 1
for digit in d1:
answer1 += digit*power1
power1 *= b1
# print(answer1)
# Compute base ten representation of number two
answer2 = 0
power2 = 1
for digit in d2:
answer2 += digit*power2
power2 *= b2
# print(answer2)
if answer1 < answer2:
print("<")
elif answer2 < answer1:
print(">")
else:
print("=")
|
673_A. Bear and Game_2858 | Bear Limak likes watching sports on TV. He is going to watch a game today. The game lasts 90 minutes and there are no breaks.
Each minute can be either interesting or boring. If 15 consecutive minutes are boring then Limak immediately turns TV off.
You know that there will be n interesting minutes t1, t2, ..., tn. Your task is to calculate for how many minutes Limak will watch the game.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 90) — the number of interesting minutes.
The second line contains n integers t1, t2, ..., tn (1 ≤ t1 < t2 < ... tn ≤ 90), given in the increasing order.
Output
Print the number of minutes Limak will watch the game.
Examples
Input
3
7 20 88
Output
35
Input
9
16 20 30 40 50 60 70 80 90
Output
15
Input
9
15 20 30 40 50 60 70 80 90
Output
90
Note
In the first sample, minutes 21, 22, ..., 35 are all boring and thus Limak will turn TV off immediately after the 35-th minute. So, he would watch the game for 35 minutes.
In the second sample, the first 15 minutes are boring.
In the third sample, there are no consecutive 15 boring minutes. So, Limak will watch the whole game. | n=int(input())
tl = list(map(int, input().split()))
time=cnt=0
while cnt <15 and time<90:
time+=1
if tl.count(time)>0:
cnt=0
else:
cnt+=1
print(time) | {
"input": [
"3\n7 20 88\n",
"9\n15 20 30 40 50 60 70 80 90\n",
"9\n16 20 30 40 50 60 70 80 90\n",
"2\n1 18\n",
"9\n6 20 27 28 40 53 59 70 85\n",
"8\n10 20 30 40 50 60 70 80\n",
"6\n13 17 32 47 60 66\n",
"1\n1\n",
"8\n5 17 20 35 42 53 67 76\n",
"1\n90\n",
"6\n14 29 43 59 70 74\n",
"76\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90\n",
"8\n15 20 30 40 50 60 73 83\n",
"14\n14 22 27 31 35 44 46 61 62 69 74 79 88 89\n",
"30\n6 11 12 15 22 24 30 31 32 33 34 35 40 42 44 45 47 50 53 54 57 58 63 67 75 77 79 81 83 88\n",
"84\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84\n",
"6\n15 30 45 60 74 89\n",
"9\n15 28 39 48 55 60 63 64 74\n",
"1\n15\n",
"9\n10 20 30 40 50 60 70 80 84\n",
"25\n1 2 3 4 5 6 7 8 9 10 11 23 36 50 65 81 82 83 84 85 86 87 88 89 90\n",
"5\n15 30 45 60 74\n",
"2\n16 50\n",
"12\n14 22 27 31 35 44 62 69 74 79 88 89\n",
"10\n15 28 39 48 55 60 63 64 74 82\n",
"60\n1 2 4 5 6 7 11 14 16 18 20 21 22 23 24 25 26 33 34 35 36 37 38 39 41 42 43 44 46 47 48 49 52 55 56 57 58 59 60 61 63 64 65 67 68 70 71 72 73 74 75 77 78 80 82 83 84 85 86 88\n",
"6\n15 30 45 60 75 84\n",
"90\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90\n",
"3\n1 20 90\n",
"8\n1 16 30 31 32 33 34 50\n",
"72\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89\n",
"12\n1 3 6 10 15 21 28 36 45 55 66 78\n",
"1\n16\n",
"5\n15 30 45 60 75\n",
"9\n6 20 27 28 40 53 59 70 79\n",
"6\n25 17 32 47 60 66\n",
"1\n5\n",
"6\n14 21 43 59 70 74\n",
"1\n9\n",
"2\n13 50\n",
"6\n12 30 45 60 75 84\n",
"72\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 55 56 57 58 59 59 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89\n",
"1\n3\n",
"5\n15 30 45 66 75\n",
"3\n7 39 88\n",
"1\n11\n",
"5\n15 16 45 66 75\n",
"9\n2 20 30 40 50 60 70 80 20\n",
"1\n4\n",
"1\n8\n",
"12\n14 22 27 31 35 71 62 69 74 79 88 89\n",
"6\n15 30 45 60 84 84\n",
"3\n1 20 22\n",
"1\n10\n",
"6\n14 22 43 59 70 74\n",
"1\n6\n",
"6\n16 30 45 60 74 89\n",
"12\n1 4 6 10 15 21 28 36 45 55 66 78\n",
"9\n15 24 30 40 50 60 70 80 90\n",
"9\n16 20 30 40 50 60 70 80 20\n",
"6\n25 17 32 47 60 83\n",
"1\n7\n",
"6\n16 30 45 29 74 89\n",
"6\n12 39 45 60 75 84\n",
"3\n7 39 90\n",
"9\n15 24 30 43 50 60 70 80 90\n",
"6\n25 17 47 47 60 83\n",
"1\n2\n",
"6\n16 30 45 29 83 89\n",
"5\n15 16 21 66 75\n",
"3\n7 39 62\n",
"6\n25 29 47 47 60 83\n",
"6\n16 30 45 29 83 77\n",
"5\n15 16 21 44 75\n",
"3\n7 39 24\n",
"6\n25 29 47 47 17 83\n",
"6\n16 30 45 56 83 77\n",
"5\n11 16 21 44 75\n",
"3\n7 39 42\n",
"3\n7 62 42\n",
"3\n13 62 42\n",
"3\n13 72 42\n",
"3\n19 72 42\n",
"3\n19 80 42\n",
"3\n38 80 42\n",
"3\n38 80 74\n",
"3\n35 80 74\n",
"3\n68 80 74\n",
"3\n68 80 17\n",
"3\n68 88 17\n",
"3\n68 86 17\n",
"3\n53 86 17\n",
"3\n27 86 17\n",
"3\n27 86 29\n",
"3\n27 67 29\n",
"3\n36 67 29\n",
"3\n17 67 29\n",
"3\n17 67 22\n",
"2\n2 18\n",
"1\n13\n",
"5\n9 30 45 60 74\n",
"2\n23 50\n",
"8\n1 8 30 31 32 33 34 50\n",
"12\n1 3 2 10 15 21 28 36 45 55 66 78\n",
"5\n22 30 45 60 75\n",
"3\n7 40 88\n",
"9\n16 20 30 36 50 60 70 80 90\n",
"9\n6 18 27 28 40 53 59 70 79\n",
"6\n25 17 22 47 60 66\n",
"6\n16 30 45 60 74 58\n",
"2\n12 50\n",
"6\n12 30 45 69 75 84\n",
"72\n3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 55 56 57 58 59 59 61 62 63 64 65 66 67 68 62 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89\n",
"9\n15 24 30 40 50 60 76 80 90\n",
"1\n20\n",
"6\n18 30 45 29 74 89\n",
"6\n12 39 45 49 75 84\n",
"3\n3 39 90\n"
],
"output": [
"35\n",
"90\n",
"15\n",
"16\n",
"90\n",
"90\n",
"81\n",
"16\n",
"90\n",
"15\n",
"58\n",
"90\n",
"90\n",
"90\n",
"90\n",
"90\n",
"90\n",
"89\n",
"30\n",
"90\n",
"80\n",
"89\n",
"15\n",
"59\n",
"90\n",
"90\n",
"90\n",
"90\n",
"16\n",
"49\n",
"54\n",
"90\n",
"15\n",
"90\n",
"90\n",
"15\n",
"20\n",
"36\n",
"24\n",
"28\n",
"27\n",
"54\n",
"18\n",
"60\n",
"22\n",
"26\n",
"31\n",
"17\n",
"19\n",
"23\n",
"50\n",
"75\n",
"16\n",
"25\n",
"37\n",
"21\n",
"15\n",
"90\n",
"90\n",
"15\n",
"15\n",
"22\n",
"15\n",
"27\n",
"22\n",
"90\n",
"15\n",
"17\n",
"15\n",
"36\n",
"22\n",
"15\n",
"15\n",
"36\n",
"22\n",
"15\n",
"15\n",
"36\n",
"22\n",
"22\n",
"28\n",
"28\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"15\n",
"17\n",
"28\n",
"24\n",
"15\n",
"23\n",
"90\n",
"15\n",
"22\n",
"15\n",
"90\n",
"15\n",
"15\n",
"27\n",
"27\n",
"54\n",
"75\n",
"15\n",
"15\n",
"27\n",
"18\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bear Limak likes watching sports on TV. He is going to watch a game today. The game lasts 90 minutes and there are no breaks.
Each minute can be either interesting or boring. If 15 consecutive minutes are boring then Limak immediately turns TV off.
You know that there will be n interesting minutes t1, t2, ..., tn. Your task is to calculate for how many minutes Limak will watch the game.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 90) — the number of interesting minutes.
The second line contains n integers t1, t2, ..., tn (1 ≤ t1 < t2 < ... tn ≤ 90), given in the increasing order.
Output
Print the number of minutes Limak will watch the game.
Examples
Input
3
7 20 88
Output
35
Input
9
16 20 30 40 50 60 70 80 90
Output
15
Input
9
15 20 30 40 50 60 70 80 90
Output
90
Note
In the first sample, minutes 21, 22, ..., 35 are all boring and thus Limak will turn TV off immediately after the 35-th minute. So, he would watch the game for 35 minutes.
In the second sample, the first 15 minutes are boring.
In the third sample, there are no consecutive 15 boring minutes. So, Limak will watch the whole game.
### Input:
3
7 20 88
### Output:
35
### Input:
9
15 20 30 40 50 60 70 80 90
### Output:
90
### Code:
n=int(input())
tl = list(map(int, input().split()))
time=cnt=0
while cnt <15 and time<90:
time+=1
if tl.count(time)>0:
cnt=0
else:
cnt+=1
print(time) |
698_B. Fix a Tree_2862 | A tree is an undirected connected graph without cycles.
Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).
<image> For this rooted tree the array p is [2, 3, 3, 2].
Given a sequence p1, p2, ..., pn, one is able to restore a tree:
1. There must be exactly one index r that pr = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex pi.
A sequence p1, p2, ..., pn is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.
You are given a sequence a1, a2, ..., an, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).
Output
In the first line print the minimum number of elements to change, in order to get a valid sequence.
In the second line, print any valid sequence possible to get from (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.
Examples
Input
4
2 3 3 4
Output
1
2 3 4 4
Input
5
3 2 2 5 3
Output
0
3 2 2 5 3
Input
8
2 3 5 4 1 6 6 7
Output
2
2 3 7 8 1 6 6 7
Note
In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because p4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.
<image>
In the second sample, the given sequence is already valid. | from collections import defaultdict
from sys import stdin,setrecursionlimit
setrecursionlimit(10**6)
import threading
def f(a):
n=len(a)
a=list(map(lambda s:s-1,a))
root=None
for i in range(len(a)):
if a[i]==i:
root=i
vis=[0]*(n)
traitors=[]
for i in range(0,n):
cycle=-1
cur=i
move=set()
while vis[cur]==0:
vis[cur]=1
move.add(cur)
if a[cur] in move:
cycle=cur
cur=a[cur]
if cycle!=-1:
traitors.append(cycle)
ans=len(traitors)-1
if root==None:
a[traitors[0]]=traitors[0]
root=traitors[0]
ans+=1
for i in traitors:
if i!=root:
a[i]=root
print(ans)
a=list(map(lambda s:s+1,a))
return a
n=input()
a=list(map(int,input().strip().split()))
print(*f(a)) | {
"input": [
"5\n3 2 2 5 3\n",
"8\n2 3 5 4 1 6 6 7\n",
"4\n2 3 3 4\n",
"3\n2 1 1\n",
"6\n6 2 6 2 4 2\n",
"2\n1 2\n",
"8\n2 1 2 2 6 5 6 6\n",
"18\n2 3 4 5 2 7 8 9 10 7 11 12 14 15 13 17 18 18\n",
"7\n1 2 3 4 5 6 7\n",
"7\n4 3 2 6 3 5 2\n",
"7\n7 5 3 1 2 1 5\n",
"7\n1 6 4 4 5 6 7\n",
"6\n6 2 1 2 4 2\n",
"7\n1 2 3 4 5 1 7\n",
"7\n4 3 2 6 5 5 2\n",
"7\n1 2 3 4 7 1 7\n",
"7\n4 3 1 6 5 5 2\n",
"7\n1 2 3 7 7 1 7\n",
"6\n3 2 6 2 4 2\n",
"2\n2 2\n",
"8\n2 1 2 2 6 5 6 2\n",
"7\n7 5 3 1 4 1 5\n",
"4\n3 3 3 4\n",
"7\n1 2 3 4 5 1 4\n",
"7\n4 3 2 6 5 5 3\n",
"7\n4 3 1 6 5 2 2\n",
"7\n4 1 1 6 5 2 2\n",
"7\n1 2 3 1 5 1 4\n",
"7\n4 1 1 6 5 3 2\n",
"7\n4 1 1 6 4 3 2\n",
"7\n4 1 1 6 4 3 1\n",
"7\n7 1 2 6 4 3 1\n",
"7\n7 1 2 6 4 3 2\n",
"7\n7 2 2 6 4 3 2\n",
"7\n7 4 2 6 4 3 2\n",
"3\n2 2 1\n",
"18\n2 3 4 5 2 7 8 9 2 7 11 12 14 15 13 17 18 18\n",
"7\n1 2 3 5 5 6 7\n",
"7\n4 3 2 7 3 5 2\n",
"7\n7 5 3 1 2 1 6\n",
"7\n1 6 4 2 5 6 7\n",
"5\n5 2 2 5 3\n",
"6\n4 2 1 2 4 2\n",
"7\n4 3 4 6 5 5 3\n",
"7\n5 3 1 6 5 5 2\n",
"7\n7 2 3 1 4 1 5\n",
"4\n3 3 1 4\n",
"7\n6 3 2 6 5 5 3\n",
"7\n4 3 1 6 5 1 2\n",
"7\n1 2 2 7 5 1 4\n",
"7\n4 1 1 6 5 1 2\n",
"7\n1 2 3 1 3 1 4\n",
"7\n5 1 1 6 5 3 2\n",
"7\n4 1 1 6 2 3 1\n",
"7\n7 2 2 6 4 3 4\n",
"7\n1 4 4 6 4 3 2\n",
"18\n2 3 4 5 2 7 4 9 2 7 11 12 14 15 13 17 18 18\n",
"6\n4 2 1 2 4 3\n",
"7\n4 3 4 6 3 5 3\n",
"7\n5 3 2 6 5 5 2\n",
"4\n3 3 2 4\n",
"7\n4 3 1 7 5 1 2\n",
"7\n1 2 2 7 5 1 3\n",
"7\n1 2 3 2 3 1 4\n",
"7\n4 1 1 7 2 3 1\n",
"7\n7 2 1 6 4 3 4\n",
"18\n2 3 4 5 2 7 4 6 2 7 11 12 14 15 13 17 18 18\n",
"6\n4 2 1 2 1 3\n",
"7\n5 3 2 6 5 1 2\n",
"7\n4 3 1 7 5 1 1\n",
"7\n1 2 3 7 5 1 4\n",
"7\n7 1 1 6 4 3 1\n",
"7\n1 4 2 6 4 3 2\n",
"7\n6 1 1 6 4 3 2\n",
"7\n4 1 2 6 4 3 2\n",
"7\n5 1 2 6 4 3 2\n",
"7\n1 4 2 7 5 1 3\n"
],
"output": [
"0\n3 2 2 5 3 ",
"2 \n2 3 5 4 4 4 6 7 \n",
"1 \n2 3 3 3 \n",
"1\n2 2 1 ",
"0\n6 2 6 2 4 2 ",
"1 \n1 1 \n",
"2 \n2 2 2 2 6 2 6 6 \n",
"5 \n2 3 4 5 11 7 8 9 10 11 11 11 14 15 11 17 18 11 \n",
"6 \n1 1 1 1 1 1 1 \n",
"1\n4 3 3 6 3 5 2 ",
"1\n7 5 3 1 3 1 5 ",
"4 \n1 6 4 1 1 1 1 \n",
"0\n6 2 1 2 4 2\n",
"5\n1 1 1 1 1 1 1\n",
"1\n4 5 2 6 5 5 2\n",
"4\n1 1 1 1 7 1 1\n",
"0\n4 3 1 6 5 5 2\n",
"3\n1 1 1 7 7 1 1\n",
"0\n3 2 6 2 4 2\n",
"0\n2 2\n",
"2\n1 1 2 2 1 5 6 2\n",
"1\n3 5 3 1 4 1 5\n",
"1\n3 3 3 3\n",
"4\n1 1 1 1 1 1 4\n",
"1\n4 5 2 6 5 5 3\n",
"1\n5 3 1 6 5 2 2\n",
"1\n5 1 1 6 5 2 2\n",
"3\n1 1 1 1 1 1 4\n",
"1\n5 1 1 6 5 3 2\n",
"1\n1 1 1 6 4 3 2\n",
"1\n1 1 1 6 4 3 1\n",
"1\n1 1 2 6 4 3 1\n",
"1\n1 1 2 6 4 3 2\n",
"0\n7 2 2 6 4 3 2\n",
"1\n7 2 2 6 4 3 2\n",
"0\n2 2 1\n",
"4\n2 11 4 5 2 7 8 9 2 7 11 11 11 15 13 17 18 11\n",
"5\n1 1 1 5 1 1 1\n",
"1\n4 2 2 7 3 5 2\n",
"2\n3 3 3 1 2 1 6\n",
"3\n1 6 4 2 1 1 1\n",
"0\n5 2 2 5 3\n",
"0\n4 2 1 2 4 2\n",
"0\n4 3 4 6 5 5 3\n",
"0\n5 3 1 6 5 5 2\n",
"2\n2 2 2 1 4 1 5\n",
"1\n4 3 1 4\n",
"1\n6 5 2 6 5 5 3\n",
"1\n5 3 1 6 5 1 2\n",
"3\n1 1 2 1 1 1 4\n",
"1\n5 1 1 6 5 1 2\n",
"2\n1 1 1 1 3 1 4\n",
"0\n5 1 1 6 5 3 2\n",
"1\n1 1 1 6 2 3 1\n",
"0\n7 2 2 6 4 3 4\n",
"1\n1 4 4 1 4 3 2\n",
"4\n2 11 4 5 2 7 4 9 2 7 11 11 11 15 13 17 18 11\n",
"0\n4 2 1 2 4 3\n",
"1\n4 3 4 4 3 5 3\n",
"1\n5 5 2 6 5 5 2\n",
"1\n3 3 4 4\n",
"1\n5 3 1 7 5 1 2\n",
"2\n1 1 2 7 1 1 3\n",
"2\n1 1 1 2 3 1 4\n",
"1\n1 1 1 7 2 3 1\n",
"1\n2 2 1 6 4 3 4\n",
"4\n2 11 4 5 2 7 4 6 2 7 11 11 11 15 13 17 18 11\n",
"0\n4 2 1 2 1 3\n",
"1\n5 5 2 6 5 1 2\n",
"1\n5 3 1 7 5 1 1\n",
"4\n1 1 1 1 1 1 4\n",
"1\n1 1 1 6 4 3 1\n",
"1\n1 1 2 6 4 3 2\n",
"1\n1 1 1 6 4 3 2\n",
"1\n1 1 2 6 4 3 2\n",
"1\n1 1 2 6 4 3 2\n",
"2\n1 1 2 7 1 1 3\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A tree is an undirected connected graph without cycles.
Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).
<image> For this rooted tree the array p is [2, 3, 3, 2].
Given a sequence p1, p2, ..., pn, one is able to restore a tree:
1. There must be exactly one index r that pr = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex pi.
A sequence p1, p2, ..., pn is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.
You are given a sequence a1, a2, ..., an, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).
Output
In the first line print the minimum number of elements to change, in order to get a valid sequence.
In the second line, print any valid sequence possible to get from (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.
Examples
Input
4
2 3 3 4
Output
1
2 3 4 4
Input
5
3 2 2 5 3
Output
0
3 2 2 5 3
Input
8
2 3 5 4 1 6 6 7
Output
2
2 3 7 8 1 6 6 7
Note
In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because p4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.
<image>
In the second sample, the given sequence is already valid.
### Input:
5
3 2 2 5 3
### Output:
0
3 2 2 5 3
### Input:
8
2 3 5 4 1 6 6 7
### Output:
2
2 3 5 4 4 4 6 7
### Code:
from collections import defaultdict
from sys import stdin,setrecursionlimit
setrecursionlimit(10**6)
import threading
def f(a):
n=len(a)
a=list(map(lambda s:s-1,a))
root=None
for i in range(len(a)):
if a[i]==i:
root=i
vis=[0]*(n)
traitors=[]
for i in range(0,n):
cycle=-1
cur=i
move=set()
while vis[cur]==0:
vis[cur]=1
move.add(cur)
if a[cur] in move:
cycle=cur
cur=a[cur]
if cycle!=-1:
traitors.append(cycle)
ans=len(traitors)-1
if root==None:
a[traitors[0]]=traitors[0]
root=traitors[0]
ans+=1
for i in traitors:
if i!=root:
a[i]=root
print(ans)
a=list(map(lambda s:s+1,a))
return a
n=input()
a=list(map(int,input().strip().split()))
print(*f(a)) |
719_B. Anatoly and Cockroaches_2866 | Anatoly lives in the university dorm as many other students do. As you know, cockroaches are also living there together with students. Cockroaches might be of two colors: black and red. There are n cockroaches living in Anatoly's room.
Anatoly just made all his cockroaches to form a single line. As he is a perfectionist, he would like the colors of cockroaches in the line to alternate. He has a can of black paint and a can of red paint. In one turn he can either swap any two cockroaches, or take any single cockroach and change it's color.
Help Anatoly find out the minimum number of turns he needs to make the colors of cockroaches in the line alternate.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of cockroaches.
The second line contains a string of length n, consisting of characters 'b' and 'r' that denote black cockroach and red cockroach respectively.
Output
Print one integer — the minimum number of moves Anatoly has to perform in order to make the colors of cockroaches in the line to alternate.
Examples
Input
5
rbbrr
Output
1
Input
5
bbbbb
Output
2
Input
3
rbr
Output
0
Note
In the first sample, Anatoly has to swap third and fourth cockroaches. He needs 1 turn to do this.
In the second sample, the optimum answer is to paint the second and the fourth cockroaches red. This requires 2 turns.
In the third sample, the colors of cockroaches in the line are alternating already, thus the answer is 0. | #http://codeforces.com/problemset/problem/719/B
#solved
n = int(input())
s = input()
red_black = True
swap_red = {"b": 0, "r": 0}
swap_black = {"b": 0, "r": 0}
for c in s:
if red_black is True and c != "b":
swap_black["r"] += 1
elif red_black is False and c != "r":
swap_black["b"] += 1
if red_black is True and c != "r":
swap_red["b"] += 1
elif red_black is False and c != "b":
swap_red["r"] += 1
red_black = True if red_black is False else False
black = (swap_black[max(swap_black, key=swap_black.get)] - swap_black[min(swap_black, key=swap_black.get)]) + swap_black[min(swap_black, key=swap_black.get)]
red = (swap_red[max(swap_red, key=swap_red.get)] - swap_red[min(swap_red, key=swap_red.get)]) + swap_red[min(swap_red, key=swap_red.get)]
print(int(min(red, black)))
| {
"input": [
"5\nrbbrr\n",
"5\nbbbbb\n",
"3\nrbr\n",
"166\nrbbbbbbbbbbbbrbrrbbrbbbrbbbbbbbbbbrbbbbbbrbbbrbbbbbrbbbbbbbrbbbbbbbrbbrbbbbbbbbrbbbbbbbbbbbbbbrrbbbrbbbbbbbbbbbbbbrbrbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbbbbbbbbbbbb\n",
"7\nrrbrbrb\n",
"1\nr\n",
"2\nbb\n",
"18\nrrrrrrrrrrrrrrrrrb\n",
"8\nrbbrbrbr\n",
"1\nb\n",
"13\nrbbbrbrrbrrbb\n",
"100\nbrbbbrrrbbrbrbbrbbrbbbbrbbrrbbbrrbbbbrbrbbbbbbbbbbbbbbbbrrrrbbbbrrrbbbbbbbrbrrbrbbbbrrrbbbbrbbrbbbrb\n",
"2\nrb\n",
"2\nrr\n",
"2\nbr\n",
"7\nbrbrbrr\n",
"18\nbrrrrrrrrrrrrrrrrr\n",
"100\nbrbbbrbbrbbbbrrrbbbbrbrrbrbbbbbbbrrrbbbbrrrrbbbbbbbbbbbbbbbbrbrbbbbrrbbbrrbbrbbbbrbbrbbrbrbbrrrbbbrb\n",
"8\nrrbbrbbr\n",
"13\nrbrbbbrrbrrbb\n",
"166\nrbbbbbbbbbbbrrbrrbbbbbbrbbbbbbbbbbrbbbbbbrbbbrbbbbbrbbbbbbbrbbbbbbbrbbrbbbbbbbbrbbbbbbbbbbbbbbrrbbbrbbbbbbbbbbbbbbrbrbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbbbbbbbbbbbb\n",
"166\nbbbbbbbbbbbbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbrbrbbbbbbbbbbbbbbrbbbrrbbbbbbbbbbbbbbrbbbbbbbbrbbrbbbbbbbrbbbbbbbrbbbbbrbbbrbbbbbbrbbbbbbbbbbrbbbrbbrrbrbbbbbbbbbbbbr\n",
"5\nrbrbr\n",
"100\nbrbbbrrbbbrbrbbrbbrbbbbrbbrrbbbrrbbbbrbrbbbbbbbbbbbbbbrbrrrrbbbbrrbbbbrbbbrbrrbrbbbbrrrbbbbrbbrbbbrb\n",
"8\nrbrbrbbr\n",
"5\nrrbbr\n",
"8\nrbbrbbrr\n",
"3\nbrr\n",
"18\nrrrrrrrrrbrrrrrrrr\n",
"13\nrbrrbbrrbbrbb\n",
"13\nrbbbrbrbrrrbb\n",
"7\nbrrrbbr\n",
"18\nrrrrrrrrrrrrrrbrrr\n",
"8\nrbbbrrbr\n",
"3\nrrb\n",
"18\nrrrrrrrrbrrrrrrrrr\n",
"8\nrbrrbbbr\n",
"8\nbbrrbbrr\n",
"8\nbbrbbrrr\n",
"7\nbrbrrrb\n",
"8\nrbbbrbrr\n",
"13\nrbrrbbrbbrrbb\n",
"13\nbbrbbrrbbrrbr\n",
"8\nrrbbrrbb\n",
"7\nbrrrbrb\n",
"13\nbbrrbbrbbrrbr\n",
"7\nbrrbbrr\n",
"7\nbbrrbrr\n",
"8\nrbrrrbbb\n",
"8\nrbbrbrrb\n",
"18\nrrrrrrrrrrrbrrrrrr\n",
"18\nrrrbrrrrrrrrrrrrrr\n",
"7\nrrrrbbb\n",
"13\nrbrbbrrbbrrbb\n",
"7\nrrbbrrb\n",
"7\nrrbrrbb\n",
"166\nbbbbbbbbbbbbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbrbrbbbbbbbbbbbbbbrbbbrrbbbbbbbbbbbbbbrbbbbbbbbrbbrbbbbbbbrbbbbbbbrbbbbbrbbbrbbbbbbrbbbbbbbbbbrbbbbbbrrbrrbbbbbbbbbbbr\n",
"8\nbbbrrrbr\n",
"7\nbbbrrrr\n",
"8\nrbrbbrbr\n",
"100\nbrbbbrrrbbrbrbbrbbrbbbbrbbrrbbbrrbbbbrbrbbbbbbbbbbbbbbrbrrrrbbbbrrbbbbbbbbrbrrbrbbbbrrrbbbbrbbrbbbrb\n",
"13\nbbrrbrrbbbrbr\n",
"13\nrbbbrrrbrrbbb\n",
"7\nrrbrbbr\n",
"18\nrrrrrrbrrrrrrrrrrr\n",
"8\nbbrbrrbr\n",
"13\nrrrbbbrbbrrbb\n",
"7\nbrrbrrb\n",
"13\nrbrrbbbbbrrrb\n",
"8\nbbrrbrbr\n",
"13\nbrrrbrbbbbrbr\n",
"13\nrrbbrrbbrrbbb\n",
"100\nbrbbbrbbrbbbbrrrbbbbrbrrbrbbbrbbbbrrbbbbrrrrbrbbbbbbbbbbbbbbrbrbbbbrrbbbrrbbrbbbbrbbrbbrbrbbbrrbbbrb\n",
"13\nrbrbbbbrbrrrb\n",
"13\nrrbrrrbbrbbbb\n",
"13\nbrbrrrbbrbbrb\n",
"13\nbrbbrbbrrrbrb\n",
"13\nbbrrbrrbrbbbr\n",
"5\nrrbrb\n",
"8\nrrrbrbbb\n",
"5\nbrbrr\n",
"13\nbbrbrrrbbrrbb\n",
"7\nrbbrrrb\n",
"8\nbrbbrrbr\n",
"8\nrrbrbbbr\n",
"13\nrbrrbbrbbbrrb\n",
"7\nrrrbbrb\n",
"7\nrbrrbbr\n",
"18\nrrrrrbrrrrrrrrrrrr\n",
"166\nbbbbbbbbbrbbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbrbrbbbbbbbbbbbbbbrbbbrrbbbbbbbbbbbbbbrbbbbbbbbrbbrbbbbbbbbbbbbbbbrbbbbbrbbbrbbbbbbrbbbbbbbbbbrbbbrbbrrbrbbbbbbbbbbbbr\n",
"8\nrbrrbrbb\n",
"13\nbrrrbbbbbrrrb\n",
"8\nrbrbrrbb\n",
"13\nbbrrbbrrrbrbb\n",
"7\nrbbrrbr\n",
"13\nbrrbbbrbbrrbr\n",
"166\nrbbbbbbbbbbbbrbrrbbrbbbrbbbbbbbbbbrbbbbbbrbbbrbbbbbrbbbbbbbbbbbbbbbrbbrbbbbbbbbrbbbbbbbbbbbbbbrrbbbrbbbbbbbbbbbbbbrbrbbbbbbbbbbbrbbbbbbbbbbbbbbrbbbbbbbbbbbbrbbbbbbbbb\n",
"7\nbbrrrrb\n"
],
"output": [
"1\n",
"2\n",
"0\n",
"70\n",
"1\n",
"0\n",
"1\n",
"8\n",
"1\n",
"0\n",
"3\n",
"34\n",
"0\n",
"1\n",
"0\n",
"1\n",
"8\n",
"34\n",
"2\n",
"3\n",
"71\n",
"70\n",
"0\n",
"33\n",
"1\n",
"1\n",
"2\n",
"1\n",
"8\n",
"3\n",
"2\n",
"2\n",
"8\n",
"2\n",
"1\n",
"8\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"3\n",
"3\n",
"2\n",
"1\n",
"3\n",
"2\n",
"2\n",
"1\n",
"2\n",
"8\n",
"8\n",
"2\n",
"3\n",
"2\n",
"2\n",
"71\n",
"1\n",
"2\n",
"2\n",
"34\n",
"3\n",
"3\n",
"2\n",
"8\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n",
"3\n",
"3\n",
"33\n",
"3\n",
"3\n",
"2\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"3\n",
"2\n",
"1\n",
"1\n",
"3\n",
"2\n",
"1\n",
"8\n",
"71\n",
"2\n",
"2\n",
"1\n",
"3\n",
"1\n",
"3\n",
"71\n",
"2\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Anatoly lives in the university dorm as many other students do. As you know, cockroaches are also living there together with students. Cockroaches might be of two colors: black and red. There are n cockroaches living in Anatoly's room.
Anatoly just made all his cockroaches to form a single line. As he is a perfectionist, he would like the colors of cockroaches in the line to alternate. He has a can of black paint and a can of red paint. In one turn he can either swap any two cockroaches, or take any single cockroach and change it's color.
Help Anatoly find out the minimum number of turns he needs to make the colors of cockroaches in the line alternate.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of cockroaches.
The second line contains a string of length n, consisting of characters 'b' and 'r' that denote black cockroach and red cockroach respectively.
Output
Print one integer — the minimum number of moves Anatoly has to perform in order to make the colors of cockroaches in the line to alternate.
Examples
Input
5
rbbrr
Output
1
Input
5
bbbbb
Output
2
Input
3
rbr
Output
0
Note
In the first sample, Anatoly has to swap third and fourth cockroaches. He needs 1 turn to do this.
In the second sample, the optimum answer is to paint the second and the fourth cockroaches red. This requires 2 turns.
In the third sample, the colors of cockroaches in the line are alternating already, thus the answer is 0.
### Input:
5
rbbrr
### Output:
1
### Input:
5
bbbbb
### Output:
2
### Code:
#http://codeforces.com/problemset/problem/719/B
#solved
n = int(input())
s = input()
red_black = True
swap_red = {"b": 0, "r": 0}
swap_black = {"b": 0, "r": 0}
for c in s:
if red_black is True and c != "b":
swap_black["r"] += 1
elif red_black is False and c != "r":
swap_black["b"] += 1
if red_black is True and c != "r":
swap_red["b"] += 1
elif red_black is False and c != "b":
swap_red["r"] += 1
red_black = True if red_black is False else False
black = (swap_black[max(swap_black, key=swap_black.get)] - swap_black[min(swap_black, key=swap_black.get)]) + swap_black[min(swap_black, key=swap_black.get)]
red = (swap_red[max(swap_red, key=swap_red.get)] - swap_red[min(swap_red, key=swap_red.get)]) + swap_red[min(swap_red, key=swap_red.get)]
print(int(min(red, black)))
|
787_A. The Monster_2874 | A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....
<image>
The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.
Input
The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).
The second line contains two integers c and d (1 ≤ c, d ≤ 100).
Output
Print the first time Rick and Morty will scream at the same time, or - 1 if they will never scream at the same time.
Examples
Input
20 2
9 19
Output
82
Input
2 1
16 12
Output
-1
Note
In the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82.
In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time. | import math
R=lambda:list(map(int,input().split()))
a,b=R()
c,d=R()
if abs(b-d)%math.gcd(a,c)!=0:
print(-1)
exit(0)
while b != d:
if b<d: b+=a
else: d+=c
print(b)
| {
"input": [
"20 2\n9 19\n",
"2 1\n16 12\n",
"84 82\n38 6\n",
"2 3\n2 2\n",
"2 3\n4 99\n",
"3 7\n3 6\n",
"11 81\n49 7\n",
"1 1\n1 100\n",
"6 10\n12 14\n",
"2 10\n6 20\n",
"97 2\n99 100\n",
"17 19\n44 75\n",
"39 52\n88 78\n",
"4 2\n4 4\n",
"1 1\n1 1\n",
"46 71\n16 49\n",
"3 2\n7 2\n",
"87 22\n98 32\n",
"46 30\n34 62\n",
"59 96\n34 48\n",
"74 88\n77 37\n",
"45 63\n98 53\n",
"59 70\n48 54\n",
"41 85\n95 46\n",
"100 100\n100 100\n",
"55 94\n3 96\n",
"18 4\n77 78\n",
"89 93\n84 87\n",
"40 4\n81 40\n",
"2 3\n2 5\n",
"7 25\n39 85\n",
"87 37\n91 29\n",
"98 1\n99 2\n",
"46 44\n23 55\n",
"1 100\n3 1\n",
"39 21\n95 89\n",
"22 81\n80 88\n",
"1 100\n1 100\n",
"94 37\n34 7\n",
"70 11\n74 27\n",
"18 18\n71 71\n",
"2 3\n2 3\n",
"94 55\n20 96\n",
"100 3\n100 5\n",
"3 3\n3 1\n",
"69 48\n39 9\n",
"39 7\n97 91\n",
"1 5\n1 5\n",
"98 1\n99 100\n",
"69 11\n48 34\n",
"2 2\n2 10\n",
"17 45\n42 65\n",
"2 2\n2 1\n",
"1 100\n100 1\n",
"7 7\n7 14\n",
"93 74\n99 93\n",
"15 63\n51 13\n",
"69 30\n41 16\n",
"84 82\n38 7\n",
"2 3\n4 47\n",
"11 81\n49 11\n",
"1 2\n1 100\n",
"6 10\n14 14\n",
"17 33\n44 75\n",
"39 74\n88 78\n",
"1 1\n1 2\n",
"3 0\n7 2\n",
"87 22\n98 64\n",
"46 24\n34 62\n",
"19 96\n34 48\n",
"20 63\n98 53\n",
"59 67\n48 54\n",
"3 85\n95 46\n",
"40 4\n81 23\n",
"7 22\n39 85\n",
"87 34\n91 29\n",
"98 0\n99 2\n",
"1 100\n2 1\n",
"39 21\n2 89\n",
"94 37\n30 7\n",
"67 11\n74 27\n",
"18 18\n53 71\n",
"5 3\n3 1\n",
"69 48\n39 18\n",
"39 7\n97 74\n",
"1 5\n1 8\n",
"1 110\n100 1\n",
"20 2\n9 10\n",
"2 2\n16 12\n",
"84 121\n38 7\n",
"20 81\n49 11\n",
"17 40\n44 75\n",
"39 74\n88 152\n",
"2 1\n1 2\n",
"48 71\n5 49\n",
"3 1\n7 2\n",
"87 22\n119 64\n",
"46 24\n20 62\n",
"59 67\n61 54\n",
"2 0\n2 4\n",
"7 22\n39 79\n",
"87 34\n91 40\n",
"46 47\n42 55\n",
"39 21\n2 34\n",
"94 27\n30 7\n",
"67 1\n74 27\n",
"18 1\n53 71\n",
"39 7\n79 74\n",
"1 5\n1 14\n",
"2 1\n3 2\n",
"20 81\n47 11\n",
"17 7\n44 75\n",
"31 74\n88 152\n",
"2 5\n2 2\n",
"6 7\n3 6\n",
"4 2\n4 7\n",
"48 71\n16 49\n",
"100 110\n100 100\n",
"18 4\n33 78\n",
"2 0\n2 5\n",
"46 44\n42 55\n",
"22 81\n44 88\n",
"2 4\n2 3\n",
"94 55\n20 88\n",
"98 1\n99 000\n",
"69 5\n48 34\n",
"2 2\n2 19\n",
"17 45\n68 65\n",
"4 2\n2 1\n",
"7 7\n7 20\n",
"15 63\n51 22\n",
"2 1\n2 2\n",
"4 3\n4 47\n",
"1 7\n3 6\n",
"2 2\n1 100\n",
"6 7\n14 14\n",
"2 2\n4 7\n",
"19 44\n34 48\n",
"16 63\n98 53\n",
"5 85\n95 46\n",
"18 4\n33 53\n",
"30 4\n81 23\n",
"2 81\n44 88\n",
"94 55\n22 88\n",
"69 48\n39 14\n",
"27 5\n48 34\n",
"2 2\n2 11\n",
"4 2\n4 1\n",
"7 7\n7 9\n",
"15 63\n51 26\n",
"33 2\n9 10\n",
"84 170\n38 7\n",
"1 3\n4 47\n",
"1 10\n3 6\n",
"2 2\n1 000\n",
"6 7\n14 23\n",
"2 2\n8 7\n",
"2 2\n1 2\n"
],
"output": [
"82\n",
"-1\n",
"82\n",
"-1\n",
"99\n",
"-1\n",
"301\n",
"100\n",
"-1\n",
"20\n",
"4852\n",
"427\n",
"1222\n",
"-1\n",
"1\n",
"209\n",
"2\n",
"718\n",
"674\n",
"1748\n",
"1346\n",
"3483\n",
"1014\n",
"331\n",
"100\n",
"204\n",
"1156\n",
"5967\n",
"364\n",
"5\n",
"319\n",
"211\n",
"9605\n",
"-1\n",
"100\n",
"3414\n",
"-1\n",
"100\n",
"789\n",
"2321\n",
"1278\n",
"3\n",
"-1\n",
"-1\n",
"-1\n",
"48\n",
"1255\n",
"5\n",
"9703\n",
"-1\n",
"10\n",
"317\n",
"-1\n",
"101\n",
"14\n",
"-1\n",
"-1\n",
"1410\n",
"-1\n",
"47\n",
"158\n",
"100\n",
"28\n",
"339\n",
"2102\n",
"2\n",
"9\n",
"1240\n",
"300\n",
"286\n",
"543\n",
"1542\n",
"331\n",
"1724\n",
"85\n",
"2122\n",
"9506\n",
"101\n",
"99\n",
"37\n",
"2691\n",
"972\n",
"13\n",
"876\n",
"1723\n",
"8\n",
"201\n",
"82\n",
"12\n",
"121\n",
"501\n",
"295\n",
"152\n",
"3\n",
"119\n",
"16\n",
"1849\n",
"162\n",
"2250\n",
"4\n",
"274\n",
"3862\n",
"139\n",
"60\n",
"967\n",
"1877\n",
"919\n",
"943\n",
"14\n",
"5\n",
"481\n",
"75\n",
"2616\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"99\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"47\n",
"9\n",
"100\n",
"-1\n",
"-1\n",
"82\n",
"543\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"47\n",
"12\n",
"2\n",
"37\n",
"-1\n",
"2\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....
<image>
The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.
Input
The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).
The second line contains two integers c and d (1 ≤ c, d ≤ 100).
Output
Print the first time Rick and Morty will scream at the same time, or - 1 if they will never scream at the same time.
Examples
Input
20 2
9 19
Output
82
Input
2 1
16 12
Output
-1
Note
In the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82.
In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time.
### Input:
20 2
9 19
### Output:
82
### Input:
2 1
16 12
### Output:
-1
### Code:
import math
R=lambda:list(map(int,input().split()))
a,b=R()
c,d=R()
if abs(b-d)%math.gcd(a,c)!=0:
print(-1)
exit(0)
while b != d:
if b<d: b+=a
else: d+=c
print(b)
|
808_E. Selling Souvenirs_2878 | After several latest reforms many tourists are planning to visit Berland, and Berland people understood that it's an opportunity to earn money and changed their jobs to attract tourists. Petya, for example, left the IT corporation he had been working for and started to sell souvenirs at the market.
This morning, as usual, Petya will come to the market. Petya has n different souvenirs to sell; ith souvenir is characterised by its weight wi and cost ci. Petya knows that he might not be able to carry all the souvenirs to the market. So Petya wants to choose a subset of souvenirs such that its total weight is not greater than m, and total cost is maximum possible.
Help Petya to determine maximum possible total cost.
Input
The first line contains two integers n and m (1 ≤ n ≤ 100000, 1 ≤ m ≤ 300000) — the number of Petya's souvenirs and total weight that he can carry to the market.
Then n lines follow. ith line contains two integers wi and ci (1 ≤ wi ≤ 3, 1 ≤ ci ≤ 109) — the weight and the cost of ith souvenir.
Output
Print one number — maximum possible total cost of souvenirs that Petya can carry to the market.
Examples
Input
1 1
2 1
Output
0
Input
2 2
1 3
2 2
Output
3
Input
4 3
3 10
2 7
2 8
1 1
Output
10 | def f():
n, m = map(int, input().split())
l = list(tuple(map(int, input().split())) for _ in range(n))
l.sort(key=lambda e: (0, 6, 3, 2)[e[0]] * e[1], reverse=True)
last, r = [0] * 4, 0
for i, (w, c) in enumerate(l):
if m < w:
break
m -= w
r += c
last[w] = c
else:
return r
if not m:
return r
res, tail = [r], (None, [], [], [])
for w, c in l[i:]:
tail[w].append(c)
for w in 1, 2, 3:
tail[w].append(0)
_, t1, t2, t3 = tail
if m == 1:
res.append(r + t1[0])
if last[1]:
res.append(r - last[1] + t2[0])
if last[2]:
res.append(r - last[2] + t3[0])
if last[3]:
r -= last[3]
res += (r + sum(t1[:4]), r + sum(t1[:2]) + t2[0], r + sum(t2[:2]))
else: # m == 2
res += (r + sum(t1[:2]), r + t2[0])
if last[1]:
res.append(r - last[1] + t3[0])
if last[2]:
res.append(r - last[2] + t3[0] + t1[0])
return max(res)
def main():
print(f())
if __name__ == '__main__':
main()
| {
"input": [
"4 3\n3 10\n2 7\n2 8\n1 1\n",
"2 2\n1 3\n2 2\n",
"1 1\n2 1\n",
"52 102\n3 199\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n2 100\n",
"7 12\n2 10\n2 8\n2 1\n3 8\n3 8\n3 7\n1 7\n",
"4 28\n2 2\n3 1\n3 10\n1 9\n",
"1 2\n2 10\n",
"1 29\n2 8\n",
"4 2\n3 4\n3 8\n1 1\n1 4\n",
"6 5\n3 1\n3 1\n1 2\n2 9\n3 10\n1 8\n",
"6 18\n3 3\n1 10\n2 10\n3 6\n1 3\n2 3\n",
"9 19\n2 5\n2 3\n3 9\n1 9\n3 8\n3 5\n3 4\n3 2\n3 6\n",
"3 4\n2 10\n2 10\n3 15\n",
"6 7\n2 5\n2 4\n3 9\n3 2\n3 1\n3 8\n",
"3 4\n1 4\n2 10\n3 100\n",
"9 15\n3 8\n1 2\n2 5\n1 5\n3 3\n1 7\n1 7\n2 7\n2 9\n",
"20 25\n2 13\n3 11\n1 32\n1 43\n3 85\n1 14\n2 57\n1 54\n1 38\n2 96\n2 89\n3 64\n1 79\n2 73\n1 73\n2 34\n1 52\n1 79\n1 42\n3 34\n",
"8 6\n1 9\n1 5\n1 3\n1 10\n3 8\n1 6\n1 4\n1 2\n",
"9 10\n3 6\n2 1\n2 4\n2 3\n3 6\n3 1\n1 8\n2 4\n3 3\n",
"8 21\n2 6\n3 3\n3 7\n3 8\n3 8\n3 8\n2 6\n3 9\n",
"5 9\n2 8\n3 7\n2 6\n1 4\n2 7\n",
"40 45\n2 82\n2 70\n2 48\n3 50\n2 15\n1 23\n1 80\n2 46\n1 20\n3 8\n3 81\n2 27\n1 59\n1 15\n3 95\n2 82\n2 40\n2 9\n2 61\n1 49\n2 5\n2 82\n1 55\n2 11\n1 26\n1 33\n1 2\n1 7\n3 57\n2 29\n1 59\n2 50\n3 63\n1 40\n1 99\n2 91\n2 39\n3 50\n1 75\n3 77\n",
"5 7\n1 8\n2 13\n2 13\n3 20\n3 14\n",
"61 120\n3 5\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n",
"10 12\n3 7\n3 6\n3 8\n3 2\n1 9\n2 5\n2 1\n2 5\n2 10\n2 9\n",
"5 5\n3 5\n2 6\n3 2\n1 1\n1 6\n",
"13 23\n3 17\n2 83\n1 81\n3 83\n3 59\n3 71\n2 61\n3 8\n3 64\n2 80\n3 47\n1 46\n1 82\n",
"10 6\n1 8\n1 10\n1 7\n2 9\n3 8\n1 8\n1 7\n1 4\n3 1\n3 8\n",
"10 5\n1 9\n1 8\n2 10\n3 4\n3 1\n2 2\n3 6\n1 1\n3 8\n2 2\n",
"1 1\n1 10\n",
"2 1\n1 5\n2 11\n",
"2 40\n1 10\n3 6\n",
"4 4\n2 13\n2 15\n2 5\n1 9\n",
"6 12\n1 7\n1 10\n2 8\n1 2\n2 9\n3 5\n",
"70 203\n1 105\n1 105\n1 105\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n",
"6 6\n1 6\n1 4\n1 8\n3 2\n3 2\n2 8\n",
"10 2\n3 4\n3 5\n3 7\n1 10\n1 2\n1 2\n1 8\n3 2\n1 8\n3 3\n",
"7 6\n2 9\n3 10\n1 2\n2 6\n3 6\n2 1\n1 3\n",
"8 5\n3 9\n3 3\n1 4\n3 1\n2 5\n3 1\n3 6\n3 1\n",
"2 4\n3 8\n1 6\n",
"4 28\n2 2\n2 1\n3 10\n1 9\n",
"1 13\n2 8\n",
"4 2\n3 4\n3 9\n1 1\n1 4\n",
"3 4\n2 10\n2 10\n3 4\n",
"6 7\n2 5\n2 4\n3 9\n3 2\n3 1\n3 7\n",
"9 29\n3 8\n1 2\n2 5\n1 5\n3 3\n1 7\n1 7\n2 7\n2 9\n",
"20 25\n2 13\n3 2\n1 32\n1 43\n3 85\n1 14\n2 57\n1 54\n1 38\n2 96\n2 89\n3 64\n1 79\n2 73\n1 73\n2 34\n1 52\n1 79\n1 42\n3 34\n",
"8 6\n1 9\n1 5\n1 3\n1 10\n3 8\n1 6\n1 5\n1 2\n",
"9 10\n3 6\n3 1\n2 4\n2 3\n3 6\n3 1\n1 8\n2 4\n3 3\n",
"8 21\n2 6\n3 3\n3 7\n3 8\n3 8\n3 7\n2 6\n3 9\n",
"5 9\n1 8\n3 7\n2 6\n1 4\n2 7\n",
"61 120\n3 5\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 2\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n2 3\n",
"10 12\n3 7\n3 6\n3 8\n3 4\n1 9\n2 5\n2 1\n2 5\n2 10\n2 9\n",
"5 5\n3 1\n2 6\n3 2\n1 1\n1 6\n",
"13 23\n3 17\n1 83\n1 81\n3 83\n3 59\n3 71\n2 61\n3 8\n3 64\n2 80\n3 47\n1 46\n1 82\n",
"10 6\n1 8\n1 10\n1 7\n2 9\n3 8\n1 8\n1 7\n1 4\n3 1\n3 6\n",
"10 5\n1 9\n1 8\n2 8\n3 4\n3 1\n2 2\n3 6\n1 1\n3 8\n2 2\n",
"1 2\n1 10\n",
"6 12\n1 7\n1 17\n2 8\n1 2\n2 9\n3 5\n",
"70 203\n1 105\n1 105\n1 105\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 491\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n",
"4 3\n3 10\n2 7\n2 14\n1 1\n",
"1 2\n2 1\n",
"4 2\n3 4\n3 9\n1 1\n1 8\n",
"20 25\n2 13\n3 2\n1 32\n1 43\n3 85\n1 14\n2 57\n1 54\n1 38\n2 96\n2 89\n3 64\n1 79\n2 73\n1 73\n2 34\n1 52\n1 79\n1 44\n3 34\n",
"5 9\n1 8\n3 7\n2 6\n1 8\n2 7\n",
"10 12\n3 7\n3 6\n3 7\n3 4\n1 9\n2 5\n2 1\n2 5\n2 10\n2 9\n",
"13 23\n3 17\n1 83\n1 81\n3 83\n3 59\n3 71\n2 61\n3 8\n3 64\n2 80\n3 47\n1 46\n1 103\n",
"10 6\n1 3\n1 10\n1 7\n2 9\n3 8\n1 8\n1 7\n1 4\n3 1\n3 6\n",
"70 203\n1 105\n1 105\n1 105\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 404\n3 300\n3 300\n3 300\n3 491\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n3 300\n",
"1 2\n3 1\n",
"4 2\n3 4\n3 9\n1 1\n1 3\n",
"20 25\n2 13\n3 2\n1 32\n1 43\n3 85\n1 14\n2 57\n1 54\n1 38\n2 96\n2 89\n3 64\n1 79\n2 73\n1 73\n2 47\n1 52\n1 79\n1 44\n3 34\n",
"8 5\n1 9\n1 5\n1 3\n1 10\n3 8\n1 6\n1 5\n1 2\n",
"9 10\n3 6\n2 1\n2 7\n2 3\n3 6\n3 1\n1 8\n2 4\n3 4\n",
"8 21\n2 6\n3 3\n3 7\n3 16\n3 8\n3 7\n2 6\n3 6\n",
"13 23\n3 17\n1 83\n1 81\n3 83\n3 59\n3 71\n2 61\n3 8\n3 64\n2 13\n3 47\n1 46\n1 103\n",
"10 6\n1 3\n1 10\n1 7\n2 9\n3 8\n1 8\n1 7\n1 8\n3 1\n3 6\n",
"1 3\n1 19\n",
"2 1\n1 5\n3 11\n",
"6 6\n1 6\n1 4\n1 8\n3 2\n3 2\n2 2\n",
"2 3\n1 3\n2 2\n",
"1 25\n2 8\n",
"3 6\n2 10\n2 10\n3 4\n",
"6 7\n2 5\n2 4\n3 9\n3 2\n3 2\n3 7\n",
"8 11\n1 9\n1 5\n1 3\n1 10\n3 8\n1 6\n1 5\n1 2\n",
"9 10\n3 6\n2 1\n2 4\n2 3\n3 6\n3 1\n1 8\n2 4\n3 4\n",
"8 21\n2 6\n3 3\n3 7\n3 8\n3 8\n3 7\n2 6\n3 6\n",
"5 5\n3 1\n2 6\n3 2\n1 1\n2 6\n",
"1 3\n1 10\n",
"6 12\n1 7\n1 7\n2 8\n1 2\n2 9\n3 5\n",
"6 6\n2 6\n1 4\n1 8\n3 2\n3 2\n2 2\n",
"6 12\n1 1\n1 7\n2 8\n1 2\n2 9\n3 5\n",
"6 6\n2 6\n1 4\n1 14\n3 2\n3 2\n2 2\n",
"1 2\n3 2\n"
],
"output": [
"10\n",
"3\n",
"0\n",
"5100\n",
"41\n",
"22\n",
"10\n",
"8\n",
"5\n",
"20\n",
"35\n",
"46\n",
"20\n",
"18\n",
"104\n",
"51\n",
"990\n",
"37\n",
"25\n",
"52\n",
"28\n",
"1605\n",
"46\n",
"180\n",
"46\n",
"13\n",
"711\n",
"44\n",
"28\n",
"10\n",
"5\n",
"16\n",
"28\n",
"41\n",
"20310\n",
"26\n",
"18\n",
"22\n",
"14\n",
"14\n",
"22\n",
"8\n",
"5\n",
"20\n",
"18\n",
"53\n",
"990\n",
"38\n",
"25\n",
"51\n",
"32\n",
"179\n",
"46\n",
"13\n",
"757\n",
"44\n",
"26\n",
"10\n",
"48\n",
"20501\n",
"15\n",
"1\n",
"9\n",
"992\n",
"36\n",
"45\n",
"778\n",
"41\n",
"20605\n",
"0\n",
"4\n",
"1005\n",
"35\n",
"28\n",
"56\n",
"711\n",
"43\n",
"19\n",
"5\n",
"20\n",
"5\n",
"8\n",
"20\n",
"18\n",
"48\n",
"25\n",
"48\n",
"13\n",
"10\n",
"38\n",
"20\n",
"32\n",
"26\n",
"0\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
After several latest reforms many tourists are planning to visit Berland, and Berland people understood that it's an opportunity to earn money and changed their jobs to attract tourists. Petya, for example, left the IT corporation he had been working for and started to sell souvenirs at the market.
This morning, as usual, Petya will come to the market. Petya has n different souvenirs to sell; ith souvenir is characterised by its weight wi and cost ci. Petya knows that he might not be able to carry all the souvenirs to the market. So Petya wants to choose a subset of souvenirs such that its total weight is not greater than m, and total cost is maximum possible.
Help Petya to determine maximum possible total cost.
Input
The first line contains two integers n and m (1 ≤ n ≤ 100000, 1 ≤ m ≤ 300000) — the number of Petya's souvenirs and total weight that he can carry to the market.
Then n lines follow. ith line contains two integers wi and ci (1 ≤ wi ≤ 3, 1 ≤ ci ≤ 109) — the weight and the cost of ith souvenir.
Output
Print one number — maximum possible total cost of souvenirs that Petya can carry to the market.
Examples
Input
1 1
2 1
Output
0
Input
2 2
1 3
2 2
Output
3
Input
4 3
3 10
2 7
2 8
1 1
Output
10
### Input:
4 3
3 10
2 7
2 8
1 1
### Output:
10
### Input:
2 2
1 3
2 2
### Output:
3
### Code:
def f():
n, m = map(int, input().split())
l = list(tuple(map(int, input().split())) for _ in range(n))
l.sort(key=lambda e: (0, 6, 3, 2)[e[0]] * e[1], reverse=True)
last, r = [0] * 4, 0
for i, (w, c) in enumerate(l):
if m < w:
break
m -= w
r += c
last[w] = c
else:
return r
if not m:
return r
res, tail = [r], (None, [], [], [])
for w, c in l[i:]:
tail[w].append(c)
for w in 1, 2, 3:
tail[w].append(0)
_, t1, t2, t3 = tail
if m == 1:
res.append(r + t1[0])
if last[1]:
res.append(r - last[1] + t2[0])
if last[2]:
res.append(r - last[2] + t3[0])
if last[3]:
r -= last[3]
res += (r + sum(t1[:4]), r + sum(t1[:2]) + t2[0], r + sum(t2[:2]))
else: # m == 2
res += (r + sum(t1[:2]), r + t2[0])
if last[1]:
res.append(r - last[1] + t3[0])
if last[2]:
res.append(r - last[2] + t3[0] + t1[0])
return max(res)
def main():
print(f())
if __name__ == '__main__':
main()
|
833_A. The Meaningless Game_2881 | <image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 ≤ n ≤ 350000) is given.
Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
from bisect import bisect_left , bisect_right
import math
def ii():
return int(input())
def li():
return list(map(int,input().split()))
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
no = "No"
yes = "Yes"
def solve():
a,b = li()
x = (pow(a*b,1/3))
x=round(x)
if x*x*x==a*b and a%x==b%x==0:
print(yes)
else:
print(no)
t = 1
t = int(input())
for _ in range(t):
solve()
| {
"input": [
"6\n2 4\n75 45\n8 8\n16 16\n247 994\n1000000000 1000000\n",
"1\n1062961 1031\n",
"1\n3331 11095561\n",
"1\n2 3\n",
"3\n1 1\n8 27\n1000 1331\n",
"1\n90 72\n",
"1\n12004 18012002\n",
"1\n3 10\n",
"1\n16 8\n",
"1\n3 1\n",
"1\n31159 970883281\n",
"1\n6 12\n",
"1\n9907 98148649\n",
"1\n1062961 534\n",
"3\n1 1\n8 5\n1000 1331\n",
"6\n2 4\n75 45\n8 8\n16 5\n247 994\n1000000000 1000000\n",
"1\n1 1\n",
"3\n1 2\n4 5\n1000 1247\n",
"1\n1369 11095561\n",
"1\n90 65\n",
"1\n12004 14979606\n",
"1\n1 10\n",
"1\n1 8\n",
"1\n5 1\n",
"1\n59808 970883281\n",
"1\n7 12\n",
"1\n9907 193212989\n",
"1\n1751864 534\n",
"1\n1369 695441\n",
"3\n1 1\n8 5\n1000 1652\n",
"1\n90 50\n",
"1\n12004 23485980\n",
"1\n2 10\n",
"1\n1 13\n",
"1\n59808 1147135943\n",
"1\n5 12\n",
"1\n9907 77741179\n",
"6\n2 4\n75 45\n8 8\n16 7\n247 994\n1000000000 1000000\n",
"1\n2682349 534\n",
"1\n1369 411325\n",
"3\n1 1\n8 5\n1000 1247\n",
"1\n90 19\n",
"1\n12033 23485980\n",
"1\n2 19\n",
"1\n1 12\n",
"1\n1 2\n",
"1\n1029 1147135943\n",
"1\n5 21\n",
"1\n365 77741179\n",
"1\n2682349 821\n",
"1\n113 411325\n",
"3\n1 1\n4 5\n1000 1247\n",
"1\n90 1\n",
"1\n21331 23485980\n",
"1\n2 12\n",
"1\n1 11\n",
"1\n1009 1147135943\n",
"1\n1 21\n",
"1\n347 77741179\n",
"1\n2075461 821\n",
"1\n137 411325\n",
"1\n169 1\n",
"1\n42429 23485980\n",
"1\n1410 1147135943\n",
"1\n682 77741179\n",
"1\n1698406 821\n",
"1\n170 411325\n",
"3\n1 2\n4 5\n1000 1948\n",
"1\n37 1\n",
"1\n32885 23485980\n",
"1\n1410 895339346\n",
"1\n837 77741179\n",
"1\n594056 821\n",
"1\n252 411325\n",
"1\n66 1\n",
"1\n17961 23485980\n",
"1\n2817 895339346\n",
"1\n837 150201939\n",
"1\n142712 821\n",
"1\n252 144541\n",
"1\n47 1\n",
"1\n28408 23485980\n",
"1\n2819 895339346\n",
"1\n337 150201939\n",
"1\n142712 413\n",
"1\n252 203303\n",
"1\n28408 1691073\n"
],
"output": [
"Yes\nYes\nYes\nNo\nNo\nYes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\nNo\nNo\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No",
"Yes\nNo\nNo",
"Yes\nYes\nYes\nNo\nNo\nYes",
"Yes",
"No\nNo\nNo",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"Yes\nNo\nNo",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"Yes\nYes\nYes\nNo\nNo\nYes",
"No",
"No",
"Yes\nNo\nNo",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"Yes\nNo\nNo",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No\nNo\nNo",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No",
"No"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 ≤ n ≤ 350000) is given.
Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
### Input:
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
### Output:
Yes
Yes
Yes
No
No
Yes
### Input:
1
1062961 1031
### Output:
Yes
### Code:
import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
from bisect import bisect_left , bisect_right
import math
def ii():
return int(input())
def li():
return list(map(int,input().split()))
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
no = "No"
yes = "Yes"
def solve():
a,b = li()
x = (pow(a*b,1/3))
x=round(x)
if x*x*x==a*b and a%x==b%x==0:
print(yes)
else:
print(no)
t = 1
t = int(input())
for _ in range(t):
solve()
|
878_B. Teams Formation_2887 | This time the Berland Team Olympiad in Informatics is held in a remote city that can only be reached by one small bus. Bus has n passenger seats, seat i can be occupied only by a participant from the city ai.
Today the bus has completed m trips, each time bringing n participants. The participants were then aligned in one line in the order they arrived, with people from the same bus standing in the order of their seats (i. e. if we write down the cities where the participants came from, we get the sequence a1, a2, ..., an repeated m times).
After that some teams were formed, each consisting of k participants form the same city standing next to each other in the line. Once formed, teams left the line. The teams were formed until there were no k neighboring participants from the same city.
Help the organizers determine how many participants have left in the line after that process ended. We can prove that answer doesn't depend on the order in which teams were selected.
Input
The first line contains three integers n, k and m (1 ≤ n ≤ 105, 2 ≤ k ≤ 109, 1 ≤ m ≤ 109).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number of city, person from which must take seat i in the bus.
Output
Output the number of remaining participants in the line.
Examples
Input
4 2 5
1 2 3 1
Output
12
Input
1 9 10
1
Output
1
Input
3 2 10
1 2 1
Output
0
Note
In the second example, the line consists of ten participants from the same city. Nine of them will form a team. At the end, only one participant will stay in the line. | import sys
from collections import deque
input=sys.stdin.readline
n,k,m=map(int,input().split())
a=list(map(int,input().split()))
r=a[0]
flag=0
for i in range(n):
if r!=a[i]:
flag=1
break
if flag==0:
print((m*n)%k)
sys.exit()
if k>n:
print(m*n)
sys.exit()
curr=a[0]
tmp=1
que=deque([(a[0],1)])
for i in range(1,n):
if a[i]==curr:
tmp+=1
que.append((a[i],tmp))
if tmp==k:
for j in range(k):
que.pop()
if que:
tmp=que[-1][1]
curr=que[-1][0]
else:
curr=-1
else:
tmp=1
curr=a[i]
que.append((a[i],tmp))
quecop=[]
for i in que:
quecop.append(i[0])
leftrem=0
rightrem=0
if not que:
print(0)
sys.exit()
while que[0][0]==que[-1][0]:
r=que[0][0]
count1=0
p=len(que)
count2=p-1
while count1<p and que[count1][0]==r:
count1+=1
if count1==p:
break
while count2>=0 and que[count2][0]==r:
count2-=1
if count1+p-1-count2<k:
break
leftrem+=count1
rightrem+=k-count1
for i in range(count1):
que.popleft()
for i in range(k-count1):
que.pop()
if que:
t=que[0][0]
flag=0
for i in que:
if i[0]!=t:
flag=1
break
if flag:
print(leftrem+rightrem+len(que)*m)
else:
r=[]
for i in range(leftrem):
if r and r[-1][0]==quecop[i]:
r[-1][1]+=1
else:
r.append([quecop[i],1])
if r and r[-1][0]==que[0][0]:
r[-1][0]=(r[-1][0]+(len(que)*m))%k
if r[-1][1]==0:
r.pop()
else:
if (len(que)*m)%k:
r.append([que[0][0],(len(que)*m)%k])
for i in range(len(quecop)-rightrem,len(quecop)):
if r and r[-1][0]==quecop[i]:
r[-1][1]+=1
if r[-1][1]==k:
r.pop()
else:
r.append([quecop[i],1])
finans=0
for i in r:
finans+=i[1]
print(finans) | {
"input": [
"4 2 5\n1 2 3 1\n",
"1 9 10\n1\n",
"3 2 10\n1 2 1\n",
"10 5 1000000000\n1 1 1 2 2 1 2 2 2 2\n",
"5 3 3\n1 2 2 1 1\n",
"2 4 1\n1 1\n",
"1 1000000000 1000000000\n100000\n",
"5 3 2\n1 1 2 1 1\n",
"5 2 4\n1 2 3 2 1\n",
"1 10 10\n1\n",
"2 4 1\n1 0\n",
"5 3 2\n1 1 3 1 1\n",
"1 7 10\n1\n",
"4 2 5\n1 2 4 1\n",
"1 18 10\n1\n",
"3 2 10\n1 3 1\n",
"4 3 5\n1 2 4 1\n",
"5 3 3\n1 2 3 1 1\n",
"5 2 3\n1 3 3 1 1\n",
"4 5 1\n2 2 4 1\n",
"10 5 1000000000\n1 1 1 2 2 1 2 2 3 2\n",
"4 2 2\n1 2 3 1\n",
"5 2 5\n1 2 3 1 1\n",
"4 5 2\n4 0 4 1\n",
"2 3 1\n1 0\n",
"5 3 2\n1 2 3 1 1\n",
"3 2 14\n1 3 1\n",
"4 5 5\n1 2 4 1\n",
"5 2 3\n1 2 3 1 1\n",
"4 5 5\n2 2 4 1\n",
"4 5 1\n2 4 4 1\n",
"4 5 1\n2 0 4 1\n",
"4 5 1\n4 0 4 1\n",
"4 5 1\n4 0 4 2\n",
"5 3 3\n1 2 2 2 1\n",
"2 4 1\n1 2\n",
"1 1000000000 1000000000\n110000\n",
"5 2 4\n1 2 1 2 1\n",
"1 10 2\n1\n",
"3 2 11\n1 2 1\n",
"4 2 5\n1 2 4 2\n",
"5 3 2\n1 2 3 0 1\n",
"3 2 22\n1 3 1\n",
"4 10 5\n1 2 4 1\n",
"4 5 5\n2 2 4 0\n",
"5 2 3\n1 0 3 1 1\n",
"4 5 1\n2 0 6 1\n",
"10 5 1000000000\n1 1 1 2 0 1 2 2 3 2\n",
"2 4 1\n1 4\n",
"1 1000000000 1000000000\n110100\n",
"1 3 2\n1\n",
"4 2 2\n1 2 3 0\n",
"3 2 11\n2 2 1\n",
"4 2 5\n1 2 5 2\n",
"5 3 2\n1 2 3 -1 1\n"
],
"output": [
"12\n",
"1\n",
"0\n",
"10000000000\n",
"0\n",
"2\n",
"0\n",
"7\n",
"0\n",
"0\n",
"2\n",
"7\n",
"3\n",
"12\n",
"10\n",
"0\n",
"20\n",
"9\n",
"1\n",
"4\n",
"10000000000\n",
"6\n",
"15\n",
"8\n",
"2\n",
"7\n",
"0\n",
"20\n",
"9\n",
"20\n",
"4\n",
"4\n",
"4\n",
"4\n",
"0\n",
"2\n",
"0\n",
"0\n",
"2\n",
"3\n",
"20\n",
"10\n",
"0\n",
"20\n",
"20\n",
"9\n",
"4\n",
"10000000000\n",
"2\n",
"0\n",
"2\n",
"8\n",
"1\n",
"20\n",
"10\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This time the Berland Team Olympiad in Informatics is held in a remote city that can only be reached by one small bus. Bus has n passenger seats, seat i can be occupied only by a participant from the city ai.
Today the bus has completed m trips, each time bringing n participants. The participants were then aligned in one line in the order they arrived, with people from the same bus standing in the order of their seats (i. e. if we write down the cities where the participants came from, we get the sequence a1, a2, ..., an repeated m times).
After that some teams were formed, each consisting of k participants form the same city standing next to each other in the line. Once formed, teams left the line. The teams were formed until there were no k neighboring participants from the same city.
Help the organizers determine how many participants have left in the line after that process ended. We can prove that answer doesn't depend on the order in which teams were selected.
Input
The first line contains three integers n, k and m (1 ≤ n ≤ 105, 2 ≤ k ≤ 109, 1 ≤ m ≤ 109).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number of city, person from which must take seat i in the bus.
Output
Output the number of remaining participants in the line.
Examples
Input
4 2 5
1 2 3 1
Output
12
Input
1 9 10
1
Output
1
Input
3 2 10
1 2 1
Output
0
Note
In the second example, the line consists of ten participants from the same city. Nine of them will form a team. At the end, only one participant will stay in the line.
### Input:
4 2 5
1 2 3 1
### Output:
12
### Input:
1 9 10
1
### Output:
1
### Code:
import sys
from collections import deque
input=sys.stdin.readline
n,k,m=map(int,input().split())
a=list(map(int,input().split()))
r=a[0]
flag=0
for i in range(n):
if r!=a[i]:
flag=1
break
if flag==0:
print((m*n)%k)
sys.exit()
if k>n:
print(m*n)
sys.exit()
curr=a[0]
tmp=1
que=deque([(a[0],1)])
for i in range(1,n):
if a[i]==curr:
tmp+=1
que.append((a[i],tmp))
if tmp==k:
for j in range(k):
que.pop()
if que:
tmp=que[-1][1]
curr=que[-1][0]
else:
curr=-1
else:
tmp=1
curr=a[i]
que.append((a[i],tmp))
quecop=[]
for i in que:
quecop.append(i[0])
leftrem=0
rightrem=0
if not que:
print(0)
sys.exit()
while que[0][0]==que[-1][0]:
r=que[0][0]
count1=0
p=len(que)
count2=p-1
while count1<p and que[count1][0]==r:
count1+=1
if count1==p:
break
while count2>=0 and que[count2][0]==r:
count2-=1
if count1+p-1-count2<k:
break
leftrem+=count1
rightrem+=k-count1
for i in range(count1):
que.popleft()
for i in range(k-count1):
que.pop()
if que:
t=que[0][0]
flag=0
for i in que:
if i[0]!=t:
flag=1
break
if flag:
print(leftrem+rightrem+len(que)*m)
else:
r=[]
for i in range(leftrem):
if r and r[-1][0]==quecop[i]:
r[-1][1]+=1
else:
r.append([quecop[i],1])
if r and r[-1][0]==que[0][0]:
r[-1][0]=(r[-1][0]+(len(que)*m))%k
if r[-1][1]==0:
r.pop()
else:
if (len(que)*m)%k:
r.append([que[0][0],(len(que)*m)%k])
for i in range(len(quecop)-rightrem,len(quecop)):
if r and r[-1][0]==quecop[i]:
r[-1][1]+=1
if r[-1][1]==k:
r.pop()
else:
r.append([quecop[i],1])
finans=0
for i in r:
finans+=i[1]
print(finans) |
901_D. Weighting a Tree_2890 | You are given a connected undirected graph with n vertices and m edges. The vertices are enumerated from 1 to n.
You are given n integers c1, c2, ..., cn, each of them is between - n and n, inclusive. It is also guaranteed that the parity of cv equals the parity of degree of vertex v. The degree of a vertex is the number of edges connected to it.
You are to write a weight between - 2·n2 and 2·n2 (inclusive) on each edge in such a way, that for each vertex v the sum of weights on edges connected to this vertex is equal to cv, or determine that this is impossible.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, n - 1 ≤ m ≤ 105) — the number of vertices and the number of edges.
The next line contains n integers c1, c2, ..., cn ( - n ≤ ci ≤ n), where ci is the required sum of weights of edges connected to vertex i. It is guaranteed that the parity of ci equals the parity of degree of vertex i.
The next m lines describe edges of the graph. The i-th of these lines contains two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), meaning that the i-th edge connects vertices ai and bi.
It is guaranteed that the given graph is connected and does not contain loops and multiple edges.
Output
If there is no solution, print "NO".
Otherwise print "YES" and then m lines, the i-th of them is the weight of the i-th edge wi ( - 2·n2 ≤ wi ≤ 2·n2).
Examples
Input
3 3
2 2 2
1 2
2 3
1 3
Output
YES
1
1
1
Input
4 3
-1 0 2 1
1 2
2 3
3 4
Output
YES
-1
1
1
Input
6 6
3 5 5 5 1 5
1 4
3 2
4 3
4 5
3 5
5 6
Output
YES
3
5
3
-1
-3
5
Input
4 4
4 4 2 4
1 2
2 3
3 4
4 1
Output
NO |
def divisors(M):
d=[]
i=1
while M>=i**2:
if M%i==0:
d.append(i)
if i**2!=M:
d.append(M//i)
i=i+1
return d
def popcount(x):
x = x - ((x >> 1) & 0x55555555)
x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
x = (x + (x >> 4)) & 0x0f0f0f0f
x = x + (x >> 8)
x = x + (x >> 16)
return x & 0x0000007f
def eratosthenes(n):
res=[0 for i in range(n+1)]
prime=set([])
for i in range(2,n+1):
if not res[i]:
prime.add(i)
for j in range(1,n//i+1):
res[i*j]=1
return prime
def factorization(n):
res=[]
for p in prime:
if n%p==0:
while n%p==0:
n//=p
res.append(p)
if n!=1:
res.append(n)
return res
def euler_phi(n):
res = n
for x in range(2,n+1):
if x ** 2 > n:
break
if n%x==0:
res = res//x * (x-1)
while n%x==0:
n //= x
if n!=1:
res = res//n * (n-1)
return res
def ind(b,n):
res=0
while n%b==0:
res+=1
n//=b
return res
def isPrimeMR(n):
d = n - 1
d = d // (d & -d)
L = [2, 3, 5, 7, 11, 13, 17]
for a in L:
t = d
y = pow(a, t, n)
if y == 1: continue
while y != n - 1:
y = (y * y) % n
if y == 1 or t == n - 1: return 0
t <<= 1
return 1
def findFactorRho(n):
from math import gcd
m = 1 << n.bit_length() // 8
for c in range(1, 99):
f = lambda x: (x * x + c) % n
y, r, q, g = 2, 1, 1, 1
while g == 1:
x = y
for i in range(r):
y = f(y)
k = 0
while k < r and g == 1:
ys = y
for i in range(min(m, r - k)):
y = f(y)
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
while g == 1:
ys = f(ys)
g = gcd(abs(x - ys), n)
if g < n:
if isPrimeMR(g): return g
elif isPrimeMR(n // g): return n // g
return findFactorRho(g)
def primeFactor(n):
i = 2
ret = {}
rhoFlg = 0
while i*i <= n:
k = 0
while n % i == 0:
n //= i
k += 1
if k: ret[i] = k
i += 1 + i % 2
if i == 101 and n >= 2 ** 20:
while n > 1:
if isPrimeMR(n):
ret[n], n = 1, 1
else:
rhoFlg = 1
j = findFactorRho(n)
k = 0
while n % j == 0:
n //= j
k += 1
ret[j] = k
if n > 1: ret[n] = 1
if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
return ret
def divisors(n):
res = [1]
prime = primeFactor(n)
for p in prime:
newres = []
for d in res:
for j in range(prime[p]+1):
newres.append(d*p**j)
res = newres
res.sort()
return res
def xorfactorial(num):
if num==0:
return 0
elif num==1:
return 1
elif num==2:
return 3
elif num==3:
return 0
else:
x=baseorder(num)
return (2**x)*((num-2**x+1)%2)+function(num-2**x)
def xorconv(n,X,Y):
if n==0:
res=[(X[0]*Y[0])%mod]
return res
x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
res1=xorconv(n-1,x,y)
res2=xorconv(n-1,z,w)
former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
former=list(map(lambda x:x%mod,former))
latter=list(map(lambda x:x%mod,latter))
return former+latter
def merge_sort(A,B):
pos_A,pos_B = 0,0
n,m = len(A),len(B)
res = []
while pos_A < n and pos_B < m:
a,b = A[pos_A],B[pos_B]
if a < b:
res.append(a)
pos_A += 1
else:
res.append(b)
pos_B += 1
res += A[pos_A:]
res += B[pos_B:]
return res
class UnionFindVerSize():
def __init__(self, N):
self._parent = [n for n in range(0, N)]
self._size = [1] * N
self.group = N
def find_root(self, x):
if self._parent[x] == x: return x
self._parent[x] = self.find_root(self._parent[x])
stack = [x]
while self._parent[stack[-1]]!=stack[-1]:
stack.append(self._parent[stack[-1]])
for v in stack:
self._parent[v] = stack[-1]
return self._parent[x]
def unite(self, x, y):
gx = self.find_root(x)
gy = self.find_root(y)
if gx == gy: return
self.group -= 1
if self._size[gx] < self._size[gy]:
self._parent[gx] = gy
self._size[gy] += self._size[gx]
else:
self._parent[gy] = gx
self._size[gx] += self._size[gy]
def get_size(self, x):
return self._size[self.find_root(x)]
def is_same_group(self, x, y):
return self.find_root(x) == self.find_root(y)
class WeightedUnionFind():
def __init__(self,N):
self.parent = [i for i in range(N)]
self.size = [1 for i in range(N)]
self.val = [0 for i in range(N)]
self.flag = True
self.edge = [[] for i in range(N)]
def dfs(self,v,pv):
stack = [(v,pv)]
new_parent = self.parent[pv]
while stack:
v,pv = stack.pop()
self.parent[v] = new_parent
for nv,w in self.edge[v]:
if nv!=pv:
self.val[nv] = self.val[v] + w
stack.append((nv,v))
def unite(self,x,y,w):
if not self.flag:
return
if self.parent[x]==self.parent[y]:
self.flag = (self.val[x] - self.val[y] == w)
return
if self.size[self.parent[x]]>self.size[self.parent[y]]:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[x] += self.size[y]
self.val[y] = self.val[x] - w
self.dfs(y,x)
else:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[y] += self.size[x]
self.val[x] = self.val[y] + w
self.dfs(x,y)
class Dijkstra():
class Edge():
def __init__(self, _to, _cost):
self.to = _to
self.cost = _cost
def __init__(self, V):
self.G = [[] for i in range(V)]
self._E = 0
self._V = V
@property
def E(self):
return self._E
@property
def V(self):
return self._V
def add_edge(self, _from, _to, _cost):
self.G[_from].append(self.Edge(_to, _cost))
self._E += 1
def shortest_path(self, s):
import heapq
que = []
d = [10**15] * self.V
d[s] = 0
heapq.heappush(que, (0, s))
while len(que) != 0:
cost, v = heapq.heappop(que)
if d[v] < cost: continue
for i in range(len(self.G[v])):
e = self.G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
heapq.heappush(que, (d[e.to], e.to))
return d
#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
N = len(s)
Z_alg = [0]*N
Z_alg[0] = N
i = 1
j = 0
while i < N:
while i+j < N and s[j] == s[i+j]:
j += 1
Z_alg[i] = j
if j == 0:
i += 1
continue
k = 1
while i+k < N and k + Z_alg[k]<j:
Z_alg[i+k] = Z_alg[k]
k += 1
i += k
j -= k
return Z_alg
class BIT():
def __init__(self,n,mod=0):
self.BIT = [0]*(n+1)
self.num = n
self.mod = mod
def query(self,idx):
res_sum = 0
mod = self.mod
while idx > 0:
res_sum += self.BIT[idx]
if mod:
res_sum %= mod
idx -= idx&(-idx)
return res_sum
#Ai += x O(logN)
def update(self,idx,x):
mod = self.mod
while idx <= self.num:
self.BIT[idx] += x
if mod:
self.BIT[idx] %= mod
idx += idx&(-idx)
return
class dancinglink():
def __init__(self,n,debug=False):
self.n = n
self.debug = debug
self._left = [i-1 for i in range(n)]
self._right = [i+1 for i in range(n)]
self.exist = [True for i in range(n)]
def pop(self,k):
if self.debug:
assert self.exist[k]
L = self._left[k]
R = self._right[k]
if L!=-1:
if R!=self.n:
self._right[L],self._left[R] = R,L
else:
self._right[L] = self.n
elif R!=self.n:
self._left[R] = -1
self.exist[k] = False
def left(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._left[res]
if res==-1:
break
k -= 1
return res
def right(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._right[res]
if res==self.n:
break
k -= 1
return res
class SparseTable():
def __init__(self,A,merge_func,ide_ele):
N=len(A)
n=N.bit_length()
self.table=[[ide_ele for i in range(n)] for i in range(N)]
self.merge_func=merge_func
for i in range(N):
self.table[i][0]=A[i]
for j in range(1,n):
for i in range(0,N-2**j+1):
f=self.table[i][j-1]
s=self.table[i+2**(j-1)][j-1]
self.table[i][j]=self.merge_func(f,s)
def query(self,s,t):
b=t-s+1
m=b.bit_length()-1
return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])
class BinaryTrie:
class node:
def __init__(self,val):
self.left = None
self.right = None
self.max = val
def __init__(self):
self.root = self.node(-10**15)
def append(self,key,val):
pos = self.root
for i in range(29,-1,-1):
pos.max = max(pos.max,val)
if key>>i & 1:
if pos.right is None:
pos.right = self.node(val)
pos = pos.right
else:
pos = pos.right
else:
if pos.left is None:
pos.left = self.node(val)
pos = pos.left
else:
pos = pos.left
pos.max = max(pos.max,val)
def search(self,M,xor):
res = -10**15
pos = self.root
for i in range(29,-1,-1):
if pos is None:
break
if M>>i & 1:
if xor>>i & 1:
if pos.right:
res = max(res,pos.right.max)
pos = pos.left
else:
if pos.left:
res = max(res,pos.left.max)
pos = pos.right
else:
if xor>>i & 1:
pos = pos.right
else:
pos = pos.left
if pos:
res = max(res,pos.max)
return res
def solveequation(edge,ans,n,m):
#edge=[[to,dire,id]...]
x=[0]*m
used=[False]*n
for v in range(n):
if used[v]:
continue
y = dfs(v)
if y!=0:
return False
return x
def dfs(v):
used[v]=True
r=ans[v]
for to,dire,id in edge[v]:
if used[to]:
continue
y=dfs(to)
if dire==-1:
x[id]=y
else:
x[id]=-y
r+=y
return r
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
self.size = n
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
if r==self.size:
r = self.num
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r - 1])
l >>= 1
r >>= 1
return res
def bisect_l(self,l,r,x):
l += self.num
r += self.num
Lmin = -1
Rmin = -1
while l<r:
if l & 1:
if self.tree[l] <= x and Lmin==-1:
Lmin = l
l += 1
if r & 1:
if self.tree[r-1] <=x:
Rmin = r-1
l >>= 1
r >>= 1
if Lmin != -1:
pos = Lmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
elif Rmin != -1:
pos = Rmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
else:
return -1
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
n,m = mi()
c = li()
edge = [[] for i in range(n)]
for i in range(m):
u,v = mi()
edge[u-1].append((v-1,i))
edge[v-1].append((u-1,i))
parent = [(-1,-1) for v in range(n)]
tree_edge = [[] for v in range(n)]
depth = [0 for v in range(n)]
special = None
stack = [0]
cnt = [0 for v in range(n)]
while stack:
v = stack[-1]
if cnt[v]==len(edge[v]):
stack.pop()
else:
nv,idx = edge[v][cnt[v]]
cnt[v] += 1
if nv==0 or parent[nv]!=(-1,-1):
if depth[nv] < depth[v] and (depth[v]-depth[nv])%2==0 and not special:
special = (v,nv,idx)
else:
parent[nv] = (v,idx)
depth[nv] = depth[v] + 1
tree_edge[v].append((nv,idx))
stack.append(nv)
if not special:
even = 0
odd = 0
for v in range(n):
if depth[v]&1:
odd += c[v]
else:
even += c[v]
if odd!=even:
print("NO")
else:
print("YES")
deq = deque([0])
topo = []
while deq:
v = deq.popleft()
topo.append(v)
for nv,idx in tree_edge[v]:
deq.append(nv)
ans = [0 for i in range(m)]
for v in topo[::-1]:
if v==0:
continue
_,i = parent[v]
ans[i] = c[v]
for nv,idx in tree_edge[v] :
ans[i] -= ans[idx]
print(*ans,sep="\n")
else:
print("YES")
even = 0
odd = 0
for v in range(n):
if depth[v]&1:
odd += c[v]
else:
even += c[v]
ans = [0 for i in range(m)]
v,nv,idx = special
if depth[v]&1:
ans[idx] -= (even-odd)//2
c[v] += (even-odd)//2
c[nv] += (even-odd)//2
else:
ans[idx] -= (odd-even)//2
c[v] += (odd-even)//2
c[nv] += (odd-even)//2
#print(ans)
deq = deque([0])
topo = []
while deq:
v = deq.popleft()
topo.append(v)
for nv,idx in tree_edge[v]:
deq.append(nv)
for v in topo[::-1]:
if v==0:
continue
_,i = parent[v]
ans[i] = c[v]
for nv,idx in tree_edge[v] :
ans[i] -= ans[idx]
print(*ans,sep="\n")
| {
"input": [
"6 6\n3 5 5 5 1 5\n1 4\n3 2\n4 3\n4 5\n3 5\n5 6\n",
"4 4\n4 4 2 4\n1 2\n2 3\n3 4\n4 1\n",
"3 3\n2 2 2\n1 2\n2 3\n1 3\n",
"4 3\n-1 0 2 1\n1 2\n2 3\n3 4\n",
"2 1\n1 1\n2 1\n",
"8 12\n-6 2 -3 2 6 -7 1 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n3 1\n",
"10 13\n3 4 -3 8 6 4 -5 1 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-23 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 3\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"2 1\n1 1\n1 2\n",
"5 7\n4 1 5 3 -1\n2 4\n5 4\n5 2\n1 5\n1 2\n4 1\n1 3\n",
"10 12\n5 1 1 8 -8 10 -3 -2 1 7\n5 3\n8 2\n10 9\n4 6\n5 6\n4 5\n5 10\n4 7\n8 4\n3 1\n3 6\n6 10\n",
"20 40\n-9 -10 -9 15 -3 -5 -17 -10 -6 2 -13 19 10 -15 15 -14 17 0 7 -8\n3 17\n6 18\n15 12\n2 5\n18 3\n16 20\n6 17\n20 10\n10 18\n9 12\n15 3\n6 4\n15 16\n20 6\n20 9\n9 4\n4 8\n14 5\n11 7\n12 11\n3 13\n14 19\n7 17\n16 14\n19 7\n12 13\n14 13\n13 11\n9 14\n13 17\n8 19\n5 20\n2 17\n2 16\n12 5\n8 1\n20 3\n6 2\n5 18\n13 8\n",
"8 12\n-6 2 -3 2 6 -7 1 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n6 1\n",
"10 12\n5 1 1 8 -8 10 -3 -2 1 7\n5 3\n8 2\n10 9\n4 6\n5 6\n4 5\n5 10\n4 7\n8 4\n3 1\n1 6\n6 10\n",
"20 40\n-9 -10 -9 15 -3 -5 -17 -10 -6 2 -13 19 10 -15 15 -14 17 0 7 -8\n3 17\n6 18\n15 12\n2 5\n18 3\n16 20\n6 17\n20 10\n10 18\n9 12\n15 3\n6 4\n15 16\n20 6\n20 9\n9 4\n4 8\n14 5\n11 7\n12 11\n3 13\n14 19\n7 17\n16 14\n19 7\n12 13\n14 13\n13 11\n9 14\n13 17\n8 19\n5 20\n2 17\n2 6\n12 5\n8 1\n20 3\n6 2\n5 18\n13 8\n",
"5 7\n4 1 3 3 -1\n2 4\n5 4\n5 2\n1 5\n1 2\n4 1\n1 3\n",
"10 12\n5 1 1 8 -8 10 -3 -2 1 7\n5 3\n8 2\n10 9\n4 1\n5 6\n4 5\n5 10\n4 7\n8 4\n3 1\n3 6\n6 10\n",
"4 3\n-1 0 2 1\n1 4\n2 3\n3 4\n",
"10 13\n5 4 -3 8 6 1 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n10 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 13\n3 4 -4 8 6 4 -5 1 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 3\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"4 3\n-1 0 2 2\n1 2\n2 3\n3 4\n",
"8 12\n-6 2 -3 2 1 -7 1 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n6 1\n",
"8 12\n-6 2 -3 2 6 -7 2 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n3 1\n",
"10 13\n3 4 -3 8 6 4 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-23 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 0 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 3\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"2 1\n2 1\n1 2\n",
"10 13\n3 4 -4 8 6 4 -5 1 5 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 13\n3 4 0 8 6 4 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -7 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 13\n3 4 0 0 6 4 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -7 9 -19 -39 -25 -32 32 -36 28 1 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"2 1\n1 0\n2 1\n",
"10 13\n3 4 -3 8 6 4 -5 1 3 -12\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 13\n3 4 -4 8 6 4 -5 1 3 -11\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -32 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 3\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"8 12\n-6 2 -3 1 1 -7 1 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n6 1\n",
"8 12\n-6 2 -3 1 6 -7 2 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 3\n8 4\n3 7\n7 6\n3 1\n",
"10 13\n3 4 -3 8 6 1 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n29 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -7 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 14 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 13\n3 4 0 0 6 4 -5 2 3 -7\n9 5\n9 2\n10 3\n2 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -7 12 -19 -39 -25 -32 32 -36 28 1 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 13\n3 4 -3 8 9 4 -5 1 3 -12\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 12\n5 1 1 8 -8 10 -3 -2 1 7\n5 3\n8 2\n10 9\n4 1\n5 6\n4 5\n10 10\n4 7\n8 4\n3 1\n3 6\n6 10\n",
"10 13\n3 4 -4 8 6 4 -5 1 3 -11\n9 5\n9 2\n10 4\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 13\n5 4 -3 8 6 1 -5 2 3 -7\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"43 52\n-29 -18 -35 21 -12 38 -35 -11 28 -20 27 -7 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 55 -30 -40 14 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 5\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n20 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 13\n3 4 0 0 6 4 -5 2 3 -7\n9 5\n9 2\n10 3\n2 4\n3 5\n4 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 13\n3 4 -3 8 9 4 -5 1 3 -12\n9 5\n9 2\n10 3\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 3\n7 8\n",
"10 13\n3 4 -4 8 6 4 -5 0 3 -11\n9 5\n9 2\n10 4\n1 4\n3 5\n9 1\n6 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"10 13\n3 4 -4 8 6 4 -5 0 3 -11\n9 5\n9 2\n10 4\n1 4\n3 5\n9 1\n7 10\n10 4\n3 1\n2 7\n1 6\n1 7\n7 8\n",
"8 12\n-6 2 -3 2 6 -7 1 -5\n2 1\n5 6\n1 6\n1 4\n8 2\n2 7\n2 5\n8 6\n8 4\n3 7\n7 6\n3 1\n",
"43 52\n-23 -18 -35 21 -12 38 -35 -11 28 -20 27 -5 9 -19 -39 -25 -32 32 -36 28 11 37 1 -25 -22 9 -15 21 25 -39 10 36 -30 -40 22 26 25 -27 -22 -38 -1 18 -13\n33 40\n31 23\n30 26\n21 17\n6 2\n41 19\n32 39\n32 23\n13 14\n25 35\n31 30\n19 32\n25 22\n34 36\n7 40\n23 6\n40 12\n1 3\n23 43\n36 13\n18 33\n17 32\n7 3\n21 34\n41 35\n20 7\n23 1\n41 8\n25 19\n16 29\n42 5\n40 21\n9 37\n17 41\n30 10\n41 18\n39 1\n20 24\n20 4\n42 3\n20 25\n5 16\n31 9\n42 28\n10 11\n19 42\n31 38\n25 2\n31 27\n17 25\n13 15\n31 20\n",
"10 12\n5 1 1 8 -8 10 -3 -2 1 7\n5 3\n8 2\n10 9\n4 6\n5 6\n4 5\n5 10\n4 7\n8 4\n3 1\n2 6\n6 10\n",
"6 6\n3 5 5 5 1 5\n1 4\n3 2\n4 1\n4 5\n3 5\n5 6\n",
"4 4\n4 4 2 4\n1 2\n2 3\n3 2\n4 1\n",
"4 3\n-1 0 4 1\n1 2\n2 3\n3 4\n"
],
"output": [
"YES\n 3\n 5\n 3\n -1\n -3\n 5\n",
"NO\n",
"YES\n 1\n 1\n 1\n",
"YES\n -1\n 1\n 1\n",
"YES\n 1\n",
"NO\n",
"YES\n -7\n 10\n -16\n 3\n 13\n 0\n 4\n 5\n 0\n -6\n 0\n 0\n 1\n",
"NO\n",
"YES\n 1\n",
"YES\n 2\n 1\n -1\n -1\n 0\n 0\n 5\n",
"YES\n-4\n1\n1\n17\n-7\n-3\n6\n-3\n-3\n5\n0\n0\n",
"YES\n -30\n -21\n -23\n -10\n 21\n -52\n 0\n 2\n 0\n -9\n 0\n 16\n 38\n 0\n 42\n 0\n -1\n 7\n -64\n 51\n 0\n 7\n 47\n 0\n 0\n 0\n 10\n 0\n -39\n 0\n 0\n 0\n 0\n 0\n 0\n -9\n 0\n 0\n 0\n 0\n",
"NO\n",
"YES\n-4\n1\n1\n11\n-7\n3\n0\n-3\n-3\n5\n0\n6\n",
"YES\n-30\n-21\n-23\n-10\n21\n-52\n0\n2\n0\n-9\n0\n16\n38\n0\n42\n0\n-1\n7\n-64\n51\n0\n7\n47\n0\n0\n0\n10\n0\n-39\n0\n0\n0\n0\n0\n0\n-9\n0\n0\n0\n0\n",
"YES\n3\n0\n-2\n1\n0\n0\n3\n",
"YES\n-10\n1\n1\n5\n-7\n9\n0\n-3\n-3\n0\n11\n6\n",
"YES\n-1\n0\n2\n",
"YES\n-8\n11\n-17\n2\n14\n3\n1\n6\n0\n-7\n0\n0\n2\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n-10\n1\n1\n5\n-7\n9\n0\n-3\n-3\n0\n11\n6\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n-4\n1\n1\n11\n-7\n3\n0\n-3\n-3\n5\n0\n6\n",
"NO\n",
"NO\n",
"NO\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a connected undirected graph with n vertices and m edges. The vertices are enumerated from 1 to n.
You are given n integers c1, c2, ..., cn, each of them is between - n and n, inclusive. It is also guaranteed that the parity of cv equals the parity of degree of vertex v. The degree of a vertex is the number of edges connected to it.
You are to write a weight between - 2·n2 and 2·n2 (inclusive) on each edge in such a way, that for each vertex v the sum of weights on edges connected to this vertex is equal to cv, or determine that this is impossible.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, n - 1 ≤ m ≤ 105) — the number of vertices and the number of edges.
The next line contains n integers c1, c2, ..., cn ( - n ≤ ci ≤ n), where ci is the required sum of weights of edges connected to vertex i. It is guaranteed that the parity of ci equals the parity of degree of vertex i.
The next m lines describe edges of the graph. The i-th of these lines contains two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi), meaning that the i-th edge connects vertices ai and bi.
It is guaranteed that the given graph is connected and does not contain loops and multiple edges.
Output
If there is no solution, print "NO".
Otherwise print "YES" and then m lines, the i-th of them is the weight of the i-th edge wi ( - 2·n2 ≤ wi ≤ 2·n2).
Examples
Input
3 3
2 2 2
1 2
2 3
1 3
Output
YES
1
1
1
Input
4 3
-1 0 2 1
1 2
2 3
3 4
Output
YES
-1
1
1
Input
6 6
3 5 5 5 1 5
1 4
3 2
4 3
4 5
3 5
5 6
Output
YES
3
5
3
-1
-3
5
Input
4 4
4 4 2 4
1 2
2 3
3 4
4 1
Output
NO
### Input:
6 6
3 5 5 5 1 5
1 4
3 2
4 3
4 5
3 5
5 6
### Output:
YES
3
5
3
-1
-3
5
### Input:
4 4
4 4 2 4
1 2
2 3
3 4
4 1
### Output:
NO
### Code:
def divisors(M):
d=[]
i=1
while M>=i**2:
if M%i==0:
d.append(i)
if i**2!=M:
d.append(M//i)
i=i+1
return d
def popcount(x):
x = x - ((x >> 1) & 0x55555555)
x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
x = (x + (x >> 4)) & 0x0f0f0f0f
x = x + (x >> 8)
x = x + (x >> 16)
return x & 0x0000007f
def eratosthenes(n):
res=[0 for i in range(n+1)]
prime=set([])
for i in range(2,n+1):
if not res[i]:
prime.add(i)
for j in range(1,n//i+1):
res[i*j]=1
return prime
def factorization(n):
res=[]
for p in prime:
if n%p==0:
while n%p==0:
n//=p
res.append(p)
if n!=1:
res.append(n)
return res
def euler_phi(n):
res = n
for x in range(2,n+1):
if x ** 2 > n:
break
if n%x==0:
res = res//x * (x-1)
while n%x==0:
n //= x
if n!=1:
res = res//n * (n-1)
return res
def ind(b,n):
res=0
while n%b==0:
res+=1
n//=b
return res
def isPrimeMR(n):
d = n - 1
d = d // (d & -d)
L = [2, 3, 5, 7, 11, 13, 17]
for a in L:
t = d
y = pow(a, t, n)
if y == 1: continue
while y != n - 1:
y = (y * y) % n
if y == 1 or t == n - 1: return 0
t <<= 1
return 1
def findFactorRho(n):
from math import gcd
m = 1 << n.bit_length() // 8
for c in range(1, 99):
f = lambda x: (x * x + c) % n
y, r, q, g = 2, 1, 1, 1
while g == 1:
x = y
for i in range(r):
y = f(y)
k = 0
while k < r and g == 1:
ys = y
for i in range(min(m, r - k)):
y = f(y)
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
while g == 1:
ys = f(ys)
g = gcd(abs(x - ys), n)
if g < n:
if isPrimeMR(g): return g
elif isPrimeMR(n // g): return n // g
return findFactorRho(g)
def primeFactor(n):
i = 2
ret = {}
rhoFlg = 0
while i*i <= n:
k = 0
while n % i == 0:
n //= i
k += 1
if k: ret[i] = k
i += 1 + i % 2
if i == 101 and n >= 2 ** 20:
while n > 1:
if isPrimeMR(n):
ret[n], n = 1, 1
else:
rhoFlg = 1
j = findFactorRho(n)
k = 0
while n % j == 0:
n //= j
k += 1
ret[j] = k
if n > 1: ret[n] = 1
if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
return ret
def divisors(n):
res = [1]
prime = primeFactor(n)
for p in prime:
newres = []
for d in res:
for j in range(prime[p]+1):
newres.append(d*p**j)
res = newres
res.sort()
return res
def xorfactorial(num):
if num==0:
return 0
elif num==1:
return 1
elif num==2:
return 3
elif num==3:
return 0
else:
x=baseorder(num)
return (2**x)*((num-2**x+1)%2)+function(num-2**x)
def xorconv(n,X,Y):
if n==0:
res=[(X[0]*Y[0])%mod]
return res
x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
res1=xorconv(n-1,x,y)
res2=xorconv(n-1,z,w)
former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
former=list(map(lambda x:x%mod,former))
latter=list(map(lambda x:x%mod,latter))
return former+latter
def merge_sort(A,B):
pos_A,pos_B = 0,0
n,m = len(A),len(B)
res = []
while pos_A < n and pos_B < m:
a,b = A[pos_A],B[pos_B]
if a < b:
res.append(a)
pos_A += 1
else:
res.append(b)
pos_B += 1
res += A[pos_A:]
res += B[pos_B:]
return res
class UnionFindVerSize():
def __init__(self, N):
self._parent = [n for n in range(0, N)]
self._size = [1] * N
self.group = N
def find_root(self, x):
if self._parent[x] == x: return x
self._parent[x] = self.find_root(self._parent[x])
stack = [x]
while self._parent[stack[-1]]!=stack[-1]:
stack.append(self._parent[stack[-1]])
for v in stack:
self._parent[v] = stack[-1]
return self._parent[x]
def unite(self, x, y):
gx = self.find_root(x)
gy = self.find_root(y)
if gx == gy: return
self.group -= 1
if self._size[gx] < self._size[gy]:
self._parent[gx] = gy
self._size[gy] += self._size[gx]
else:
self._parent[gy] = gx
self._size[gx] += self._size[gy]
def get_size(self, x):
return self._size[self.find_root(x)]
def is_same_group(self, x, y):
return self.find_root(x) == self.find_root(y)
class WeightedUnionFind():
def __init__(self,N):
self.parent = [i for i in range(N)]
self.size = [1 for i in range(N)]
self.val = [0 for i in range(N)]
self.flag = True
self.edge = [[] for i in range(N)]
def dfs(self,v,pv):
stack = [(v,pv)]
new_parent = self.parent[pv]
while stack:
v,pv = stack.pop()
self.parent[v] = new_parent
for nv,w in self.edge[v]:
if nv!=pv:
self.val[nv] = self.val[v] + w
stack.append((nv,v))
def unite(self,x,y,w):
if not self.flag:
return
if self.parent[x]==self.parent[y]:
self.flag = (self.val[x] - self.val[y] == w)
return
if self.size[self.parent[x]]>self.size[self.parent[y]]:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[x] += self.size[y]
self.val[y] = self.val[x] - w
self.dfs(y,x)
else:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[y] += self.size[x]
self.val[x] = self.val[y] + w
self.dfs(x,y)
class Dijkstra():
class Edge():
def __init__(self, _to, _cost):
self.to = _to
self.cost = _cost
def __init__(self, V):
self.G = [[] for i in range(V)]
self._E = 0
self._V = V
@property
def E(self):
return self._E
@property
def V(self):
return self._V
def add_edge(self, _from, _to, _cost):
self.G[_from].append(self.Edge(_to, _cost))
self._E += 1
def shortest_path(self, s):
import heapq
que = []
d = [10**15] * self.V
d[s] = 0
heapq.heappush(que, (0, s))
while len(que) != 0:
cost, v = heapq.heappop(que)
if d[v] < cost: continue
for i in range(len(self.G[v])):
e = self.G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
heapq.heappush(que, (d[e.to], e.to))
return d
#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
N = len(s)
Z_alg = [0]*N
Z_alg[0] = N
i = 1
j = 0
while i < N:
while i+j < N and s[j] == s[i+j]:
j += 1
Z_alg[i] = j
if j == 0:
i += 1
continue
k = 1
while i+k < N and k + Z_alg[k]<j:
Z_alg[i+k] = Z_alg[k]
k += 1
i += k
j -= k
return Z_alg
class BIT():
def __init__(self,n,mod=0):
self.BIT = [0]*(n+1)
self.num = n
self.mod = mod
def query(self,idx):
res_sum = 0
mod = self.mod
while idx > 0:
res_sum += self.BIT[idx]
if mod:
res_sum %= mod
idx -= idx&(-idx)
return res_sum
#Ai += x O(logN)
def update(self,idx,x):
mod = self.mod
while idx <= self.num:
self.BIT[idx] += x
if mod:
self.BIT[idx] %= mod
idx += idx&(-idx)
return
class dancinglink():
def __init__(self,n,debug=False):
self.n = n
self.debug = debug
self._left = [i-1 for i in range(n)]
self._right = [i+1 for i in range(n)]
self.exist = [True for i in range(n)]
def pop(self,k):
if self.debug:
assert self.exist[k]
L = self._left[k]
R = self._right[k]
if L!=-1:
if R!=self.n:
self._right[L],self._left[R] = R,L
else:
self._right[L] = self.n
elif R!=self.n:
self._left[R] = -1
self.exist[k] = False
def left(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._left[res]
if res==-1:
break
k -= 1
return res
def right(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._right[res]
if res==self.n:
break
k -= 1
return res
class SparseTable():
def __init__(self,A,merge_func,ide_ele):
N=len(A)
n=N.bit_length()
self.table=[[ide_ele for i in range(n)] for i in range(N)]
self.merge_func=merge_func
for i in range(N):
self.table[i][0]=A[i]
for j in range(1,n):
for i in range(0,N-2**j+1):
f=self.table[i][j-1]
s=self.table[i+2**(j-1)][j-1]
self.table[i][j]=self.merge_func(f,s)
def query(self,s,t):
b=t-s+1
m=b.bit_length()-1
return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])
class BinaryTrie:
class node:
def __init__(self,val):
self.left = None
self.right = None
self.max = val
def __init__(self):
self.root = self.node(-10**15)
def append(self,key,val):
pos = self.root
for i in range(29,-1,-1):
pos.max = max(pos.max,val)
if key>>i & 1:
if pos.right is None:
pos.right = self.node(val)
pos = pos.right
else:
pos = pos.right
else:
if pos.left is None:
pos.left = self.node(val)
pos = pos.left
else:
pos = pos.left
pos.max = max(pos.max,val)
def search(self,M,xor):
res = -10**15
pos = self.root
for i in range(29,-1,-1):
if pos is None:
break
if M>>i & 1:
if xor>>i & 1:
if pos.right:
res = max(res,pos.right.max)
pos = pos.left
else:
if pos.left:
res = max(res,pos.left.max)
pos = pos.right
else:
if xor>>i & 1:
pos = pos.right
else:
pos = pos.left
if pos:
res = max(res,pos.max)
return res
def solveequation(edge,ans,n,m):
#edge=[[to,dire,id]...]
x=[0]*m
used=[False]*n
for v in range(n):
if used[v]:
continue
y = dfs(v)
if y!=0:
return False
return x
def dfs(v):
used[v]=True
r=ans[v]
for to,dire,id in edge[v]:
if used[to]:
continue
y=dfs(to)
if dire==-1:
x[id]=y
else:
x[id]=-y
r+=y
return r
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
self.size = n
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
if r==self.size:
r = self.num
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r - 1])
l >>= 1
r >>= 1
return res
def bisect_l(self,l,r,x):
l += self.num
r += self.num
Lmin = -1
Rmin = -1
while l<r:
if l & 1:
if self.tree[l] <= x and Lmin==-1:
Lmin = l
l += 1
if r & 1:
if self.tree[r-1] <=x:
Rmin = r-1
l >>= 1
r >>= 1
if Lmin != -1:
pos = Lmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
elif Rmin != -1:
pos = Rmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
else:
return -1
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
n,m = mi()
c = li()
edge = [[] for i in range(n)]
for i in range(m):
u,v = mi()
edge[u-1].append((v-1,i))
edge[v-1].append((u-1,i))
parent = [(-1,-1) for v in range(n)]
tree_edge = [[] for v in range(n)]
depth = [0 for v in range(n)]
special = None
stack = [0]
cnt = [0 for v in range(n)]
while stack:
v = stack[-1]
if cnt[v]==len(edge[v]):
stack.pop()
else:
nv,idx = edge[v][cnt[v]]
cnt[v] += 1
if nv==0 or parent[nv]!=(-1,-1):
if depth[nv] < depth[v] and (depth[v]-depth[nv])%2==0 and not special:
special = (v,nv,idx)
else:
parent[nv] = (v,idx)
depth[nv] = depth[v] + 1
tree_edge[v].append((nv,idx))
stack.append(nv)
if not special:
even = 0
odd = 0
for v in range(n):
if depth[v]&1:
odd += c[v]
else:
even += c[v]
if odd!=even:
print("NO")
else:
print("YES")
deq = deque([0])
topo = []
while deq:
v = deq.popleft()
topo.append(v)
for nv,idx in tree_edge[v]:
deq.append(nv)
ans = [0 for i in range(m)]
for v in topo[::-1]:
if v==0:
continue
_,i = parent[v]
ans[i] = c[v]
for nv,idx in tree_edge[v] :
ans[i] -= ans[idx]
print(*ans,sep="\n")
else:
print("YES")
even = 0
odd = 0
for v in range(n):
if depth[v]&1:
odd += c[v]
else:
even += c[v]
ans = [0 for i in range(m)]
v,nv,idx = special
if depth[v]&1:
ans[idx] -= (even-odd)//2
c[v] += (even-odd)//2
c[nv] += (even-odd)//2
else:
ans[idx] -= (odd-even)//2
c[v] += (odd-even)//2
c[nv] += (odd-even)//2
#print(ans)
deq = deque([0])
topo = []
while deq:
v = deq.popleft()
topo.append(v)
for nv,idx in tree_edge[v]:
deq.append(nv)
for v in topo[::-1]:
if v==0:
continue
_,i = parent[v]
ans[i] = c[v]
for nv,idx in tree_edge[v] :
ans[i] -= ans[idx]
print(*ans,sep="\n")
|
924_A. Mystical Mosaic_2894 | There is a rectangular grid of n rows of m initially-white cells each.
Arkady performed a certain number (possibly zero) of operations on it. In the i-th operation, a non-empty subset of rows Ri and a non-empty subset of columns Ci are chosen. For each row r in Ri and each column c in Ci, the intersection of row r and column c is coloured black.
There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of (i, j) (i < j) exists such that <image> or <image>, where <image> denotes intersection of sets, and <image> denotes the empty set.
You are to determine whether a valid sequence of operations exists that produces a given final grid.
Input
The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 50) — the number of rows and columns of the grid, respectively.
Each of the following n lines contains a string of m characters, each being either '.' (denoting a white cell) or '#' (denoting a black cell), representing the desired setup.
Output
If the given grid can be achieved by any valid sequence of operations, output "Yes"; otherwise output "No" (both without quotes).
You can print each character in any case (upper or lower).
Examples
Input
5 8
.#.#..#.
.....#..
.#.#..#.
#.#....#
.....#..
Output
Yes
Input
5 5
..#..
..#..
#####
..#..
..#..
Output
No
Input
5 9
........#
#........
..##.#...
.......#.
....#.#.#
Output
No
Note
For the first example, the desired setup can be produced by 3 operations, as is shown below.
<image>
For the second example, the desired setup cannot be produced, since in order to colour the center row, the third row and all columns must be selected in one operation, but after that no column can be selected again, hence it won't be possible to colour the other cells in the center column. | def read_data():
n, m = map(int, input().strip().split())
a = []
for i in range(n):
line = list(input().strip())
for j in range(len(line)):
if line[j] == ".":
line[j] = 0
else:
line[j] = 1
a.append(line)
return n, m, a
def get_step(i,j):
rows = []
cols = []
for k in range(m):
if a[i][k] == 1:
cols.append(k)
if k in usedc:
return "No"
else:
usedc.append(k)
for k in range(n):
if a[k][j] == 1:
rows.append(k)
if k in usedr:
return "No"
else:
usedr.append(k)
for row in rows:
for col in cols:
if a[row][col] == 0:
return "No"
else:
a[row][col] = 0
return "Ok"
def solve():
for i in range(n):
for j in range(m):
if a[i][j] == 1:
step = get_step(i,j)
if step == "No":
return "No"
return "Yes"
n, m, a = read_data()
usedr = []
usedc = []
print(solve())
| {
"input": [
"5 9\n........#\n#........\n..##.#...\n.......#.\n....#.#.#\n",
"5 5\n..#..\n..#..\n#####\n..#..\n..#..\n",
"5 8\n.#.#..#.\n.....#..\n.#.#..#.\n#.#....#\n.....#..\n",
"9 5\n.....\n#....\n..#..\n.....\n.#..#\n...#.\n.#...\n....#\n.....\n",
"4 10\n..#......#\n.....##...\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"2 50\n...#.##.###...#.#..##....##..........#.#..#.#####.\n...#.##.###...#.#..##....##..........#.#..#.#####.\n",
"1 1\n#\n",
"3 3\n.##\n#.#\n##.\n",
"50 8\n.....#..\n........\n........\n.....#..\n.....#..\n........\n........\n........\n........\n...#....\n...#....\n........\n...#....\n#.#.#...\n...#....\n...#....\n........\n...#....\n...#....\n...#....\n........\n#.#.#...\n.....#..\n........\n#.#.#...\n#.#.#...\n#.#.#...\n...#....\n........\n........\n........\n#.#.#...\n........\n.....#..\n........\n........\n........\n........\n........\n........\n.....#..\n........\n........\n........\n.....#..\n#.#.#...\n...#....\n........\n........\n........\n",
"1 1\n.\n",
"25 16\n.............#..\n.............#..\n.......#...#....\n............#...\n.....#..........\n.....#..........\n#...............\n................\n........#.......\n................\n................\n.#..............\n#...............\n.....#..........\n.#..............\n............#...\n................\n................\n................\n........#.......\n..#.............\n..........#.....\n.......#...#....\n.............#..\n..........#.....\n",
"25 16\n..............#.\n................\n...#...#........\n........#.#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n.........#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#..............\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"10 15\n.......#.......\n.....#.........\n....#..........\n....#..........\n.....#.........\n.....#.........\n#.............#\n...#..#........\n...............\n.............#.\n",
"4 10\n###..#..##\n...##..#..\n.##..#..#.\n.........#\n",
"2 5\n.####\n#..##\n",
"5 2\n##\n##\n..\n##\n..\n",
"2 2\n##\n#.\n",
"50 1\n.\n.\n#\n.\n#\n.\n#\n.\n.\n#\n#\n#\n.\n#\n#\n#\n#\n.\n.\n.\n.\n.\n.\n.\n.\n.\n#\n#\n#\n#\n.\n.\n.\n.\n.\n#\n.\n.\n.\n#\n#\n.\n.\n#\n#\n.\n.\n#\n#\n.\n",
"5 2\n#.\n##\n##\n#.\n..\n",
"2 3\n#.#\n###\n",
"2 1\n.\n#\n",
"2 3\n#.#\n##.\n",
"10 10\n..........\n..........\n..........\n..........\n.#.......#\n#.........\n......#...\n..........\n..........\n#.....#...\n",
"4 4\n###.\n##.#\n#.##\n.###\n",
"9 5\n.....\n#....\n..#..\n.....\n.#..#\n...#.\n.#...\n..-.#\n.....\n",
"0 10\n###..#..##\n...##..#..\n.##..#..#.\n.........#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n.........#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#..............\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"0 2\n##\n#.\n",
"5 2\n#.\n##\n#\"\n#.\n..\n",
"1 3\n#.#\n###\n",
"1 1\n.\n#\n",
"4 4\n###.\n#$.#\n#.##\n.###\n",
"5 9\n........#\n#........\n..##.#...\n.#.......\n....#.#.#\n",
"5 8\n.#.#..#.\n.....#..\n.#..#.#.\n#.#....#\n.....#..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n.........#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............/.\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"0 4\n##\n#.\n",
"5 2\n#.\n##\n#\"\n.#\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"0 4\n#\"\n#.\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n.-\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"0 1\n#\"\n#.\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n.#\n..\n..\n.#\n.-\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"0 1\n#\"\n#-\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"1 10\n..#......#\n.....##...\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n./\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"25 16\n.............#..\n.............#..\n.......#...#....\n............#...\n.....#..........\n.....#..........\n#...............\n................\n........#.......\n................\n................\n.#..............\n#...............\n..........#.....\n.#..............\n............#...\n................\n................\n................\n........#.......\n..#.............\n..........#.....\n.......#...#....\n.............#..\n..........#.....\n",
"10 15\n.......#.......\n.....#.........\n....#..........\n....#..........\n.....#.........\n.....#.........\n#..#...........\n...#..#........\n...............\n.............#.\n",
"4 4\n###.\n##.#\n#.$#\n.###\n",
"5 8\n.#.#..#.\n.....#..\n.#..#.#.\n#.#.-..#\n.....#..\n",
"9 5\n.....\n#....\n..#..\n.....\n#..#.\n...#.\n.#...\n..-.#\n.....\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n/.\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n...../...#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#..............\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"0 1\n##\n#.\n",
"5 2\n#.\n##\n#\"\n#.\n-.\n",
"0 1\n.\n#\n",
"5 9\n........#\n#........\n...#.##..\n.#.......\n....#.#.#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n./\n..\n..\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n.........#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............/.\n................\n......#.....#...\n.......#......./\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"0 4\n#!\n#.\n",
"0 2\n#.\n##\n#\"\n.#\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.$\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"0 3\n#\"\n#.\n",
"0 0\n#\"\n#-\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n-#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n/.\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n#.\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"1 10\n..#......#\n...##.....\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n./\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.$\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"25 16\n.............#..\n.............#..\n.......#...#....\n............#...\n.....#..........\n.....#..........\n#...............\n................\n........#.......\n................\n................\n.#..............\n#...............\n..........#.....\n.#..............\n...#............\n................\n................\n................\n........#.......\n..#.............\n..........#.....\n.......#...#....\n.............#..\n..........#.....\n",
"10 15\n.......#.......\n.....#.........\n....#..........\n....#..........\n.....#.........\n.....#.........\n#..#...........\n...#..#........\n.....-.........\n.............#.\n",
"4 4\n.###\n##.#\n#.$#\n.###\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n-.\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n/.\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n...../...#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............-.\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#..............\n",
"0 1\n#$\n#.\n",
"5 2\n.#\n##\n#\"\n#.\n-.\n",
"0 1\n.\n$\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.$\n..\n./\n..\n..\n..\n..\n",
"0 2\n#!\n#.\n",
"0 3\n#\"\n#-\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.\"\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n.#\n..\n..\n..\n.#\n.#\n-#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n/.\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.#\n..\n.#\n/.\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n#.\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n#.\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"0 10\n..#......#\n...##.....\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n.-\n..\n.#\n./\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.$\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"10 15\n.......#.......\n.....#.........\n....#..........\n....#..........\n.....#.........\n.....#.........\n#..#...........\n...#..#........\n.....-.........\n-............#.\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n-.\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.%\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n/.\n..\n..\n",
"25 16\n..............#.\n................\n...#...#........\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n...../...#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............-.\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#.........-....\n",
"5 2\n.#\n##\n##\n#.\n-.\n",
"0 1\n-\n$\n",
"0 2\n#!\n.#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n..\n..\n.\"\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n-#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n/.\n.#\n.-\n..\n#.\n..\n..\n.#\n.-\n./\n.#\n..\n.$\n..\n.#\n/.\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n#.\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n#.\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.$\n..\n..\n..\n..\n.-\n..\n",
"0 10\n..#./....#\n...##.....\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n#.\n..\n..\n.#\n.-\n..\n.#\n./\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.$\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"50 2\n..\n..\n.#\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n-.\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n.%\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n/.\n..\n..\n",
"25 16\n..............#.\n................\n...#...........#\n......#...#.....\n..............##\n..............#.\n.......#........\n......#.........\n............#...\n...../...#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............-.\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#.........-....\n",
"0 1\n-\n%\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n-.\n..\n.\"\n.-\n./\n.#\n..\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n-#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n#.\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n#.\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.$\n..\n..\n..\n..\n.-\n/.\n",
"0 10\n..#./-...#\n...##.....\n#.........\n.#.......#\n",
"50 2\n..\n..\n#.\n..\n#.\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n#.\n..\n..\n.#\n.-\n..\n.#\n./\n.#\n..\n.#\n..\n.#\n.#\n.#\n..\n..\n..\n.#\n.$\n.#\n..\n..\n.#\n.#\n..\n..\n..\n..\n..\n..\n",
"50 2\n..\n..\n.#\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n..\n..\n..\n.#\n..\n..\n.#\n..\n..\n.#\n-.\n..\n.#\n..\n.#\n..\n.#\n..\n.#\n%.\n.#\n..\n..\n..\n.#\n.#\n.#\n..\n..\n.#\n.#\n..\n..\n..\n/.\n..\n..\n",
"25 16\n..............#.\n................\n...#...........#\n......#...#.....\n..............##\n..............#.\n.......#....../.\n......#.........\n............#...\n...../...#.....#\n..............#.\n.......#........\n#...........#...\n...#.#..........\n.#............-.\n................\n......#.....#...\n.......#........\n........#.....#.\n................\n......#.........\n..#.............\n................\n...#.#..........\n.#.........-....\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n.#\n##\n./\n..\n..\n.#\n.-\n..\n#.\n-.\n..\n.\"\n.-\n./\n.#\n/.\n.#\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n.#\n-#\n..\n..\n.#\n.#\n..\n..\n..\n..\n.-\n..\n",
"50 2\n..\n..\n#.\n..\n.#\n..\n..\n..\n.#\n..\n..\n#.\n##\n./\n..\n./\n.#\n.-\n..\n#.\n..\n..\n#.\n.-\n./\n.#\n..\n#.\n..\n.#\n..\n.#\n.$\n#.\n..\n..\n..\n.#\n#.\n.#\n..\n..\n.#\n.$\n..\n..\n..\n..\n.-\n/.\n"
],
"output": [
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There is a rectangular grid of n rows of m initially-white cells each.
Arkady performed a certain number (possibly zero) of operations on it. In the i-th operation, a non-empty subset of rows Ri and a non-empty subset of columns Ci are chosen. For each row r in Ri and each column c in Ci, the intersection of row r and column c is coloured black.
There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of (i, j) (i < j) exists such that <image> or <image>, where <image> denotes intersection of sets, and <image> denotes the empty set.
You are to determine whether a valid sequence of operations exists that produces a given final grid.
Input
The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 50) — the number of rows and columns of the grid, respectively.
Each of the following n lines contains a string of m characters, each being either '.' (denoting a white cell) or '#' (denoting a black cell), representing the desired setup.
Output
If the given grid can be achieved by any valid sequence of operations, output "Yes"; otherwise output "No" (both without quotes).
You can print each character in any case (upper or lower).
Examples
Input
5 8
.#.#..#.
.....#..
.#.#..#.
#.#....#
.....#..
Output
Yes
Input
5 5
..#..
..#..
#####
..#..
..#..
Output
No
Input
5 9
........#
#........
..##.#...
.......#.
....#.#.#
Output
No
Note
For the first example, the desired setup can be produced by 3 operations, as is shown below.
<image>
For the second example, the desired setup cannot be produced, since in order to colour the center row, the third row and all columns must be selected in one operation, but after that no column can be selected again, hence it won't be possible to colour the other cells in the center column.
### Input:
5 9
........#
#........
..##.#...
.......#.
....#.#.#
### Output:
No
### Input:
5 5
..#..
..#..
#####
..#..
..#..
### Output:
No
### Code:
def read_data():
n, m = map(int, input().strip().split())
a = []
for i in range(n):
line = list(input().strip())
for j in range(len(line)):
if line[j] == ".":
line[j] = 0
else:
line[j] = 1
a.append(line)
return n, m, a
def get_step(i,j):
rows = []
cols = []
for k in range(m):
if a[i][k] == 1:
cols.append(k)
if k in usedc:
return "No"
else:
usedc.append(k)
for k in range(n):
if a[k][j] == 1:
rows.append(k)
if k in usedr:
return "No"
else:
usedr.append(k)
for row in rows:
for col in cols:
if a[row][col] == 0:
return "No"
else:
a[row][col] = 0
return "Ok"
def solve():
for i in range(n):
for j in range(m):
if a[i][j] == 1:
step = get_step(i,j)
if step == "No":
return "No"
return "Yes"
n, m, a = read_data()
usedr = []
usedc = []
print(solve())
|
952_C. Ravioli Sort_2898 | Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}. | n = int(input())
l = [int(x) for x in input().split()]
while len(l) > 1:
if len([i for i in range(len(l)-1) if abs(l[i] - l[i+1]) > 1 ])>0:
print ('NO')
exit(0)
l.remove(max(l))
print('YES')
| {
"input": [
"3\n3 1 2\n",
"3\n1 2 3\n",
"4\n90 91 90 91\n",
"4\n54 54 54 55\n",
"10\n55 39 93 42 97 40 36 38 11 97\n",
"3\n90 39 98\n",
"5\n21 57 40 94 17\n",
"8\n46 4 30 85 52 6 84 13\n",
"6\n47 100 96 2 96 43\n",
"4\n61 28 3 81\n",
"5\n14 91 91 91 84\n",
"3\n22 23 24\n",
"1\n13\n",
"9\n13 80 13 38 98 85 11 73 74\n",
"10\n95 51 52 8 44 39 77 17 96 88\n",
"3\n40 40 40\n",
"4\n16 17 17 18\n",
"3\n68 67 67\n",
"4\n83 100 81 75\n",
"9\n71 71 70 70 71 70 69 70 71\n",
"10\n9 9 9 10 10 9 8 8 9 9\n",
"6\n87 86 86 86 85 86\n",
"5\n64 63 63 62 61\n",
"3\n76 9 12\n",
"4\n61 60 60 60\n",
"7\n23 37 39 8 72 31 85\n",
"10\n67 67 67 67 67 67 67 67 67 67\n",
"4\n92 18 29 93\n",
"4\n14 15 15 16\n",
"10\n79 84 22 38 23 22 33 42 13 96\n",
"7\n20 21 95 73 49 98 53\n",
"10\n28 61 23 73 61 33 45 55 18 43\n",
"9\n15 14 14 13 13 12 13 13 14\n",
"5\n46 46 47 46 45\n",
"7\n35 91 87 78 17 71 63\n",
"3\n69 26 73\n",
"10\n16 17 16 15 14 15 16 17 16 15\n",
"9\n95 7 97 61 90 7 30 65 39\n",
"10\n2 83 18 65 58 95 37 51 86 47\n",
"6\n59 59 60 60 59 58\n",
"4\n90 91 83 91\n",
"1\n17\n",
"4\n59 54 54 55\n",
"10\n55 39 93 63 97 40 36 38 11 97\n",
"5\n21 57 40 94 0\n",
"8\n86 4 30 85 52 6 84 13\n",
"6\n47 110 96 2 96 43\n",
"4\n61 28 4 81\n",
"5\n14 91 91 91 0\n",
"3\n22 6 24\n",
"9\n13 80 13 38 98 85 11 73 30\n",
"10\n95 51 52 8 44 39 60 17 96 88\n",
"3\n47 40 40\n",
"4\n83 110 81 75\n",
"10\n9 9 4 10 10 9 8 8 9 9\n",
"3\n30 9 12\n",
"4\n61 49 60 60\n",
"7\n23 37 46 8 72 31 85\n",
"4\n92 26 29 93\n",
"10\n79 84 22 29 23 22 33 42 13 96\n",
"7\n20 21 95 73 49 153 53\n",
"10\n28 61 23 73 61 62 45 55 18 43\n",
"5\n46 86 47 46 45\n",
"7\n35 91 87 85 17 71 63\n",
"3\n65 26 73\n",
"10\n16 17 16 4 14 15 16 17 16 15\n",
"9\n95 8 97 61 90 7 30 65 39\n",
"10\n2 83 18 65 58 44 37 51 86 47\n",
"6\n59 59 60 59 59 58\n",
"3\n2 1 2\n",
"3\n1 2 1\n",
"4\n90 30 83 91\n",
"10\n105 39 93 63 97 40 36 38 11 97\n",
"5\n21 94 40 94 0\n",
"8\n86 4 30 85 98 6 84 13\n",
"6\n47 110 178 2 96 43\n",
"4\n3 28 4 81\n",
"5\n14 91 91 91 1\n",
"3\n41 6 24\n",
"1\n7\n",
"9\n13 80 13 38 98 85 11 79 30\n",
"10\n95 51 0 8 44 39 60 17 96 88\n",
"3\n66 40 40\n",
"4\n83 110 81 47\n",
"10\n9 9 4 10 10 9 10 8 9 9\n",
"3\n46 9 12\n",
"7\n23 37 46 3 72 31 85\n",
"4\n92 26 29 65\n",
"10\n79 91 22 29 23 22 33 42 13 96\n",
"7\n20 21 95 73 49 153 103\n",
"10\n28 61 41 73 61 62 45 55 18 43\n",
"5\n46 78 47 46 45\n",
"7\n35 91 87 85 17 106 63\n",
"3\n72 26 73\n",
"10\n16 17 16 4 14 15 16 7 16 15\n",
"9\n95 8 97 61 90 7 30 128 39\n",
"10\n2 83 18 65 58 44 37 13 86 47\n",
"6\n59 59 60 20 59 58\n",
"3\n3 0 2\n",
"3\n1 4 1\n",
"4\n90 16 83 91\n",
"10\n105 39 79 63 97 40 36 38 11 97\n",
"5\n21 94 40 161 0\n",
"8\n86 6 30 85 98 6 84 13\n",
"6\n47 100 178 2 96 43\n",
"4\n3 28 0 81\n",
"5\n14 91 91 0 1\n",
"3\n41 5 24\n",
"1\n14\n",
"9\n13 80 22 38 98 85 11 79 30\n",
"10\n95 51 0 8 44 39 60 16 96 88\n",
"3\n66 40 68\n",
"4\n83 110 97 47\n",
"3\n62 9 12\n",
"7\n23 37 76 3 72 31 85\n",
"4\n92 26 29 122\n",
"10\n109 91 22 29 23 22 33 42 13 96\n",
"7\n20 21 74 73 49 153 103\n",
"10\n1 61 41 73 61 62 45 55 18 43\n",
"7\n35 91 87 85 6 106 63\n",
"3\n72 16 73\n",
"10\n16 17 16 7 14 15 16 7 16 15\n",
"9\n95 8 97 45 90 7 30 128 39\n",
"10\n2 83 18 65 58 44 37 13 86 33\n",
"6\n59 59 60 20 59 91\n",
"3\n3 0 4\n",
"3\n1 6 1\n",
"4\n90 16 155 91\n",
"10\n105 15 79 63 97 40 36 38 11 97\n",
"5\n21 94 40 139 0\n",
"8\n41 6 30 85 98 6 84 13\n",
"6\n47 100 178 2 96 82\n",
"4\n3 28 1 81\n",
"5\n14 130 91 0 1\n",
"3\n41 5 17\n",
"1\n18\n",
"9\n13 80 22 23 98 85 11 79 30\n",
"10\n95 51 0 8 44 52 60 16 96 88\n",
"3\n66 36 68\n",
"4\n80 110 97 47\n"
],
"output": [
"NO",
"YES",
"YES",
"YES",
"NO",
"NO",
"NO",
"NO",
"NO",
"NO",
"NO",
"YES",
"YES",
"NO",
"NO",
"YES",
"YES",
"YES",
"NO",
"YES",
"YES",
"YES",
"YES",
"NO",
"YES",
"NO",
"YES",
"NO",
"YES",
"NO",
"NO",
"NO",
"YES",
"YES",
"NO",
"NO",
"YES",
"NO",
"NO",
"YES",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
### Input:
3
3 1 2
### Output:
NO
### Input:
3
1 2 3
### Output:
YES
### Code:
n = int(input())
l = [int(x) for x in input().split()]
while len(l) > 1:
if len([i for i in range(len(l)-1) if abs(l[i] - l[i+1]) > 1 ])>0:
print ('NO')
exit(0)
l.remove(max(l))
print('YES')
|
979_E. Kuro and Topological Parity_2901 | Kuro has recently won the "Most intelligent cat ever" contest. The three friends then decided to go to Katie's home to celebrate Kuro's winning. After a big meal, they took a small break then started playing games.
Kuro challenged Katie to create a game with only a white paper, a pencil, a pair of scissors and a lot of arrows (you can assume that the number of arrows is infinite). Immediately, Katie came up with the game called Topological Parity.
The paper is divided into n pieces enumerated from 1 to n. Shiro has painted some pieces with some color. Specifically, the i-th piece has color c_{i} where c_{i} = 0 defines black color, c_{i} = 1 defines white color and c_{i} = -1 means that the piece hasn't been colored yet.
The rules of the game is simple. Players must put some arrows between some pairs of different pieces in such a way that for each arrow, the number in the piece it starts from is less than the number of the piece it ends at. Also, two different pieces can only be connected by at most one arrow. After that the players must choose the color (0 or 1) for each of the unpainted pieces. The score of a valid way of putting the arrows and coloring pieces is defined as the number of paths of pieces of alternating colors. For example, [1 → 0 → 1 → 0], [0 → 1 → 0 → 1], [1], [0] are valid paths and will be counted. You can only travel from piece x to piece y if and only if there is an arrow from x to y.
But Kuro is not fun yet. He loves parity. Let's call his favorite parity p where p = 0 stands for "even" and p = 1 stands for "odd". He wants to put the arrows and choose colors in such a way that the score has the parity of p.
It seems like there will be so many ways which satisfy Kuro. He wants to count the number of them but this could be a very large number. Let's help him with his problem, but print it modulo 10^{9} + 7.
Input
The first line contains two integers n and p (1 ≤ n ≤ 50, 0 ≤ p ≤ 1) — the number of pieces and Kuro's wanted parity.
The second line contains n integers c_{1}, c_{2}, ..., c_{n} (-1 ≤ c_{i} ≤ 1) — the colors of the pieces.
Output
Print a single integer — the number of ways to put the arrows and choose colors so the number of valid paths of alternating colors has the parity of p.
Examples
Input
3 1
-1 0 1
Output
6
Input
2 1
1 0
Output
1
Input
1 1
-1
Output
2
Note
In the first example, there are 6 ways to color the pieces and add the arrows, as are shown in the figure below. The scores are 3, 3, 5 for the first row and 5, 3, 3 for the second row, both from left to right.
<image> | n,p=map(int,input().split())
nums=[0]+list(map(int,input().split()))
mod=10**9+7
f=[[[[0]*2 for _ in range(2)] for _ in range(2)] for _ in range(n+1)]
_2=[0]*(n+1)
_2[0]=1
for i in range(1,n+1):
_2[i]=(_2[i-1]<<1)%mod
f[0][0][0][0]=1
if nums[1]!=0:
f[1][1][0][1]+=1
if nums[1]!=1:
f[1][1][1][0]+=1
for i in range(2,n+1):
for j in range(2):
for ob in range(2):
for ow in range(2):
qwq=f[i-1][j][ob][ow]
if nums[i]!=0:
if ob:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-1])%mod
if nums[i]!=1:
if ow:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-1])%mod
ans=0
for i in range(2):
for j in range(2):
ans=(ans+f[n][p][i][j])%mod
print(ans)
| {
"input": [
"3 1\n-1 0 1\n",
"2 1\n1 0\n",
"1 1\n-1\n",
"9 1\n0 1 -1 -1 -1 -1 1 1 1\n",
"16 0\n-1 0 0 1 0 0 0 0 -1 -1 -1 -1 1 1 0 1\n",
"36 0\n-1 0 0 -1 -1 -1 0 -1 0 1 -1 -1 1 1 -1 1 0 0 1 -1 1 1 -1 0 0 1 1 1 -1 1 1 -1 1 1 1 -1\n",
"37 0\n0 -1 0 0 0 -1 0 1 0 0 -1 0 -1 -1 0 1 1 0 -1 -1 -1 -1 1 -1 0 0 0 1 -1 -1 1 -1 1 1 -1 -1 -1\n",
"42 1\n0 1 -1 0 -1 0 -1 1 -1 1 0 1 1 -1 0 -1 -1 1 -1 -1 0 -1 1 -1 0 1 0 1 -1 1 -1 1 0 0 -1 0 1 0 1 1 0 0\n",
"20 1\n0 0 -1 0 1 1 1 1 -1 -1 1 1 1 -1 0 0 1 1 1 0\n",
"10 0\n1 -1 0 1 1 -1 -1 0 1 0\n",
"41 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"4 0\n1 -1 1 0\n",
"26 1\n1 -1 1 1 1 1 -1 1 -1 1 -1 -1 0 -1 -1 -1 1 0 -1 -1 0 1 -1 0 1 0\n",
"43 0\n1 0 0 -1 0 -1 0 -1 1 1 -1 1 -1 0 0 1 -1 -1 -1 0 0 -1 1 -1 -1 1 0 0 1 -1 0 -1 -1 -1 -1 -1 1 1 0 -1 -1 -1 0\n",
"50 1\n-1 -1 0 -1 1 0 1 0 1 -1 -1 0 0 0 -1 0 0 -1 0 1 -1 0 1 -1 1 -1 1 -1 -1 1 -1 -1 0 1 1 0 0 0 1 -1 -1 1 0 0 -1 0 1 1 0 0\n",
"5 1\n-1 -1 -1 -1 -1\n",
"36 1\n-1 0 0 1 1 0 -1 -1 -1 -1 1 1 0 -1 0 1 0 -1 0 -1 0 1 0 -1 -1 0 1 -1 0 -1 0 -1 1 0 1 1\n",
"4 1\n1 -1 -1 1\n",
"6 0\n-1 1 1 -1 -1 -1\n",
"34 0\n1 1 1 0 0 0 0 1 0 0 1 -1 1 1 -1 0 -1 1 1 1 0 1 1 -1 0 0 1 -1 -1 0 0 0 -1 -1\n",
"5 0\n-1 0 0 0 1\n",
"25 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"33 0\n0 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 -1 0 1 0 -1 0 0 -1 1 -1 -1 0 0 -1 0 0 1 0 1 1 1\n",
"9 0\n1 1 0 0 1 -1 -1 0 0\n",
"10 0\n1 0 -1 1 -1 0 0 1 1 0\n",
"32 1\n0 0 1 0 -1 0 1 -1 -1 -1 0 1 0 0 1 0 -1 -1 1 1 1 0 0 1 -1 -1 1 0 0 -1 0 1\n",
"17 0\n0 -1 -1 0 1 -1 0 0 -1 -1 0 -1 -1 -1 0 0 0\n",
"7 0\n1 0 -1 1 -1 1 0\n",
"20 0\n1 -1 1 -1 -1 -1 0 1 1 0 1 0 -1 1 1 -1 1 0 1 1\n",
"3 0\n0 0 0\n",
"18 0\n1 1 1 -1 0 -1 -1 0 -1 -1 0 0 -1 0 -1 0 -1 1\n",
"30 0\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"50 1\n-1 -1 -1 -1 -1 0 -1 -1 -1 0 1 0 -1 0 1 -1 -1 -1 1 0 1 -1 0 1 0 1 0 0 1 1 -1 1 -1 -1 1 1 -1 -1 0 -1 -1 1 -1 1 -1 1 1 0 0 -1\n",
"5 0\n-1 -1 -1 -1 -1\n",
"27 1\n0 -1 1 0 -1 1 1 -1 0 -1 0 0 0 -1 -1 0 0 -1 -1 0 -1 0 -1 0 0 1 1\n",
"5 1\n-1 1 0 0 -1\n",
"28 1\n0 0 1 1 -1 1 -1 1 0 -1 -1 -1 0 -1 0 -1 1 0 -1 1 0 -1 -1 0 -1 1 1 -1\n",
"4 1\n1 0 1 0\n",
"24 1\n0 0 0 1 1 0 -1 0 -1 1 -1 -1 0 0 1 1 0 -1 0 0 0 0 1 1\n",
"17 0\n-1 0 -1 1 0 0 1 1 -1 -1 -1 -1 -1 1 1 -1 -1\n",
"35 0\n0 0 -1 -1 1 -1 1 -1 1 0 1 0 -1 0 1 1 -1 1 -1 0 0 -1 0 0 1 -1 -1 0 1 1 -1 1 1 1 -1\n",
"17 1\n0 -1 -1 0 0 1 -1 -1 0 0 -1 1 0 -1 1 0 0\n",
"22 1\n0 -1 1 0 0 1 1 1 -1 -1 1 1 1 -1 1 1 0 0 -1 0 1 1\n",
"9 0\n0 -1 -1 -1 -1 -1 1 0 -1\n",
"9 1\n-1 -1 1 1 1 -1 -1 0 1\n",
"3 0\n0 -1 -1\n",
"5 0\n0 -1 0 0 0\n",
"31 0\n1 0 1 1 0 0 0 -1 -1 -1 -1 -1 0 1 1 1 0 -1 1 -1 -1 1 -1 1 1 0 0 1 1 -1 0\n",
"16 0\n1 -1 0 0 0 -1 -1 -1 0 -1 -1 1 0 0 -1 1\n",
"30 0\n1 0 1 1 0 -1 0 1 -1 0 1 -1 0 -1 1 1 -1 1 0 1 0 -1 1 1 0 1 -1 0 1 1\n",
"7 0\n1 0 1 1 -1 1 1\n",
"6 0\n-1 0 -1 1 1 1\n",
"6 1\n1 -1 -1 -1 0 0\n",
"1 0\n-1\n",
"10 1\n1 1 1 -1 0 -1 -1 1 1 0\n",
"10 1\n1 1 1 1 0 0 0 1 0 0\n",
"6 0\n0 -1 -1 0 0 -1\n",
"50 1\n-1 -1 1 0 1 1 0 -1 1 0 -1 -1 0 0 -1 -1 0 1 1 -1 1 0 -1 1 1 -1 -1 -1 1 -1 -1 0 -1 0 -1 0 0 -1 -1 0 1 -1 0 1 -1 1 0 -1 -1 1\n",
"2 1\n0 1\n",
"38 0\n-1 -1 1 1 -1 -1 1 -1 0 1 -1 1 1 1 -1 1 0 1 0 -1 1 -1 -1 0 0 1 -1 -1 0 -1 0 -1 -1 0 1 0 -1 0\n",
"27 1\n-1 0 -1 -1 -1 0 1 -1 1 0 0 -1 0 1 0 0 0 -1 -1 1 -1 -1 -1 0 1 0 0\n",
"46 0\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"40 1\n-1 1 1 1 0 -1 -1 1 1 -1 1 1 1 0 0 -1 1 0 1 -1 -1 1 0 1 1 0 1 0 0 -1 -1 1 -1 1 1 1 1 0 -1 0\n",
"41 1\n0 0 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 -1 0 1 1 1 0 0 1 1 -1 0 0 1 0 0 1 1 1 -1 0 -1 1 0 1 1 1 1\n",
"4 1\n0 1 -1 -1\n",
"2 0\n-1 -1\n",
"3 1\n0 -1 -1\n",
"38 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"6 1\n1 1 0 -1 -1 -1\n",
"17 0\n1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 -1 0\n",
"25 1\n1 0 0 -1 -1 0 1 0 -1 1 0 0 0 -1 0 0 1 -1 -1 1 -1 -1 -1 1 1\n",
"21 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"14 1\n-1 0 0 1 -1 0 0 0 -1 -1 0 -1 0 0\n",
"31 1\n1 0 0 0 0 0 0 0 -1 0 0 0 1 -1 -1 -1 0 0 -1 0 1 -1 1 0 1 1 1 1 -1 -1 1\n",
"27 1\n0 -1 -1 1 1 1 -1 1 0 0 1 -1 -1 1 -1 1 1 1 1 1 0 0 0 0 -1 -1 0\n",
"8 0\n-1 0 1 -1 1 -1 1 1\n",
"11 1\n1 0 1 0 -1 1 0 -1 -1 0 0\n",
"34 1\n1 0 -1 0 0 0 -1 1 0 1 1 1 1 1 1 -1 0 0 1 0 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 1 1 -1\n",
"1 1\n0\n",
"2 0\n-1 1\n",
"29 1\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"13 1\n-1 1 0 0 -1 0 -1 1 -1 -1 1 1 0\n",
"48 1\n1 0 0 0 1 -1 1 1 0 -1 0 -1 1 1 0 -1 -1 -1 0 0 0 1 0 1 0 -1 -1 -1 -1 1 0 1 -1 -1 -1 1 -1 0 1 0 0 1 -1 0 -1 0 0 0\n",
"37 1\n1 -1 1 -1 -1 -1 0 1 -1 -1 1 0 0 0 1 1 -1 0 -1 1 -1 0 1 -1 -1 -1 -1 -1 0 -1 0 0 -1 0 -1 -1 -1\n",
"47 1\n0 -1 0 1 0 -1 1 -1 1 -1 1 -1 0 0 -1 0 -1 1 -1 -1 0 1 -1 1 0 0 1 -1 0 1 0 1 0 1 0 1 -1 -1 1 -1 -1 -1 0 1 1 0 1\n",
"2 0\n-1 0\n",
"31 0\n1 -1 -1 0 -1 0 -1 -1 0 -1 -1 -1 1 1 0 1 -1 1 1 0 0 -1 0 1 -1 1 0 -1 1 -1 -1\n",
"17 0\n0 0 0 0 0 1 -1 -1 -1 1 -1 1 0 0 1 -1 -1\n",
"36 1\n-1 0 -1 -1 1 0 0 -1 1 0 0 -1 1 -1 1 0 1 0 0 0 1 1 1 0 1 1 0 -1 1 -1 0 0 0 1 1 -1\n",
"9 0\n0 1 -1 -1 -1 -1 1 1 1\n",
"37 0\n0 -1 0 0 0 -1 0 1 -1 0 -1 0 -1 -1 0 1 1 0 -1 -1 -1 -1 1 -1 0 0 0 1 -1 -1 1 -1 1 1 -1 -1 -1\n",
"10 0\n1 0 0 1 1 -1 -1 0 1 0\n",
"41 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0\n",
"2 0\n1 -1 1 0\n",
"26 1\n1 -1 1 1 1 1 -1 1 -1 1 0 -1 0 -1 -1 -1 1 0 -1 -1 0 1 -1 0 1 0\n",
"34 0\n1 1 1 0 0 0 0 1 0 0 1 -1 0 1 -1 0 -1 1 1 1 0 1 1 -1 0 0 1 -1 -1 0 0 0 -1 -1\n",
"5 0\n-1 0 -1 0 1\n",
"32 1\n0 0 1 0 -1 0 1 -1 -1 -1 0 1 0 0 1 0 -1 -1 1 1 1 0 -1 1 -1 -1 1 0 0 -1 0 1\n",
"17 0\n0 -1 -1 0 1 -1 0 -1 -1 -1 0 -1 -1 -1 0 0 0\n",
"7 0\n1 0 -1 1 -1 1 1\n",
"20 1\n1 -1 1 -1 -1 -1 0 1 1 0 1 0 -1 1 1 -1 1 0 1 1\n",
"2 0\n0 0 0\n",
"18 1\n1 1 1 -1 0 -1 -1 0 -1 -1 0 0 -1 0 -1 0 -1 1\n",
"30 0\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1\n",
"50 1\n-1 -1 -1 -1 -1 0 -1 -1 -1 0 1 0 -1 0 1 -1 -1 -1 1 0 1 -1 0 1 0 1 0 0 0 1 -1 1 -1 -1 1 1 -1 -1 0 -1 -1 1 -1 1 -1 1 1 0 0 -1\n",
"5 1\n0 1 0 0 -1\n",
"4 1\n0 0 1 1 -1 1 -1 1 0 -1 -1 -1 0 -1 0 -1 1 0 -1 1 0 -1 -1 0 -1 1 1 -1\n",
"24 1\n0 0 0 1 1 -1 -1 0 -1 1 -1 -1 0 0 1 1 0 -1 0 0 0 0 1 1\n",
"9 1\n-1 -1 0 1 1 -1 -1 0 1\n",
"5 0\n0 -1 0 0 -1\n",
"30 0\n1 0 1 1 0 -1 0 1 -1 -1 1 -1 0 -1 1 1 -1 1 0 1 0 -1 1 1 0 1 -1 0 1 1\n",
"1 0\n0\n",
"6 1\n0 -1 -1 0 0 -1\n",
"38 0\n-1 -1 1 1 -1 -1 1 -1 0 1 -1 1 1 1 -1 1 0 1 -1 -1 1 -1 -1 0 0 1 -1 -1 0 -1 0 -1 -1 0 1 0 -1 0\n",
"27 1\n-1 0 -1 -1 -1 0 1 -1 1 0 0 -1 -1 1 0 0 0 -1 -1 1 -1 -1 -1 0 1 0 0\n",
"46 0\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1\n",
"31 1\n-1 1 1 1 0 -1 -1 1 1 -1 1 1 1 0 0 -1 1 0 1 -1 -1 1 0 1 1 0 1 0 0 -1 -1 1 -1 1 1 1 1 0 -1 0\n",
"4 1\n0 1 0 -1\n",
"3 1\n1 -1 -1\n",
"38 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1\n",
"5 1\n1 1 0 -1 -1 -1\n",
"25 1\n1 0 0 -1 -1 0 1 0 -1 1 0 0 0 -1 0 0 1 -1 -1 0 -1 -1 -1 1 1\n",
"21 0\n0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0\n",
"14 1\n-1 0 -1 1 -1 0 0 0 -1 -1 0 -1 0 0\n",
"8 0\n0 0 1 -1 1 -1 1 1\n",
"2 1\n-1 1\n",
"29 1\n0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
"13 1\n-1 1 0 0 0 0 -1 1 -1 -1 1 1 0\n",
"48 1\n1 0 0 0 1 -1 1 1 1 -1 0 -1 1 1 0 -1 -1 -1 0 0 0 1 0 1 0 -1 -1 -1 -1 1 0 1 -1 -1 -1 1 -1 0 1 0 0 1 -1 0 -1 0 0 0\n",
"37 1\n1 -1 1 -1 -1 -1 0 1 -1 -1 1 0 0 0 1 0 -1 0 -1 1 -1 0 1 -1 -1 -1 -1 -1 0 -1 0 0 -1 0 -1 -1 -1\n",
"47 1\n0 -1 0 1 1 -1 1 -1 1 -1 1 -1 0 0 -1 0 -1 1 -1 -1 0 1 -1 1 0 0 1 -1 0 1 0 1 0 1 0 1 -1 -1 1 -1 -1 -1 0 1 1 0 1\n",
"36 1\n-1 0 -1 -1 1 0 0 -1 1 0 0 -1 1 -1 1 0 1 -1 0 0 1 1 1 0 1 1 0 -1 1 -1 0 0 0 1 1 -1\n",
"3 1\n-1 1 1\n",
"9 0\n0 1 -1 -1 0 -1 1 1 1\n",
"37 0\n0 -1 0 0 0 -1 0 1 -1 0 -1 0 -1 -1 0 1 1 0 -1 -1 -1 -1 1 -1 0 0 0 1 -1 -1 1 0 1 1 -1 -1 -1\n",
"41 0\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0\n",
"34 0\n1 1 1 1 0 0 0 1 0 0 1 -1 0 1 -1 0 -1 1 1 1 0 1 1 -1 0 0 1 -1 -1 0 0 0 -1 -1\n",
"5 1\n-1 0 -1 0 1\n",
"32 1\n0 0 1 0 -1 0 1 -1 -1 -1 0 1 -1 0 1 0 -1 -1 1 1 1 0 -1 1 -1 -1 1 0 0 -1 0 1\n",
"17 0\n0 -1 -1 0 1 -1 -1 -1 -1 -1 0 -1 -1 -1 0 0 0\n",
"18 1\n1 1 1 -1 0 -1 -1 0 -1 -1 0 -1 -1 0 -1 0 -1 1\n",
"5 0\n0 -1 1 0 -1\n",
"30 0\n1 0 0 1 0 -1 0 1 -1 -1 1 -1 0 -1 1 1 -1 1 0 1 0 -1 1 1 0 1 -1 0 1 1\n",
"6 1\n0 -1 -1 1 0 -1\n",
"50 1\n-1 -1 1 0 1 1 0 -1 1 0 -1 -1 0 -1 -1 -1 0 1 1 -1 1 0 -1 1 1 -1 -1 -1 1 -1 -1 0 -1 0 -1 0 1 -1 -1 0 1 -1 0 1 -1 1 0 -1 -1 1\n",
"46 0\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1\n",
"50 1\n-1 -1 1 0 1 1 0 -1 1 0 -1 -1 0 -1 -1 -1 0 1 1 -1 1 0 -1 1 1 -1 -1 -1 1 -1 -1 0 -1 0 -1 0 0 -1 -1 0 1 -1 0 1 -1 1 0 -1 -1 1\n",
"2 1\n-1 0\n",
"10 0\n1 0 1 1 1 -1 -1 0 1 0\n",
"2 0\n1 -1 2 0\n",
"2 0\n1 0 0\n",
"4 1\n0 0 1 1 -1 1 -1 1 0 -1 -1 -1 0 -1 0 -1 1 0 -1 1 0 -1 0 0 -1 1 1 -1\n",
"24 1\n0 0 1 1 1 -1 -1 0 -1 1 -1 -1 0 0 1 1 0 -1 0 0 0 0 1 1\n",
"1 0\n1\n",
"31 1\n-1 1 1 1 0 -1 -1 1 1 -1 1 1 1 0 0 -1 1 0 1 -1 -1 1 0 1 1 0 1 0 0 -1 -1 1 -1 0 1 1 1 0 -1 0\n"
],
"output": [
"6\n",
"1\n",
"2\n",
"755810045\n",
"878929813\n",
"152782818\n",
"915368288\n",
"386658717\n",
"483548109\n",
"487370169\n",
"0\n",
"64\n",
"996763118\n",
"477560567\n",
"772364444\n",
"16512\n",
"693536347\n",
"120\n",
"267264\n",
"115086916\n",
"1088\n",
"322050759\n",
"52976952\n",
"438952513\n",
"743685088\n",
"247728070\n",
"310296666\n",
"4194304\n",
"841268608\n",
"0\n",
"557382306\n",
"549790477\n",
"279519499\n",
"16256\n",
"28918236\n",
"1920\n",
"618844160\n",
"32\n",
"189147304\n",
"555719737\n",
"45647242\n",
"427689083\n",
"981309322\n",
"560111071\n",
"608326411\n",
"14\n",
"768\n",
"253181331\n",
"807669877\n",
"40673917\n",
"2359296\n",
"61440\n",
"131072\n",
"0\n",
"487370169\n",
"185921272\n",
"135168\n",
"803313751\n",
"1\n",
"502273788\n",
"61073361\n",
"480432768\n",
"73320910\n",
"589337580\n",
"136\n",
"6\n",
"18\n",
"0\n",
"133120\n",
"585862415\n",
"66699122\n",
"0\n",
"829277977\n",
"186475897\n",
"69931865\n",
"56964601\n",
"67049563\n",
"132603129\n",
"1\n",
"3\n",
"733922348\n",
"621572676\n",
"763606955\n",
"916646835\n",
"716651774\n",
"3\n",
"304540143\n",
"427689083\n",
"77953873\n",
"755810045\n",
"856019167\n",
"743685088\n",
"681095711\n",
"3\n",
"498381559\n",
"194552344\n",
"1984\n",
"495456140\n",
"640731229\n",
"4325376\n",
"189946716\n",
"2\n",
"870483021\n",
"387447621\n",
"260843480\n",
"768\n",
"32\n",
"378294608\n",
"829551862\n",
"1792\n",
"519096932\n",
"0\n",
"126976\n",
"388948587\n",
"617291392\n",
"120108192\n",
"140063906\n",
"80\n",
"18\n",
"84306913\n",
"1920\n",
"634141034\n",
"573812615\n",
"819781395\n",
"536870912\n",
"1\n",
"183480587\n",
"263298526\n",
"763606955\n",
"228356749\n",
"716651774\n",
"155907746\n",
"12\n",
"877905026\n",
"915368288\n",
"521643563\n",
"115086916\n",
"2112\n",
"990912280\n",
"791531403\n",
"771314966\n",
"2176\n",
"300222383\n",
"133120\n",
"606627495\n",
"300270480\n",
"260843480\n",
"1\n",
"743685088\n",
"3\n",
"1\n",
"32\n",
"378294608\n",
"0\n",
"140063906\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kuro has recently won the "Most intelligent cat ever" contest. The three friends then decided to go to Katie's home to celebrate Kuro's winning. After a big meal, they took a small break then started playing games.
Kuro challenged Katie to create a game with only a white paper, a pencil, a pair of scissors and a lot of arrows (you can assume that the number of arrows is infinite). Immediately, Katie came up with the game called Topological Parity.
The paper is divided into n pieces enumerated from 1 to n. Shiro has painted some pieces with some color. Specifically, the i-th piece has color c_{i} where c_{i} = 0 defines black color, c_{i} = 1 defines white color and c_{i} = -1 means that the piece hasn't been colored yet.
The rules of the game is simple. Players must put some arrows between some pairs of different pieces in such a way that for each arrow, the number in the piece it starts from is less than the number of the piece it ends at. Also, two different pieces can only be connected by at most one arrow. After that the players must choose the color (0 or 1) for each of the unpainted pieces. The score of a valid way of putting the arrows and coloring pieces is defined as the number of paths of pieces of alternating colors. For example, [1 → 0 → 1 → 0], [0 → 1 → 0 → 1], [1], [0] are valid paths and will be counted. You can only travel from piece x to piece y if and only if there is an arrow from x to y.
But Kuro is not fun yet. He loves parity. Let's call his favorite parity p where p = 0 stands for "even" and p = 1 stands for "odd". He wants to put the arrows and choose colors in such a way that the score has the parity of p.
It seems like there will be so many ways which satisfy Kuro. He wants to count the number of them but this could be a very large number. Let's help him with his problem, but print it modulo 10^{9} + 7.
Input
The first line contains two integers n and p (1 ≤ n ≤ 50, 0 ≤ p ≤ 1) — the number of pieces and Kuro's wanted parity.
The second line contains n integers c_{1}, c_{2}, ..., c_{n} (-1 ≤ c_{i} ≤ 1) — the colors of the pieces.
Output
Print a single integer — the number of ways to put the arrows and choose colors so the number of valid paths of alternating colors has the parity of p.
Examples
Input
3 1
-1 0 1
Output
6
Input
2 1
1 0
Output
1
Input
1 1
-1
Output
2
Note
In the first example, there are 6 ways to color the pieces and add the arrows, as are shown in the figure below. The scores are 3, 3, 5 for the first row and 5, 3, 3 for the second row, both from left to right.
<image>
### Input:
3 1
-1 0 1
### Output:
6
### Input:
2 1
1 0
### Output:
1
### Code:
n,p=map(int,input().split())
nums=[0]+list(map(int,input().split()))
mod=10**9+7
f=[[[[0]*2 for _ in range(2)] for _ in range(2)] for _ in range(n+1)]
_2=[0]*(n+1)
_2[0]=1
for i in range(1,n+1):
_2[i]=(_2[i-1]<<1)%mod
f[0][0][0][0]=1
if nums[1]!=0:
f[1][1][0][1]+=1
if nums[1]!=1:
f[1][1][1][0]+=1
for i in range(2,n+1):
for j in range(2):
for ob in range(2):
for ow in range(2):
qwq=f[i-1][j][ob][ow]
if nums[i]!=0:
if ob:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-1])%mod
if nums[i]!=1:
if ow:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-1])%mod
ans=0
for i in range(2):
for j in range(2):
ans=(ans+f[n][p][i][j])%mod
print(ans)
|
999_F. Cards and Joy_2905 | There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j.
There are k ⋅ n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below.
The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0.
Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players.
Input
The first line of input contains two integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ 10) — the number of players and the number of cards each player will get.
The second line contains k ⋅ n integers c_1, c_2, ..., c_{k ⋅ n} (1 ≤ c_i ≤ 10^5) — the numbers written on the cards.
The third line contains n integers f_1, f_2, ..., f_n (1 ≤ f_j ≤ 10^5) — the favorite numbers of the players.
The fourth line contains k integers h_1, h_2, ..., h_k (1 ≤ h_t ≤ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k].
Output
Print one integer — the maximum possible total joy levels of the players among all possible card distributions.
Examples
Input
4 3
1 3 2 8 5 5 8 2 2 8 5 2
1 2 2 5
2 6 7
Output
21
Input
3 3
9 9 9 9 9 9 9 9 9
1 2 3
1 2 3
Output
0
Note
In the first example, one possible optimal card distribution is the following:
* Player 1 gets cards with numbers [1, 3, 8];
* Player 2 gets cards with numbers [2, 2, 8];
* Player 3 gets cards with numbers [2, 2, 8];
* Player 4 gets cards with numbers [5, 5, 5].
Thus, the answer is 2 + 6 + 6 + 7 = 21.
In the second example, no player can get a card with his favorite number. Thus, the answer is 0. | def solve():
n, k = map(int, input().split())
c = list(map(int, input().split()))
f = list(map(int, input().split()))
h = list(map(int, input().split()))
cnt = {}
for i in c:
cnt[i] = cnt.get(i, 0) + 1
likecolor = {}
for i in range(n):
likecolor.setdefault(f[i], []).append(i)
cnt[f[i]] = cnt.get(f[i], 0)
ans = 0
for key, v in likecolor.items():
n1 = len(v)
if cnt[key] >= n1 * k:
ans += n1 * h[k - 1]
continue
dp = [[-float("INF")] * (cnt[key]+1) for _ in range(n1 + 1)]
dp[0][0] = 0
for i in range(n1):
j = i + 1
for e in range(cnt[key] + 1):
dp[j][e] = max(dp[j][e], dp[i][e])
for w in range(e + 1, min(cnt[key] + 1, e + k + 1)):
dp[j][w] = max(dp[i][e] + h[w - e - 1], dp[j][w])
ans += dp[n1][cnt[key]]
print(ans)
solve()
| {
"input": [
"4 3\n1 3 2 8 5 5 8 2 2 8 5 2\n1 2 2 5\n2 6 7\n",
"3 3\n9 9 9 9 9 9 9 9 9\n1 2 3\n1 2 3\n",
"1 1\n1\n2\n1\n",
"1 1\n1\n1\n100000\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 1299 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 1442 172 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 1005 1214 1866 1432 1715 25 1240 1234 324\n52314\n",
"1 1\n1\n1\n1\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 98 102 35 149 47 136 87 4 127 142 105 78 10 123 75 67 149 81 78 34 79 62 12 43 115\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 102 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"1 1\n1\n1\n101000\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 1299 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 1442 172 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 1234 324\n52314\n",
"1 1\n1\n4\n1\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 98 102 35 149 47 136 87 4 127 142 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 102 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"4 3\n2 3 2 8 5 5 8 2 2 8 5 2\n1 2 2 5\n2 6 7\n",
"4 3\n2 1 2 8 5 5 8 2 2 8 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 98 102 37 149 47 136 87 4 127 142 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"4 3\n2 1 2 8 1 5 8 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"4 3\n4 1 2 8 1 5 8 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n8 1 4 8 0 5 4 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"4 3\n11 1 4 8 0 5 7 2 2 6 5 0\n1 2 2 5\n2 6 7\n",
"4 3\n11 0 4 8 0 5 7 2 2 6 5 0\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 1146 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 2885 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n52314\n",
"50 1\n995 1815 1146 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 2173 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 2885 1506 597 746 309 517 1761 1002 462 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n102655\n",
"3 3\n9 9 9 9 9 9 9 9 8\n1 2 3\n1 2 3\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 1442 172 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 1234 324\n52314\n",
"1 1\n1\n7\n1\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 98 102 37 149 47 136 87 4 127 142 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 102 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"3 3\n9 9 9 9 9 9 11 9 8\n1 2 3\n1 2 3\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 1442 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 1234 324\n52314\n",
"1 1\n1\n7\n2\n",
"4 3\n2 1 2 8 5 5 8 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"3 3\n9 9 9 9 6 9 11 9 8\n1 2 3\n1 2 3\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 1234 324\n52314\n",
"1 1\n1\n7\n3\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 98 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"3 3\n9 9 9 9 6 9 11 9 8\n1 2 3\n1 2 2\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 1641 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 103 10 86 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 126 130 4 148 86 3\n94393\n",
"3 3\n9 9 9 9 6 9 11 9 8\n1 2 3\n1 2 4\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 425 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 2172 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"4 3\n8 1 2 8 1 5 8 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"3 3\n9 9 9 9 4 9 11 9 8\n1 2 3\n1 2 4\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 183 899 1728 366 1270 2172 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 139 10 86 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n8 1 2 8 0 5 8 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1052 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 38 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n8 1 2 8 0 5 4 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 1839 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 123 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 45 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 1971 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 4 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 45 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n8 1 4 8 0 5 7 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 1258 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 60 135 5 30 127 61 74 45 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n11 1 4 8 0 5 7 2 2 3 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 387 1761 1002 625 496 1638 1855 1115 47 1813 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 11 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n11 1 4 8 0 5 7 2 2 6 5 2\n1 2 2 5\n2 6 7\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 625 496 1638 1855 1115 47 1813 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 143 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 1813 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 1270 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 43 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 1813 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 73 130 4 148 86 3\n94393\n",
"4 3\n11 0 4 8 0 5 7 2 2 6 5 0\n1 2 2 5\n2 6 11\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 1432 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 37 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 64 130 4 148 86 3\n94393\n",
"4 3\n11 0 4 8 0 5 7 2 2 6 5 0\n2 2 2 5\n2 6 11\n",
"50 1\n995 1815 941 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 36 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 61 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 64 130 4 148 86 3\n94393\n",
"50 1\n995 1815 1146 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 1665 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 1524 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 36 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 5 30 127 64 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 64 130 4 148 86 3\n94393\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 82 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 36 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 10 30 127 64 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 64 130 4 148 86 3\n94393\n",
"50 1\n995 1815 1146 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 2173 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 2885 1506 597 746 309 517 1761 1002 309 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 1 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 36 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 10 30 127 64 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 55 64 130 4 148 86 3\n94393\n",
"50 1\n995 1815 1146 1716 725 1098 747 627 1728 1007 34 1001 679 1742 22 1495 465 1696 507 631 689 775 1191 2173 1035 203 1564 1329 1592 1295 983 177 734 450 73 943 33 486 1078 946 947 592 1524 563 396 1541 1670 326 543 79\n176 214 1601 1758 1468 972 628 2885 1506 597 746 309 517 1761 1002 462 496 1638 1855 1115 47 3359 707 289 891 518 1247 1782 788 1449 1174 84 899 1728 366 2529 2172 327 2874 1093 223 82 1214 1866 2082 1715 25 1240 2270 324\n52314\n",
"50 1\n52 96 99 37 178 148 10 140 131 29 1 134 56 73 121 57 98 101 134 5 139 10 155 70 4 167 102 36 149 47 136 87 4 127 26 105 78 10 192 75 67 149 81 78 34 79 62 12 72 146\n31 132 59 75 4 135 138 33 33 7 135 10 30 127 64 74 45 131 12 16 74 4 101 74 70 45 29 12 137 59 24 52 25 122 64 147 92 77 23 6 19 76 26 33 64 130 4 148 86 3\n94393\n"
],
"output": [
"21\n",
"0\n",
"0\n",
"100000\n",
"104628\n",
"1\n",
"1321502\n",
"101000\n",
"104628\n",
"0\n",
"1321502\n",
"20\n",
"22\n",
"1227109\n",
"25\n",
"24\n",
"1415895\n",
"16\n",
"14\n",
"12\n",
"52314\n",
"102655\n",
"0\n",
"104628\n",
"0\n",
"1321502\n",
"0\n",
"104628\n",
"0\n",
"22\n",
"0\n",
"104628\n",
"0\n",
"1321502\n",
"0\n",
"104628\n",
"1321502\n",
"0\n",
"104628\n",
"24\n",
"0\n",
"104628\n",
"1415895\n",
"20\n",
"104628\n",
"1321502\n",
"20\n",
"104628\n",
"1321502\n",
"104628\n",
"1321502\n",
"16\n",
"104628\n",
"1321502\n",
"16\n",
"104628\n",
"1321502\n",
"16\n",
"104628\n",
"1321502\n",
"104628\n",
"1321502\n",
"104628\n",
"1321502\n",
"12\n",
"104628\n",
"1227109\n",
"12\n",
"104628\n",
"1227109\n",
"104628\n",
"1227109\n",
"1227109\n",
"52314\n",
"1227109\n",
"52314\n",
"1227109\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n players sitting at the card table. Each player has a favorite number. The favorite number of the j-th player is f_j.
There are k ⋅ n cards on the table. Each card contains a single integer: the i-th card contains number c_i. Also, you are given a sequence h_1, h_2, ..., h_k. Its meaning will be explained below.
The players have to distribute all the cards in such a way that each of them will hold exactly k cards. After all the cards are distributed, each player counts the number of cards he has that contains his favorite number. The joy level of a player equals h_t if the player holds t cards containing his favorite number. If a player gets no cards with his favorite number (i.e., t=0), his joy level is 0.
Print the maximum possible total joy levels of the players after the cards are distributed. Note that the sequence h_1, ..., h_k is the same for all the players.
Input
The first line of input contains two integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ 10) — the number of players and the number of cards each player will get.
The second line contains k ⋅ n integers c_1, c_2, ..., c_{k ⋅ n} (1 ≤ c_i ≤ 10^5) — the numbers written on the cards.
The third line contains n integers f_1, f_2, ..., f_n (1 ≤ f_j ≤ 10^5) — the favorite numbers of the players.
The fourth line contains k integers h_1, h_2, ..., h_k (1 ≤ h_t ≤ 10^5), where h_t is the joy level of a player if he gets exactly t cards with his favorite number written on them. It is guaranteed that the condition h_{t - 1} < h_t holds for each t ∈ [2..k].
Output
Print one integer — the maximum possible total joy levels of the players among all possible card distributions.
Examples
Input
4 3
1 3 2 8 5 5 8 2 2 8 5 2
1 2 2 5
2 6 7
Output
21
Input
3 3
9 9 9 9 9 9 9 9 9
1 2 3
1 2 3
Output
0
Note
In the first example, one possible optimal card distribution is the following:
* Player 1 gets cards with numbers [1, 3, 8];
* Player 2 gets cards with numbers [2, 2, 8];
* Player 3 gets cards with numbers [2, 2, 8];
* Player 4 gets cards with numbers [5, 5, 5].
Thus, the answer is 2 + 6 + 6 + 7 = 21.
In the second example, no player can get a card with his favorite number. Thus, the answer is 0.
### Input:
4 3
1 3 2 8 5 5 8 2 2 8 5 2
1 2 2 5
2 6 7
### Output:
21
### Input:
3 3
9 9 9 9 9 9 9 9 9
1 2 3
1 2 3
### Output:
0
### Code:
def solve():
n, k = map(int, input().split())
c = list(map(int, input().split()))
f = list(map(int, input().split()))
h = list(map(int, input().split()))
cnt = {}
for i in c:
cnt[i] = cnt.get(i, 0) + 1
likecolor = {}
for i in range(n):
likecolor.setdefault(f[i], []).append(i)
cnt[f[i]] = cnt.get(f[i], 0)
ans = 0
for key, v in likecolor.items():
n1 = len(v)
if cnt[key] >= n1 * k:
ans += n1 * h[k - 1]
continue
dp = [[-float("INF")] * (cnt[key]+1) for _ in range(n1 + 1)]
dp[0][0] = 0
for i in range(n1):
j = i + 1
for e in range(cnt[key] + 1):
dp[j][e] = max(dp[j][e], dp[i][e])
for w in range(e + 1, min(cnt[key] + 1, e + k + 1)):
dp[j][w] = max(dp[i][e] + h[w - e - 1], dp[j][w])
ans += dp[n1][cnt[key]]
print(ans)
solve()
|
p02537 ACL Beginner Contest - Flat Subsequence_2918 | You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | import typing
class SegTree:
def __init__(self,
op: typing.Callable[[typing.Any, typing.Any], typing.Any],
e: typing.Any,
v: typing.Union[int, typing.List[typing.Any]]):
self._op = op
self._e = e
if isinstance(v, int):
v = [e] * v
self._n = len(v)
self._log = self._ceil_pow2(self._n)
self._size = 1 << self._log
self._d = [e] * (2 * self._size)
for i in range(self._n):
self._d[self._size + i] = v[i]
for i in range(self._size - 1, 0, -1):
self._update(i)
def set(self, p: int, x: typing.Any) -> None:
assert 0 <= p < self._n
p += self._size
self._d[p] = x
for i in range(1, self._log + 1):
self._update(p >> i)
def prod(self, left: int, right: int) -> typing.Any:
assert 0 <= left <= right <= self._n
sml = self._e
smr = self._e
left += self._size
right += self._size
while left < right:
if left & 1:
sml = self._op(sml, self._d[left])
left += 1
if right & 1:
right -= 1
smr = self._op(self._d[right], smr)
left >>= 1
right >>= 1
return self._op(sml, smr)
def all_prod(self) -> typing.Any:
return self._d[1]
def _update(self, k: int) -> None:
self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
def _ceil_pow2(self, n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
N, K = map(int, input().split())
A = list(int(input()) for _ in range(N))
max_A = max(A)
seg = SegTree(max, -1, [0]*(max_A+1))
for v in A:
l = max(0, v-K)
r = min(max_A, v+K)
seg.set(v, seg.prod(l, r+1)+1)
print(seg.all_prod()) | {
"input": [
"10 3\n1\n5\n4\n3\n8\n6\n9\n7\n2\n4",
"10 3\n1\n5\n4\n3\n8\n6\n9\n7\n4\n4",
"10 3\n1\n5\n4\n3\n6\n6\n9\n7\n4\n4",
"10 3\n0\n1\n4\n3\n6\n6\n9\n7\n4\n4",
"10 3\n1\n5\n4\n3\n8\n6\n9\n7\n3\n4",
"10 3\n1\n5\n4\n3\n8\n11\n9\n7\n3\n4",
"10 1\n0\n1\n4\n0\n5\n9\n9\n7\n8\n4",
"10 1\n0\n5\n4\n3\n8\n11\n9\n7\n6\n2",
"10 3\n1\n5\n2\n0\n6\n6\n9\n8\n4\n1",
"10 0\n1\n5\n0\n3\n8\n11\n9\n7\n6\n2",
"8 0\n0\n2\n4\n0\n5\n6\n13\n7\n4\n4",
"10 3\n0\n5\n4\n3\n6\n6\n9\n7\n4\n4",
"10 3\n1\n5\n4\n3\n8\n6\n11\n7\n4\n4",
"10 3\n1\n5\n4\n3\n6\n6\n9\n6\n4\n4",
"10 3\n0\n1\n4\n0\n6\n6\n9\n7\n4\n4",
"10 3\n1\n5\n2\n3\n6\n6\n9\n6\n4\n4",
"10 3\n0\n1\n4\n0\n5\n6\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n8\n11\n9\n7\n3\n4",
"10 3\n1\n5\n2\n3\n6\n6\n9\n6\n4\n1",
"10 3\n0\n1\n4\n0\n5\n9\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n8\n11\n9\n7\n6\n4",
"10 3\n1\n5\n3\n3\n6\n6\n9\n6\n4\n1",
"10 3\n0\n1\n4\n0\n5\n9\n9\n7\n8\n4",
"10 3\n0\n5\n4\n3\n8\n11\n9\n7\n6\n2",
"10 3\n1\n5\n2\n3\n6\n6\n9\n5\n4\n1",
"10 3\n1\n5\n2\n0\n6\n6\n9\n5\n4\n1",
"10 1\n1\n5\n4\n3\n8\n11\n9\n7\n6\n2",
"10 1\n1\n5\n0\n3\n8\n11\n9\n7\n6\n2",
"10 3\n1\n5\n2\n0\n6\n6\n9\n8\n4\n2",
"10 1\n1\n5\n0\n3\n8\n11\n9\n7\n6\n1",
"10 3\n1\n5\n2\n0\n1\n6\n9\n8\n4\n2",
"10 1\n1\n8\n0\n3\n8\n11\n9\n7\n6\n1",
"10 3\n1\n5\n2\n1\n1\n6\n9\n8\n4\n2",
"10 3\n1\n5\n2\n1\n1\n6\n9\n11\n4\n2",
"10 3\n1\n5\n2\n1\n1\n7\n9\n11\n4\n2",
"10 3\n1\n5\n3\n1\n1\n7\n9\n11\n4\n2",
"10 3\n1\n5\n3\n1\n1\n7\n9\n21\n4\n2",
"7 3\n1\n5\n3\n1\n1\n7\n9\n21\n4\n2",
"7 3\n1\n5\n3\n1\n1\n7\n9\n21\n4\n0",
"10 3\n1\n5\n4\n3\n8\n9\n9\n7\n2\n4",
"10 3\n1\n7\n4\n3\n8\n6\n9\n7\n4\n4",
"10 1\n0\n5\n4\n3\n6\n6\n9\n7\n4\n4",
"10 3\n0\n1\n4\n3\n6\n12\n9\n7\n4\n4",
"10 6\n1\n5\n4\n3\n8\n6\n9\n7\n3\n4",
"10 3\n1\n5\n4\n5\n8\n6\n11\n7\n4\n4",
"10 3\n1\n5\n7\n3\n6\n6\n9\n6\n4\n4",
"10 3\n1\n1\n4\n0\n6\n6\n9\n7\n4\n4",
"10 3\n1\n5\n4\n3\n8\n7\n9\n7\n3\n4",
"10 3\n1\n5\n2\n3\n6\n6\n9\n6\n4\n7",
"10 3\n0\n2\n4\n0\n5\n6\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n8\n11\n9\n5\n3\n4",
"10 3\n1\n5\n2\n3\n6\n6\n9\n8\n4\n1",
"10 3\n0\n1\n3\n0\n5\n9\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n8\n11\n9\n7\n6\n1",
"10 3\n1\n5\n3\n3\n6\n6\n9\n9\n4\n1",
"10 3\n0\n1\n4\n0\n5\n9\n9\n1\n8\n4",
"10 3\n0\n5\n3\n3\n8\n11\n9\n7\n6\n2",
"10 3\n1\n5\n2\n3\n6\n6\n9\n5\n4\n0",
"10 1\n0\n1\n4\n0\n5\n9\n9\n7\n3\n4",
"10 2\n0\n5\n4\n3\n8\n11\n9\n7\n6\n2",
"10 4\n1\n5\n2\n0\n6\n6\n9\n5\n4\n1",
"10 1\n1\n5\n4\n3\n1\n11\n9\n7\n6\n2",
"10 3\n1\n5\n2\n0\n6\n0\n9\n8\n4\n2",
"10 1\n2\n5\n0\n3\n8\n11\n9\n7\n6\n1",
"10 3\n1\n5\n2\n0\n1\n0\n9\n8\n4\n2",
"10 1\n2\n8\n0\n3\n8\n11\n9\n7\n6\n1",
"10 3\n1\n5\n2\n1\n1\n6\n11\n8\n4\n2",
"10 3\n1\n5\n2\n1\n1\n6\n11\n11\n4\n2",
"10 1\n1\n5\n2\n1\n1\n7\n9\n11\n4\n2",
"10 3\n1\n5\n3\n1\n1\n7\n9\n21\n1\n2",
"7 3\n1\n5\n3\n1\n1\n7\n11\n21\n4\n2",
"7 3\n1\n5\n3\n1\n2\n7\n9\n21\n4\n0",
"10 3\n1\n5\n4\n3\n8\n9\n1\n7\n2\n4",
"10 4\n0\n1\n4\n3\n6\n12\n9\n7\n4\n4",
"10 6\n1\n5\n4\n3\n1\n6\n9\n7\n3\n4",
"10 3\n1\n5\n7\n3\n6\n6\n4\n6\n4\n4",
"10 3\n0\n1\n4\n0\n6\n6\n9\n7\n4\n8",
"10 3\n1\n8\n4\n3\n8\n7\n9\n7\n3\n4",
"10 3\n1\n5\n3\n3\n6\n6\n9\n6\n4\n7",
"8 3\n0\n2\n4\n0\n5\n6\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n14\n11\n9\n5\n3\n4",
"8 3\n1\n5\n2\n3\n6\n6\n9\n8\n4\n1",
"10 3\n0\n1\n3\n0\n4\n9\n9\n7\n4\n4",
"10 3\n0\n5\n4\n3\n11\n11\n9\n7\n6\n1",
"10 3\n1\n5\n3\n3\n6\n6\n13\n9\n4\n1",
"10 3\n0\n1\n8\n0\n5\n9\n9\n1\n8\n4",
"10 3\n0\n5\n3\n3\n8\n11\n9\n7\n6\n4",
"10 3\n1\n5\n2\n4\n6\n6\n9\n5\n4\n0",
"10 2\n0\n3\n4\n3\n8\n11\n9\n7\n6\n2",
"10 1\n1\n5\n4\n3\n1\n11\n9\n7\n2\n2",
"10 1\n1\n5\n0\n3\n8\n11\n9\n6\n6\n1",
"10 3\n1\n8\n2\n0\n1\n0\n9\n8\n4\n2",
"10 1\n2\n8\n0\n3\n8\n11\n14\n7\n6\n1",
"10 3\n1\n5\n2\n1\n1\n6\n11\n8\n4\n3",
"10 3\n1\n5\n2\n1\n1\n6\n12\n11\n4\n2",
"10 1\n1\n5\n2\n1\n1\n7\n10\n11\n4\n2",
"10 3\n1\n5\n6\n1\n1\n7\n9\n21\n1\n2",
"7 0\n1\n5\n3\n1\n1\n7\n11\n21\n4\n2",
"7 3\n0\n5\n3\n1\n2\n7\n9\n21\n4\n0",
"10 3\n1\n5\n4\n6\n8\n9\n1\n7\n2\n4",
"10 4\n0\n1\n4\n3\n3\n12\n9\n7\n4\n4"
],
"output": [
"7",
"8\n",
"9\n",
"10\n",
"7\n",
"6\n",
"3\n",
"4\n",
"5\n",
"1\n",
"2\n",
"9\n",
"7\n",
"9\n",
"9\n",
"9\n",
"9\n",
"6\n",
"9\n",
"7\n",
"7\n",
"9\n",
"6\n",
"6\n",
"8\n",
"6\n",
"4\n",
"3\n",
"5\n",
"3\n",
"6\n",
"4\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"4\n",
"4\n",
"6\n",
"8\n",
"5\n",
"9\n",
"10\n",
"8\n",
"8\n",
"9\n",
"6\n",
"9\n",
"9\n",
"6\n",
"7\n",
"7\n",
"6\n",
"7\n",
"5\n",
"6\n",
"7\n",
"3\n",
"4\n",
"9\n",
"4\n",
"5\n",
"3\n",
"6\n",
"4\n",
"6\n",
"6\n",
"5\n",
"6\n",
"4\n",
"4\n",
"6\n",
"9\n",
"10\n",
"8\n",
"8\n",
"6\n",
"9\n",
"7\n",
"6\n",
"7\n",
"7\n",
"5\n",
"7\n",
"5\n",
"7\n",
"7\n",
"4\n",
"5\n",
"3\n",
"6\n",
"4\n",
"6\n",
"6\n",
"5\n",
"5\n",
"3\n",
"4\n",
"7\n",
"8\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
### Input:
10 3
1
5
4
3
8
6
9
7
2
4
### Output:
7
### Input:
10 3
1
5
4
3
8
6
9
7
4
4
### Output:
8
### Code:
import typing
class SegTree:
def __init__(self,
op: typing.Callable[[typing.Any, typing.Any], typing.Any],
e: typing.Any,
v: typing.Union[int, typing.List[typing.Any]]):
self._op = op
self._e = e
if isinstance(v, int):
v = [e] * v
self._n = len(v)
self._log = self._ceil_pow2(self._n)
self._size = 1 << self._log
self._d = [e] * (2 * self._size)
for i in range(self._n):
self._d[self._size + i] = v[i]
for i in range(self._size - 1, 0, -1):
self._update(i)
def set(self, p: int, x: typing.Any) -> None:
assert 0 <= p < self._n
p += self._size
self._d[p] = x
for i in range(1, self._log + 1):
self._update(p >> i)
def prod(self, left: int, right: int) -> typing.Any:
assert 0 <= left <= right <= self._n
sml = self._e
smr = self._e
left += self._size
right += self._size
while left < right:
if left & 1:
sml = self._op(sml, self._d[left])
left += 1
if right & 1:
right -= 1
smr = self._op(self._d[right], smr)
left >>= 1
right >>= 1
return self._op(sml, smr)
def all_prod(self) -> typing.Any:
return self._d[1]
def _update(self, k: int) -> None:
self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
def _ceil_pow2(self, n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
N, K = map(int, input().split())
A = list(int(input()) for _ in range(N))
max_A = max(A)
seg = SegTree(max, -1, [0]*(max_A+1))
for v in A:
l = max(0, v-K)
r = min(max_A, v+K)
seg.set(v, seg.prod(l, r+1)+1)
print(seg.all_prod()) |
p02797 Keyence Programming Contest 2020 - Subarray Sum_2924 | Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | n, k, s = map(int, input().split())
if s == 10**9:
ans = [10**9]*k+[1]*(n-k)
else:
ans = [s]*k+[s+1]*(n-k)
print(*ans) | {
"input": [
"5 3 100",
"4 2 3",
"5 3 000",
"5 0 100",
"4 1 3",
"5 3 010",
"4 0 3",
"10 3 010",
"8 0 3",
"10 5 010",
"8 1 3",
"10 5 000",
"10 1 3",
"10 9 000",
"10 2 3",
"17 9 000",
"10 0 3",
"10 9 001",
"7 0 3",
"10 6 001",
"7 0 6",
"13 6 001",
"2 0 6",
"13 6 101",
"2 0 1",
"9 6 101",
"2 0 2",
"9 3 101",
"1 0 2",
"9 0 101",
"12 0 101",
"2 0 101",
"4 0 101",
"6 0 101",
"4 3 100",
"4 4 3",
"6 3 000",
"7 2 3",
"4 0 5",
"10 1 010",
"10 6 000",
"8 2 3",
"10 0 000",
"10 1 1",
"10 9 100",
"15 2 3",
"17 12 000",
"16 9 001",
"7 0 0",
"7 0 1",
"13 6 011",
"13 11 101",
"3 0 1",
"9 6 111",
"9 3 001",
"2 0 0",
"11 0 101",
"2 1 101",
"4 1 101",
"4 2 100",
"6 5 000",
"7 4 3",
"14 1 010",
"14 6 000",
"8 4 3",
"10 2 1",
"10 6 100",
"15 2 1",
"16 5 001",
"7 1 0",
"7 0 -1",
"13 6 111",
"4 0 1",
"5 3 001",
"13 0 101",
"2 1 001",
"4 1 100",
"6 5 100",
"7 3 3",
"4 0 0",
"18 1 010",
"14 0 000",
"10 2 2",
"10 6 110",
"15 2 0",
"32 5 001",
"1 1 0",
"10 2 000",
"13 10 111",
"8 0 1",
"5 3 101",
"13 0 111",
"3 1 100",
"7 5 3",
"4 1 1",
"18 2 010",
"21 0 000",
"3 2 2",
"10 6 111",
"5 2 0",
"32 2 001",
"2 1 0"
],
"output": [
"50 50 50 30 70",
"1 2 3 4",
"0 0 0 1 1\n",
"101 101 101 101 101\n",
"3 4 4 4\n",
"10 10 10 11 11\n",
"4 4 4 4\n",
"10 10 10 11 11 11 11 11 11 11\n",
"4 4 4 4 4 4 4 4\n",
"10 10 10 10 10 11 11 11 11 11\n",
"3 4 4 4 4 4 4 4\n",
"0 0 0 0 0 1 1 1 1 1\n",
"3 4 4 4 4 4 4 4 4 4\n",
"0 0 0 0 0 0 0 0 0 1\n",
"3 3 4 4 4 4 4 4 4 4\n",
"0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1\n",
"4 4 4 4 4 4 4 4 4 4\n",
"1 1 1 1 1 1 1 1 1 2\n",
"4 4 4 4 4 4 4\n",
"1 1 1 1 1 1 2 2 2 2\n",
"7 7 7 7 7 7 7\n",
"1 1 1 1 1 1 2 2 2 2 2 2 2\n",
"7 7\n",
"101 101 101 101 101 101 102 102 102 102 102 102 102\n",
"2 2\n",
"101 101 101 101 101 101 102 102 102\n",
"3 3\n",
"101 101 101 102 102 102 102 102 102\n",
"3\n",
"102 102 102 102 102 102 102 102 102\n",
"102 102 102 102 102 102 102 102 102 102 102 102\n",
"102 102\n",
"102 102 102 102\n",
"102 102 102 102 102 102\n",
"100 100 100 101\n",
"3 3 3 3\n",
"0 0 0 1 1 1\n",
"3 3 4 4 4 4 4\n",
"6 6 6 6\n",
"10 11 11 11 11 11 11 11 11 11\n",
"0 0 0 0 0 0 1 1 1 1\n",
"3 3 4 4 4 4 4 4\n",
"1 1 1 1 1 1 1 1 1 1\n",
"1 2 2 2 2 2 2 2 2 2\n",
"100 100 100 100 100 100 100 100 100 101\n",
"3 3 4 4 4 4 4 4 4 4 4 4 4 4 4\n",
"0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1\n",
"1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2\n",
"1 1 1 1 1 1 1\n",
"2 2 2 2 2 2 2\n",
"11 11 11 11 11 11 12 12 12 12 12 12 12\n",
"101 101 101 101 101 101 101 101 101 101 101 102 102\n",
"2 2 2\n",
"111 111 111 111 111 111 112 112 112\n",
"1 1 1 2 2 2 2 2 2\n",
"1 1\n",
"102 102 102 102 102 102 102 102 102 102 102\n",
"101 102\n",
"101 102 102 102\n",
"100 100 101 101\n",
"0 0 0 0 0 1\n",
"3 3 3 3 4 4 4\n",
"10 11 11 11 11 11 11 11 11 11 11 11 11 11\n",
"0 0 0 0 0 0 1 1 1 1 1 1 1 1\n",
"3 3 3 3 4 4 4 4\n",
"1 1 2 2 2 2 2 2 2 2\n",
"100 100 100 100 100 100 101 101 101 101\n",
"1 1 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
"0 1 1 1 1 1 1\n",
"0 0 0 0 0 0 0\n",
"111 111 111 111 111 111 112 112 112 112 112 112 112\n",
"2 2 2 2\n",
"1 1 1 2 2\n",
"102 102 102 102 102 102 102 102 102 102 102 102 102\n",
"1 2\n",
"100 101 101 101\n",
"100 100 100 100 100 101\n",
"3 3 3 4 4 4 4\n",
"1 1 1 1\n",
"10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11\n",
"1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"2 2 3 3 3 3 3 3 3 3\n",
"110 110 110 110 110 110 111 111 111 111\n",
"0 0 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"0\n",
"0 0 1 1 1 1 1 1 1 1\n",
"111 111 111 111 111 111 111 111 111 111 112 112 112\n",
"2 2 2 2 2 2 2 2\n",
"101 101 101 102 102\n",
"112 112 112 112 112 112 112 112 112 112 112 112 112\n",
"100 101 101\n",
"3 3 3 3 3 4 4\n",
"1 2 2 2\n",
"10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11\n",
"1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"2 2 3\n",
"111 111 111 111 111 111 112 112 112 112\n",
"0 0 1 1 1\n",
"1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"0 1\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
### Input:
5 3 100
### Output:
50 50 50 30 70
### Input:
4 2 3
### Output:
1 2 3 4
### Code:
n, k, s = map(int, input().split())
if s == 10**9:
ans = [10**9]*k+[1]*(n-k)
else:
ans = [s]*k+[s+1]*(n-k)
print(*ans) |
p02933 AtCoder Beginner Contest 138 - Red or Not_2928 | You will be given an integer a and a string s consisting of lowercase English letters as input.
Write a program that prints s if a is not less than 3200 and prints `red` if a is less than 3200.
Constraints
* 2800 \leq a < 5000
* s is a string of length between 1 and 10 (inclusive).
* Each character of s is a lowercase English letter.
Input
Input is given from Standard Input in the following format:
a
s
Output
If a is not less than 3200, print s; if a is less than 3200, print `red`.
Examples
Input
3200
pink
Output
pink
Input
3199
pink
Output
red
Input
4049
red
Output
red | a,s = int(input()),input()
print(s if a>=3200 else "red") | {
"input": [
"4049\nred",
"3199\npink",
"3200\npink",
"4049\nrdd",
"3199\nknip",
"3200\npinl",
"4049\nqdd",
"3200\npiml",
"4049\nqcd",
"3200\nlmip",
"4049\nqdc",
"3200\nkmip",
"4049\nddq",
"3200\nknip",
"4049\nddr",
"3200\nkniq",
"4049\ndrd",
"3200\nlniq",
"4049\ndqd",
"3200\nqinl",
"4049\ndqc",
"3200\nqiln",
"4049\nqcc",
"3200\nnliq",
"4049\nqcb",
"3200\nnlip",
"4049\nbcq",
"3200\nnlio",
"4049\nacq",
"3200\nnlin",
"4049\n`cq",
"3200\nniln",
"4049\n`bq",
"3200\nnhln",
"4049\n`bp",
"3200\nnhmn",
"4049\n`ap",
"3200\nohmn",
"4049\naap",
"3200\nohnn",
"4049\napa",
"3200\nnnho",
"4049\napb",
"3200\nnhon",
"4049\npab",
"3200\nnhoo",
"4049\nbap",
"3200\nnhno",
"4049\nabp",
"3200\nngoo",
"4049\nabq",
"3200\nogno",
"4049\nqba",
"3200\nogmo",
"4049\nqab",
"3200\nngmo",
"4049\nqbb",
"3200\nomgn",
"4049\nbbq",
"3200\nmogn",
"4049\nbbp",
"3200\nngom",
"4049\nbqb",
"3200\nogom",
"4049\nbqa",
"3200\ngomn",
"4049\naqb",
"3200\ngonm",
"4049\naqc",
"3200\nmong",
"4049\ncqa",
"3200\nmomg",
"4049\nqca",
"3200\nmnmg",
"4049\ncaq",
"3200\ngmnm",
"4049\nqbc",
"3200\nmnng",
"4049\nrbc",
"3200\ngnnm",
"4049\ncbr",
"3200\nfnnm",
"4049\ncbq",
"3200\nmnnf",
"4049\nbqc",
"3200\nfmnn",
"4049\ncqc",
"3200\nnmnf",
"4049\ncqb",
"3200\nnfnm",
"4049\nbcr",
"3200\nmnfn",
"4049\nbdr",
"3200\nfonm",
"4049\nrdb",
"3200\neonm",
"4049\nrdc",
"3200\neomn",
"4049\ncdr",
"3200\nnmoe",
"4049\nqdb",
"3200\nnnoe",
"4049\nbdq"
],
"output": [
"red",
"red",
"pink",
"rdd\n",
"red\n",
"pinl\n",
"qdd\n",
"piml\n",
"qcd\n",
"lmip\n",
"qdc\n",
"kmip\n",
"ddq\n",
"knip\n",
"ddr\n",
"kniq\n",
"drd\n",
"lniq\n",
"dqd\n",
"qinl\n",
"dqc\n",
"qiln\n",
"qcc\n",
"nliq\n",
"qcb\n",
"nlip\n",
"bcq\n",
"nlio\n",
"acq\n",
"nlin\n",
"`cq\n",
"niln\n",
"`bq\n",
"nhln\n",
"`bp\n",
"nhmn\n",
"`ap\n",
"ohmn\n",
"aap\n",
"ohnn\n",
"apa\n",
"nnho\n",
"apb\n",
"nhon\n",
"pab\n",
"nhoo\n",
"bap\n",
"nhno\n",
"abp\n",
"ngoo\n",
"abq\n",
"ogno\n",
"qba\n",
"ogmo\n",
"qab\n",
"ngmo\n",
"qbb\n",
"omgn\n",
"bbq\n",
"mogn\n",
"bbp\n",
"ngom\n",
"bqb\n",
"ogom\n",
"bqa\n",
"gomn\n",
"aqb\n",
"gonm\n",
"aqc\n",
"mong\n",
"cqa\n",
"momg\n",
"qca\n",
"mnmg\n",
"caq\n",
"gmnm\n",
"qbc\n",
"mnng\n",
"rbc\n",
"gnnm\n",
"cbr\n",
"fnnm\n",
"cbq\n",
"mnnf\n",
"bqc\n",
"fmnn\n",
"cqc\n",
"nmnf\n",
"cqb\n",
"nfnm\n",
"bcr\n",
"mnfn\n",
"bdr\n",
"fonm\n",
"rdb\n",
"eonm\n",
"rdc\n",
"eomn\n",
"cdr\n",
"nmoe\n",
"qdb\n",
"nnoe\n",
"bdq\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You will be given an integer a and a string s consisting of lowercase English letters as input.
Write a program that prints s if a is not less than 3200 and prints `red` if a is less than 3200.
Constraints
* 2800 \leq a < 5000
* s is a string of length between 1 and 10 (inclusive).
* Each character of s is a lowercase English letter.
Input
Input is given from Standard Input in the following format:
a
s
Output
If a is not less than 3200, print s; if a is less than 3200, print `red`.
Examples
Input
3200
pink
Output
pink
Input
3199
pink
Output
red
Input
4049
red
Output
red
### Input:
4049
red
### Output:
red
### Input:
3199
pink
### Output:
red
### Code:
a,s = int(input()),input()
print(s if a>=3200 else "red") |
p03069 Tenka1 Programmer Beginner Contest 2019 - Stones_2932 | There are N stones arranged in a row. Every stone is painted white or black. A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is `.`, and the stone is black if the character is `#`.
Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone. Find the minimum number of stones that needs to be recolored.
Constraints
* 1 \leq N \leq 2\times 10^5
* S is a string of length N consisting of `.` and `#`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the minimum number of stones that needs to be recolored.
Examples
Input
3
#.#
Output
1
Input
3
.#
Output
1
Input
5
.##.
Output
2
Input
9
.........
Output
0 | n = int(input())
s = input()
black = 0
ans = white = s.count('.')
for i in range(n):
if s[i] == "#":
black += 1
else:
white -= 1
ans = min(ans, black+white)
print(ans)
| {
"input": [
"3\n.#",
"5\n.##.",
"9\n.........",
"3\n#.#",
"5\n.#.#",
"3\n.##",
"3\n##.",
"5\n..##",
"5\n#..#",
"3\n.# ",
"3\n##.",
"3\n.##",
"5\n.#.#",
"5\n..##",
"5\n#..#",
"3\n.# "
],
"output": [
"1",
"2",
"0",
"1",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N stones arranged in a row. Every stone is painted white or black. A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is `.`, and the stone is black if the character is `#`.
Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone. Find the minimum number of stones that needs to be recolored.
Constraints
* 1 \leq N \leq 2\times 10^5
* S is a string of length N consisting of `.` and `#`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the minimum number of stones that needs to be recolored.
Examples
Input
3
#.#
Output
1
Input
3
.#
Output
1
Input
5
.##.
Output
2
Input
9
.........
Output
0
### Input:
3
.#
### Output:
1
### Input:
5
.##.
### Output:
2
### Code:
n = int(input())
s = input()
black = 0
ans = white = s.count('.')
for i in range(n):
if s[i] == "#":
black += 1
else:
white -= 1
ans = min(ans, black+white)
print(ans)
|
p03212 AtCoder Beginner Contest 114 - 755_2936 | You are given an integer N. Among the integers between 1 and N (inclusive), how many Shichi-Go-San numbers (literally "Seven-Five-Three numbers") are there?
Here, a Shichi-Go-San number is a positive integer that satisfies the following condition:
* When the number is written in base ten, each of the digits `7`, `5` and `3` appears at least once, and the other digits never appear.
Constraints
* 1 \leq N < 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of the Shichi-Go-San numbers between 1 and N (inclusive).
Examples
Input
575
Output
4
Input
3600
Output
13
Input
999999999
Output
26484 | n = int(input())
def bfs(s):
if int(s) > n:
return 0
return ('3' in s and '5' in s and '7' in s) + bfs(s+'3') + bfs(s+'5') + bfs(s+'7')
print(bfs('0')) | {
"input": [
"575",
"3600",
"999999999",
"60",
"1134",
"656396080",
"1260308870",
"251112438",
"3669",
"4753",
"3412",
"5825",
"471776498",
"377370744",
"563",
"35191132",
"26435227",
"635",
"5689978",
"7251994",
"2751855",
"585456",
"3750",
"406",
"75919180",
"46306075",
"536671710",
"7364190",
"5223462",
"80751",
"8949",
"3364",
"539422341",
"57418340",
"3614080",
"363",
"3738092",
"371598",
"5422200",
"91",
"1992",
"123",
"2247",
"1450760047",
"129",
"2718",
"227",
"201804316",
"79",
"268571838",
"31",
"3972",
"293620772",
"55",
"268445916",
"101",
"271400446",
"001",
"918",
"000",
"923",
"011",
"960",
"179898217",
"111",
"1809",
"86876678",
"100",
"848",
"165921475",
"010",
"993",
"325914525",
"110",
"566",
"330",
"18297862",
"25619766",
"283",
"12068734",
"274",
"18056810",
"107",
"11571688",
"81",
"7942691",
"43",
"9468117",
"62",
"32",
"8196982",
"63",
"8253711",
"97",
"12197586",
"10",
"17251712",
"3",
"2",
"10711117",
"1",
"11062499",
"0"
],
"output": [
"4",
"13",
"26484",
"0\n",
"6\n",
"20434\n",
"26484\n",
"8334\n",
"13\n",
"18\n",
"8\n",
"30\n",
"14384\n",
"13865\n",
"3\n",
"3140\n",
"2538\n",
"4\n",
"1725\n",
"1936\n",
"732\n",
"552\n",
"14\n",
"2\n",
"7732\n",
"4470\n",
"15714\n",
"2082\n",
"1334\n",
"192\n",
"42\n",
"7\n",
"16443\n",
"5980\n",
"1123\n",
"1\n",
"1188\n",
"307\n",
"1545\n",
"0\n",
"6\n",
"0\n",
"6\n",
"26484\n",
"0\n",
"6\n",
"0\n",
"8334\n",
"0\n",
"8334\n",
"0\n",
"18\n",
"8334\n",
"0\n",
"8334\n",
"0\n",
"8334\n",
"0\n",
"6\n",
"0\n",
"6\n",
"0\n",
"6\n",
"8334\n",
"0\n",
"6\n",
"8334\n",
"0\n",
"6\n",
"8334\n",
"0\n",
"6\n",
"8334\n",
"0\n",
"3\n",
"0\n",
"2538\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n",
"0\n",
"2538\n",
"0\n",
"2538\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an integer N. Among the integers between 1 and N (inclusive), how many Shichi-Go-San numbers (literally "Seven-Five-Three numbers") are there?
Here, a Shichi-Go-San number is a positive integer that satisfies the following condition:
* When the number is written in base ten, each of the digits `7`, `5` and `3` appears at least once, and the other digits never appear.
Constraints
* 1 \leq N < 10^9
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of the Shichi-Go-San numbers between 1 and N (inclusive).
Examples
Input
575
Output
4
Input
3600
Output
13
Input
999999999
Output
26484
### Input:
575
### Output:
4
### Input:
3600
### Output:
13
### Code:
n = int(input())
def bfs(s):
if int(s) > n:
return 0
return ('3' in s and '5' in s and '7' in s) + bfs(s+'3') + bfs(s+'5') + bfs(s+'7')
print(bfs('0')) |
p03361 AtCoder Beginner Contest 096 - Grid Repainting 2_2940 | We have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).
Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= `#`, and to make Square (i, j) white when s_{i, j}= `.`.
However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.
Determine if square1001 can achieve his objective.
Constraints
* H is an integer between 1 and 50 (inclusive).
* W is an integer between 1 and 50 (inclusive).
* For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W), s_{i, j} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W}
s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W}
: :
s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W}
Output
If square1001 can achieve his objective, print `Yes`; if he cannot, print `No`.
Examples
Input
3 3
.#.
###
.#.
Output
Yes
Input
3 3
.#.
.#.
Output
Yes
Input
5 5
.#.#
.#.#.
.#.#
.#.#.
.#.#
Output
No
Input
11 11
...#####...
.##.....##.
..##.##..#
..##.##..#
.........#
...###...#
.#########.
.#.#.#.#.#.
.#.#.#.##
..##.#.##..
.##..#..##.
Output
Yes | import sys
h, w = map(int, input().split())
s = [list(input()) for i in range(h)]
for i in range(h):
for j in range(w):
if s[i][j] == "#" and (i == 0 or s[i-1][j] == ".") and (i == h-1 or s[i+1][j] == ".") and (j == 0 or s[i][j-1] == ".") and (j == w-1 or s[i][j+1] == "."):
print("No")
sys.exit()
print("Yes") | {
"input": [
"3 3\n.#.\n###\n.#.",
"5 5\n.#.#\n.#.#.\n.#.#\n.#.#.\n.#.#",
"11 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.##\n..##.#.##..\n.##..#..##.",
"3 3\n.#.\n\n.#.",
"3 5\n.#.\n###\n.#.",
"5 5\n.#.#\n.#.#.\n-#.#\n.#.#.\n.#.#",
"11 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"3 6\n.#.\n###\n.#.",
"11 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"5 6\n.#.\n###\n.#.",
"11 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"6 6\n.#.\n###\n.#.",
"11 15\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"6 6\n#..\n###\n.#.",
"6 8\n#..\n###\n.#.",
"4 8\n#..\n###\n.#.",
"4 8\n..#\n###\n.#.",
"8 8\n..#\n###\n.#.",
"0 8\n..#\n###\n.#.",
"0 10\n..#\n###\n.#.",
"0 10\n..#\n#\"#\n.#.",
"0 10\n..#\n#\"#\n-#.",
"5 3\n.#.\n###\n.#.",
"11 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#...####\n..##.#.##..\n.##..#..##.",
"3 5\n.#.\n\n.#.",
"3 5\n.\".\n###\n.#.",
"3 5\n.#.#\n.#.#.\n-#.#\n.#.#.\n.#.#",
"5 11\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"3 6\n.#/\n###\n.#.",
"11 11\n...#####...\n.##.....##.\n..#\".##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"5 6\n.#.\n###\n.#-",
"11 11\n...#####...\n.##-....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"6 11\n.#.\n###\n.#.",
"11 15\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.\".#.#$\n..##.#.##..\n.##..#..##.",
"6 6\n#..\n###\n.#-",
"7 8\n#..\n###\n.#.",
"4 8\n.#.\n###\n.#.",
"4 2\n..#\n###\n.#.",
"8 5\n..#\n###\n.#.",
"0 8\n#..\n###\n.#.",
"0 7\n..#\n###\n.#.",
"-1 10\n..#\n#\"#\n.#.",
"0 10\n#..\n#\"#\n-#.",
"5 2\n.#.\n###\n.#.",
"0 5\n.#.\n\n.#.",
"3 5\n\"..\n###\n.#.",
"3 5\n.#.#\n.#.#.\n-#.#\n.#.#.\n#.#.",
"5 11\n...#####...\n.##.....##.\n..##.##..#\n..##.\"#..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"3 6\n/#.\n###\n.#.",
"6 6\n.#.\n###\n.#-",
"11 11\n...#####...\n/##-....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"6 21\n.#.\n###\n.#.",
"11 15\n...#####...\n.##.....##.\n..##.##..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.\".#.#%\n..##.#.##..\n.##..#..##.",
"6 6\n#..\n###\n-#.",
"7 8\n..#\n###\n.#.",
"4 8\n.#.\n\"##\n.#.",
"4 3\n..#\n###\n.#.",
"13 5\n..#\n###\n.#.",
"0 8\n#/.\n###\n.#.",
"0 7\n.#.\n###\n.#.",
"-1 0\n..#\n#\"#\n.#.",
"0 10\n#..\n#\"#\n.#.",
"5 2\n..#\n###\n.#.",
"-1 5\n.#.\n\n.#.",
"3 5\n\"..\n###\n.$.",
"3 5\n.#.#\n.#.#.\n-#.\"\n.#.#.\n#.#.",
"5 16\n...#####...\n.##.....##.\n..##.##..#\n..##.\"#..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"0 6\n/#.\n###\n.#.",
"6 6\n.\".\n###\n.#-",
"11 11\n...#####...\n/##-....##.\n..##.\"#..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"0 21\n.#.\n###\n.#.",
"11 15\n...#####...\n.##.....##.\n..##.##-.#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.\".#.#%\n..##.#.##..\n.##..#..##.",
"6 0\n#..\n###\n-#.",
"7 9\n..#\n###\n.#.",
"4 12\n.#.\n\"##\n.#.",
"2 3\n..#\n###\n.#.",
"13 0\n..#\n###\n.#.",
"0 8\n\"/.\n###\n.#.",
"0 0\n..#\n#\"#\n.#.",
"0 10\n#..\n\"##\n.#.",
"5 2\n..#\n###\n.#-",
"-1 5\n.#.\n\n.#-",
"3 2\n\"..\n###\n.$.",
"0 16\n...#####...\n.##.....##.\n..##.##..#\n..##.\"#..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"0 7\n/#.\n###\n.#.",
"8 6\n.\".\n###\n.#-",
"11 11\n...#####...\n/##-....##.\n..##.\"#..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.$...#.###.\n.$.#.#.#$\n..##.#.##..\n.##..#..##.",
"0 21\n#..\n###\n.#.",
"5 15\n...#####...\n.##.....##.\n..##.##-.#\n..##.##..#\n.........#\n...###...#\n.#########.\n.#...#.###.\n.$.\".#.#%\n..##.#.##..\n.##..#..##.",
"7 0\n#..\n###\n-#.",
"7 9\n./#\n###\n.#.",
"2 12\n.#.\n\"##\n.#.",
"2 3\n..#\n$##\n.#.",
"13 -1\n..#\n###\n.#.",
"-1 8\n\"/.\n###\n.#.",
"0 0\n..#\n#!#\n.#.",
"5 2\n..#\n$##\n.#-",
"-1 5\n-#.\n\n.#-",
"3 2\n..\"\n###\n.$.",
"0 16\n...#####...\n.##....##..\n..##.##..#\n..##.\"#..#\n.........#\n...###...#\n.#########.\n.#.#.#.#.#.\n.#.#.#.#$\n..##.#.##..\n.##..#..##.",
"0 7\n/#.\n$##\n.#.",
"8 9\n.\".\n###\n.#-",
"11 11\n...#####...\n/##-....##.\n..##.\"#..#\n..##.##..#\n.........#\n...###...#\n.#########.\n.$...#.###.\n.$.#.#.#$\n..##.#.##..\n.##/.#..##.",
"0 21\n..#\n###\n.#."
],
"output": [
"Yes",
"No",
"Yes",
"Yes",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n",
"Yes\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
We have a canvas divided into a grid with H rows and W columns. The square at the i-th row from the top and the j-th column from the left is represented as (i, j).
Initially, all the squares are white. square1001 wants to draw a picture with black paint. His specific objective is to make Square (i, j) black when s_{i, j}= `#`, and to make Square (i, j) white when s_{i, j}= `.`.
However, since he is not a good painter, he can only choose two squares that are horizontally or vertically adjacent and paint those squares black, for some number of times (possibly zero). He may choose squares that are already painted black, in which case the color of those squares remain black.
Determine if square1001 can achieve his objective.
Constraints
* H is an integer between 1 and 50 (inclusive).
* W is an integer between 1 and 50 (inclusive).
* For every (i, j) (1 \leq i \leq H, 1 \leq j \leq W), s_{i, j} is `#` or `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1} s_{1, 2} s_{1, 3} ... s_{1, W}
s_{2, 1} s_{2, 2} s_{2, 3} ... s_{2, W}
: :
s_{H, 1} s_{H, 2} s_{H, 3} ... s_{H, W}
Output
If square1001 can achieve his objective, print `Yes`; if he cannot, print `No`.
Examples
Input
3 3
.#.
###
.#.
Output
Yes
Input
3 3
.#.
.#.
Output
Yes
Input
5 5
.#.#
.#.#.
.#.#
.#.#.
.#.#
Output
No
Input
11 11
...#####...
.##.....##.
..##.##..#
..##.##..#
.........#
...###...#
.#########.
.#.#.#.#.#.
.#.#.#.##
..##.#.##..
.##..#..##.
Output
Yes
### Input:
3 3
.#.
###
.#.
### Output:
Yes
### Input:
5 5
.#.#
.#.#.
.#.#
.#.#.
.#.#
### Output:
No
### Code:
import sys
h, w = map(int, input().split())
s = [list(input()) for i in range(h)]
for i in range(h):
for j in range(w):
if s[i][j] == "#" and (i == 0 or s[i-1][j] == ".") and (i == h-1 or s[i+1][j] == ".") and (j == 0 or s[i][j-1] == ".") and (j == w-1 or s[i][j+1] == "."):
print("No")
sys.exit()
print("Yes") |
p03519 CODE FESTIVAL 2017 Elimination Tournament Round 1 (Parallel) - Paired Parentheses_2943 | You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327 | import sys
from heapq import heappop, heappush, heapify
def main():
input = sys.stdin.readline
N, Q = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ls = [b-a for a, b in zip(A, B)]
q_m = [-v for v in ls[1:-1] if v < 0]
q_p = [v for v in ls[1:-1] if v >= 0]
heapify(q_m)
heapify(q_p)
sum_A = sum(A)
sum_q_p = sum(q_p)
to_remove = set()
odd = len(q_p) % 2
Ans = []
ans = sum_A + sum_q_p - (min(q_p[0], q_m[0]) if odd else 0)
for _ in range(Q):
p, x, y = map(int, input().split())
p -= 1
v = y-x
sum_A += x - A[p]
if p==0 or p==2*N-1:
ans += x - A[p]
Ans.append(ans)
A[p] = x
continue
A[p] = x
odd ^= (ls[p] >= 0) ^ (v >= 0)
if v >= 0:
sum_q_p += v
if ls[p] >= 0:
sum_q_p -= ls[p]
to_remove.add(ls[p])
ls[p] = v
if v >= 0:
heappush(q_p, v)
else:
heappush(q_m, -v)
ans = sum_q_p + sum_A
if odd:
while q_p[0] in to_remove:
to_remove.remove(heappop(q_p))
while -q_m[0] in to_remove:
to_remove.remove(-heappop(q_m))
ans -= min(q_p[0], q_m[0])
Ans.append(ans)
print("\n".join(map(str, Ans)))
main()
| {
"input": [
"2 2\n1 1 7 3\n4 2 3 3\n2 4 6\n3 2 5",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -2 23",
"2 2\n1 1 6 3\n4 2 3 3\n2 4 6\n3 2 5",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -2 23",
"2 2\n1 1 6 3\n4 2 3 3\n2 1 6\n3 2 5",
"2 2\n1 1 6 3\n4 2 3 3\n2 1 6\n1 2 5",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n6 2 3 3\n2 2 6\n1 4 9",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n6 2 3 3\n2 2 9\n1 4 9",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n6 1 3 3\n2 2 9\n2 4 9",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n5 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n12 -1 3 3\n2 1 9\n2 4 6",
"2 2\n1 1 6 3\n12 -1 3 3\n3 1 9\n2 4 6",
"2 2\n2 1 6 3\n12 -1 3 5\n3 1 9\n2 1 6",
"2 2\n2 1 6 3\n12 -2 3 5\n3 1 9\n2 1 6",
"2 2\n2 1 6 3\n2 -2 3 5\n3 1 9\n1 1 6",
"2 2\n1 1 6 3\n2 -2 3 5\n3 1 9\n1 1 6",
"2 2\n1 1 6 3\n-1 -2 3 5\n3 0 9\n1 0 6",
"2 2\n1 0 6 3\n-1 0 3 5\n3 0 9\n1 0 8",
"2 2\n1 -1 11 5\n-1 0 3 5\n3 1 9\n1 0 8",
"2 2\n1 -1 11 1\n-1 0 4 5\n3 1 2\n1 0 8",
"2 2\n1 0 7 3\n4 2 3 3\n2 4 6\n3 2 5",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 16 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -2 23",
"7 7\n49 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 23",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n6 -2 29",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 17 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n6 2 0 3\n2 2 6\n1 2 5",
"2 2\n1 1 6 3\n6 2 5 3\n2 2 6\n1 2 9",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n2 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n2 -2 29",
"2 2\n1 1 6 1\n12 0 3 3\n2 2 9\n2 4 9",
"2 2\n2 1 6 3\n12 -1 3 3\n2 2 9\n2 4 9",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -91 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -3 22\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n3 -2 29",
"2 2\n1 1 6 3\n12 -1 3 3\n2 1 9\n2 4 8",
"2 1\n1 1 6 3\n12 -1 3 5\n3 1 9\n2 1 6",
"2 1\n2 1 6 3\n12 -1 3 5\n3 1 9\n2 1 6",
"2 2\n2 1 6 3\n12 -2 3 5\n3 1 12\n2 1 6",
"2 2\n2 1 6 4\n2 -2 3 5\n3 1 9\n2 1 6",
"2 2\n1 1 6 4\n2 -2 3 5\n3 1 9\n1 1 6",
"2 2\n1 1 6 3\n2 -2 3 5\n1 0 9\n1 1 6",
"2 2\n1 1 6 3\n0 -2 3 5\n3 0 18\n1 1 6",
"2 2\n2 0 11 3\n-1 0 3 5\n3 0 9\n1 0 8",
"2 2\n1 -1 11 5\n-1 0 3 5\n3 1 2\n1 0 8",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -16 20 28 46 12 13 16 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -2 23",
"7 7\n49 -20 -27 42 78 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 23",
"2 2\n1 1 6 3\n4 2 6 3\n2 1 6\n1 2 3",
"2 2\n1 1 6 3\n4 2 3 3\n3 2 6\n1 4 5",
"7 7\n34 -20 -27 42 34 26 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\n3 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n2 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 30 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 11\n2 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 34 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 14\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 28 46 14 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n5 -50 -18\n4 -32 15\n8 -7 23\n5 -15 11\n4 -2 29",
"7 7\n22 -20 -28 42 44 29 9 11 34 44 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -3 22\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -91 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 68\n12 -3 22\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n3 -2 29",
"2 2\n1 1 6 3\n12 -1 3 3\n1 1 9\n4 4 6",
"2 2\n1 1 6 3\n-2 -2 3 5\n3 0 9\n2 0 8",
"2 2\n2 0 11 3\n-1 0 3 5\n3 0 9\n1 1 8",
"2 2\n1 0 11 3\n-1 0 0 5\n3 0 9\n1 -1 8",
"2 2\n1 -1 11 3\n-1 0 3 2\n3 1 2\n1 0 8",
"7 7\n34 -20 -27 42 58 29 9 11 20 44 27 19 -31 -29\n73 -50 -16 20 28 46 12 13 16 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -2 23",
"7 7\n49 -20 -27 42 78 29 9 11 20 44 27 19 -31 -49\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 23",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 24 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -8 23\n3 -15 11\n6 -2 29",
"7 7\n34 -20 -27 42 34 26 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\n3 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n86 -50 -3 20 28 46 12 13 33 -11 -42 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 30\n3 -15 11\n4 -2 29",
"2 2\n1 1 14 3\n6 2 3 3\n2 2 9\n1 4 3",
"7 7\n22 -20 -27 42 44 29 9 11 20 30 27 19 -31 -29\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n7 -32 15\n8 -7 23\n3 -15 11\n2 -2 29",
"2 2\n1 1 6 3\n6 0 6 3\n2 1 9\n2 4 9",
"7 7\n13 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 34 46 12 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 22\n4 -50 -12\n4 -32 15\n8 -7 23\n3 -15 14\n4 -2 29",
"2 2\n1 1 6 1\n12 0 3 3\n1 2 9\n2 4 7",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -91 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 68\n12 -3 34\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n3 -2 29",
"2 3\n1 1 4 4\n12 -1 3 3\n3 1 9\n2 1 6",
"7 7\n49 -20 -27 42 90 29 9 11 20 44 27 19 -31 -49\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 23",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 24 -17\n7 27 60\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -8 23\n3 -15 11\n6 -2 29",
"2 2\n1 2 6 3\n4 1 3 3\n3 2 6\n1 4 5",
"7 7\n34 -20 -27 42 34 26 9 11 20 44 27 19 -31 -29\n57 -50 -11 20 28 46 12 9 33 -11 -48 -27 35 -17\n3 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 29",
"2 2\n0 1 14 3\n6 2 3 3\n2 2 9\n1 4 3",
"2 2\n1 1 6 0\n12 0 3 3\n1 2 9\n2 4 7",
"2 2\n2 1 1 3\n12 -1 3 4\n2 2 11\n2 4 9",
"7 7\n22 -20 -28 42 44 29 9 11 34 44 27 19 -31 -29\n57 -69 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n7 27 42\n12 -3 22\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n4 -2 29",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -91 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\n12 27 68\n12 -3 34\n5 -50 -12\n4 -32 15\n8 -7 23\n5 -15 11\n3 -2 29",
"2 2\n1 1 6 5\n1 -2 4 5\n3 0 18\n1 1 6",
"7 7\n34 -20 -27 42 58 29 9 11 3 44 27 19 -31 -29\n73 -50 -16 20 28 46 12 13 16 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -30 11\n4 -3 23",
"7 7\n49 -20 -27 42 159 29 9 11 20 44 27 19 -31 -49\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -7 23\n3 -15 11\n4 -2 23",
"7 7\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n73 -50 -11 20 28 46 12 13 5 -22 -48 -27 24 -17\n7 27 60\n12 -2 22\n4 -50 -12\n3 -32 15\n8 -8 23\n3 -15 11\n6 -2 29",
"2 2\n0 1 15 3\n6 2 3 3\n2 2 9\n1 4 3",
"2 2\n1 2 6 0\n12 0 3 3\n1 2 9\n2 4 7",
"2 2\n1 0 11 1\n0 1 3 5\n3 1 6\n1 0 1",
"2 2\n1 1 15 3\n6 2 3 3\n2 2 9\n1 4 3",
"7 7\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 7 46 15 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 13\n5 -50 -18\n4 -32 15\n8 -14 23\n5 -15 11\n4 -2 29",
"2 2\n1 1 6 5\n1 -2 8 5\n3 0 35\n1 1 6",
"2 2\n1 1 6 3\n-2 -2 1 6\n3 0 9\n3 0 2",
"2 2\n1 -2 11 2\n-1 0 6 3\n3 1 2\n1 0 8",
"2 2\n1 0 11 1\n0 2 3 5\n3 1 6\n1 0 1",
"7 7\n22 -20 -27 79 44 29 9 11 20 44 27 19 -31 -29\n57 -50 -3 20 7 46 15 13 33 -11 -25 -27 35 -17\n7 27 49\n12 -2 13\n5 -50 -18\n4 -32 15\n8 -14 23\n5 -15 11\n4 -2 29",
"2 2\n1 1 6 3\n-2 -2 1 6\n3 0 9\n3 0 4",
"2 2\n1 0 11 3\n-2 0 0 3\n1 -1 9\n1 -1 8",
"7 7\n49 -20 -27 42 159 29 9 11 20 44 27 19 -31 -49\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\n7 27 34\n12 -2 22\n3 -12 -12\n3 -52 15\n8 -7 23\n3 -15 11\n4 -2 23"
],
"output": [
"15\n15",
"311\n312\n260\n286\n296\n292\n327",
"14\n15\n",
"311\n312\n260\n286\n296\n292\n327\n",
"13\n15\n",
"13\n14\n",
"311\n312\n260\n286\n296\n292\n333\n",
"311\n312\n260\n287\n297\n319\n333\n",
"13\n16\n",
"319\n320\n268\n295\n305\n319\n333\n",
"16\n19\n",
"307\n308\n256\n283\n293\n307\n321\n",
"16\n16\n",
"322\n323\n271\n298\n308\n322\n336\n",
"322\n323\n269\n240\n239\n253\n267\n",
"322\n323\n269\n240\n239\n262\n276\n",
"16\n14\n",
"12\n19\n",
"13\n20\n",
"12\n20\n",
"12\n11\n",
"11\n11\n",
"11\n10\n",
"13\n12\n",
"15\n14\n",
"4\n3\n",
"15\n15\n",
"296\n301\n245\n271\n279\n275\n310\n",
"326\n327\n275\n301\n311\n307\n342\n",
"311\n312\n260\n286\n296\n292\n275\n",
"315\n312\n264\n290\n296\n292\n333\n",
"12\n13\n",
"15\n16\n",
"311\n312\n260\n287\n297\n321\n335\n",
"307\n308\n256\n283\n293\n307\n349\n",
"14\n14\n",
"17\n17\n",
"322\n323\n269\n240\n239\n262\n294\n",
"16\n15\n",
"12\n",
"13\n",
"15\n23\n",
"13\n21\n",
"12\n12\n",
"10\n11\n",
"20\n20\n",
"14\n12\n",
"8\n7\n",
"291\n296\n240\n271\n279\n275\n310\n",
"360\n361\n309\n335\n345\n341\n376\n",
"16\n17\n",
"12\n15\n",
"301\n302\n250\n276\n286\n282\n323\n",
"334\n335\n283\n310\n320\n348\n362\n",
"293\n294\n242\n269\n279\n293\n335\n",
"322\n323\n271\n298\n308\n325\n339\n",
"322\n323\n263\n234\n233\n262\n276\n",
"322\n326\n269\n243\n253\n276\n290\n",
"341\n342\n288\n259\n258\n281\n313\n",
"11\n12\n",
"11\n21\n",
"14\n13\n",
"13\n11\n",
"6\n5\n",
"305\n310\n254\n285\n293\n289\n324\n",
"340\n341\n289\n315\n325\n321\n356\n",
"300\n301\n249\n275\n285\n281\n264\n",
"324\n325\n273\n254\n264\n260\n301\n",
"319\n320\n268\n295\n312\n326\n340\n",
"20\n23\n",
"293\n294\n242\n223\n233\n247\n283\n",
"19\n19\n",
"313\n314\n262\n289\n299\n316\n330\n",
"10\n13\n",
"341\n354\n300\n271\n270\n293\n325\n",
"13\n20\n20\n",
"352\n353\n301\n327\n337\n333\n368\n",
"326\n327\n275\n301\n311\n307\n290\n",
"11\n14\n",
"320\n325\n269\n250\n264\n260\n301\n",
"19\n23\n",
"9\n12\n",
"19\n17\n",
"315\n319\n262\n236\n246\n269\n283\n",
"332\n298\n244\n215\n224\n247\n279\n",
"22\n22\n",
"303\n304\n252\n283\n293\n289\n324\n",
"421\n422\n370\n396\n406\n402\n437\n",
"311\n316\n260\n286\n283\n279\n262\n",
"20\n24\n",
"10\n12\n",
"9\n8\n",
"21\n24\n",
"322\n314\n254\n225\n224\n253\n267\n",
"39\n39\n",
"11\n5\n",
"5\n4\n",
"10\n9\n",
"359\n351\n291\n225\n224\n253\n267\n",
"11\n6\n",
"13\n13\n",
"421\n422\n423\n448\n453\n449\n437\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327
### Input:
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
### Output:
15
15
### Input:
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
### Output:
311
312
260
286
296
292
327
### Code:
import sys
from heapq import heappop, heappush, heapify
def main():
input = sys.stdin.readline
N, Q = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ls = [b-a for a, b in zip(A, B)]
q_m = [-v for v in ls[1:-1] if v < 0]
q_p = [v for v in ls[1:-1] if v >= 0]
heapify(q_m)
heapify(q_p)
sum_A = sum(A)
sum_q_p = sum(q_p)
to_remove = set()
odd = len(q_p) % 2
Ans = []
ans = sum_A + sum_q_p - (min(q_p[0], q_m[0]) if odd else 0)
for _ in range(Q):
p, x, y = map(int, input().split())
p -= 1
v = y-x
sum_A += x - A[p]
if p==0 or p==2*N-1:
ans += x - A[p]
Ans.append(ans)
A[p] = x
continue
A[p] = x
odd ^= (ls[p] >= 0) ^ (v >= 0)
if v >= 0:
sum_q_p += v
if ls[p] >= 0:
sum_q_p -= ls[p]
to_remove.add(ls[p])
ls[p] = v
if v >= 0:
heappush(q_p, v)
else:
heappush(q_m, -v)
ans = sum_q_p + sum_A
if odd:
while q_p[0] in to_remove:
to_remove.remove(heappop(q_p))
while -q_m[0] in to_remove:
to_remove.remove(-heappop(q_m))
ans -= min(q_p[0], q_m[0])
Ans.append(ans)
print("\n".join(map(str, Ans)))
main()
|
p03684 AtCoder Regular Contest 076 - Built?_2947 | There are N towns on a plane. The i-th town is located at the coordinates (x_i,y_i). There may be more than one town at the same coordinates.
You can build a road between two towns at coordinates (a,b) and (c,d) for a cost of min(|a-c|,|b-d|) yen (the currency of Japan). It is not possible to build other types of roads.
Your objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ x_i,y_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.
Examples
Input
3
1 5
3 9
7 8
Output
3
Input
6
8 3
4 9
12 19
18 1
13 5
7 6
Output
8 | import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
class UnionFind:
def __init__(self, size):
self.table = [-1 for _ in range(size)]
def find(self, x):
if self.table[x] < 0:
return x
else:
self.table[x] = self.find(self.table[x])
return self.table[x]
def union(self, x, y):
s1 = self.find(x)
s2 = self.find(y)
if s1 != s2:
if self.table[s1] <= self.table[s2]:
self.table[s1] += self.table[s2]
self.table[s2] = s1
else:
self.table[s2] += self.table[s1]
self.table[s1] = s2
return True
return False
def subsetall(self):
a = []
for i in range(len(self.table)):
if self.table[i] < 0:
a.append((i, -self.table[i]))
return a
def main():
N = I()
a = []
b = []
for i in range(N):
x,y = LI()
a.append((x,i))
b.append((y,i))
a.sort()
b.sort()
t = []
for i in range(1,N):
t.append((a[i][0]-a[i-1][0], a[i][1], a[i-1][1]))
t.append((b[i][0]-b[i-1][0], b[i][1], b[i-1][1]))
t.sort()
r = 0
uf = UnionFind(N)
for c,d,e in t:
if uf.union(d,e):
r += c
return r
print(main()) | {
"input": [
"6\n8 3\n4 9\n12 19\n18 1\n13 5\n7 6",
"3\n1 5\n3 9\n7 8",
"6\n8 3\n4 9\n12 19\n2 1\n13 5\n7 6",
"3\n0 5\n3 9\n7 8",
"6\n8 3\n4 9\n12 19\n2 1\n15 5\n7 6",
"3\n0 8\n3 9\n7 8",
"6\n8 3\n4 9\n12 19\n2 2\n15 5\n7 6",
"6\n8 3\n4 9\n12 19\n2 4\n12 5\n7 6",
"6\n8 3\n4 5\n12 19\n2 4\n12 5\n7 6",
"6\n7 3\n4 5\n12 19\n2 4\n12 5\n7 6",
"6\n7 3\n2 5\n12 19\n2 4\n18 5\n7 6",
"3\n-2 1\n10 22\n3 5",
"3\n-3 1\n10 22\n3 7",
"3\n-3 1\n20 22\n3 7",
"3\n-3 1\n20 22\n3 3",
"6\n7 0\n0 4\n14 51\n2 1\n19 4\n4 20",
"3\n-3 1\n20 27\n3 0",
"3\n0 0\n22 26\n6 0",
"3\n0 0\n22 26\n6 1",
"3\n-1 0\n25 48\n6 1",
"3\n-1 0\n25 48\n11 1",
"6\n1 -1\n4 5\n14 54\n1 2\n38 0\n4 5",
"3\n-1 1\n1 21\n1 1",
"3\n13 21\n1 1\n1 0",
"3\n0 8\n3 9\n9 8",
"6\n8 3\n4 9\n12 19\n2 2\n10 5\n7 6",
"3\n0 8\n3 9\n16 8",
"6\n8 3\n4 9\n12 19\n2 4\n10 5\n7 6",
"3\n0 4\n3 9\n16 8",
"3\n0 4\n3 9\n16 10",
"3\n0 4\n3 9\n3 10",
"3\n0 4\n3 17\n3 10",
"6\n7 3\n2 5\n12 19\n2 4\n12 5\n7 6",
"3\n1 4\n3 17\n3 10",
"3\n1 4\n5 17\n3 10",
"6\n7 3\n2 5\n12 19\n2 4\n18 5\n7 10",
"3\n1 3\n5 17\n3 10",
"6\n7 3\n0 5\n12 19\n2 4\n18 5\n7 10",
"3\n0 3\n5 17\n3 10",
"6\n7 3\n0 5\n12 19\n2 4\n18 5\n4 10",
"3\n-1 3\n5 17\n3 10",
"6\n7 3\n0 5\n7 19\n2 4\n18 5\n4 10",
"3\n-1 1\n5 17\n3 10",
"6\n7 0\n0 5\n7 19\n2 4\n18 5\n4 10",
"3\n-1 1\n5 17\n3 20",
"6\n7 0\n0 5\n7 31\n2 4\n18 5\n4 10",
"3\n-2 1\n5 17\n3 20",
"6\n7 0\n0 5\n7 31\n2 4\n18 5\n4 20",
"3\n-2 1\n5 22\n3 20",
"6\n7 0\n0 5\n7 31\n2 4\n18 4\n4 20",
"3\n-2 1\n5 22\n3 5",
"6\n7 0\n0 5\n7 31\n2 4\n19 4\n4 20",
"6\n7 0\n0 5\n7 31\n2 0\n19 4\n4 20",
"3\n-3 1\n10 22\n3 5",
"6\n7 0\n0 5\n7 31\n2 1\n19 4\n4 20",
"6\n7 0\n0 5\n14 31\n2 1\n19 4\n4 20",
"6\n7 0\n0 5\n14 51\n2 1\n19 4\n4 20",
"3\n-3 1\n20 27\n3 3",
"6\n13 0\n0 4\n14 51\n2 1\n19 4\n4 20",
"6\n13 0\n0 4\n14 51\n2 0\n19 4\n4 20",
"3\n-2 1\n20 27\n3 0",
"6\n13 0\n1 4\n14 51\n2 0\n19 4\n4 20",
"3\n-2 1\n13 27\n3 0",
"6\n13 0\n0 4\n14 51\n1 0\n19 4\n4 20",
"3\n-1 1\n13 27\n3 0",
"6\n13 0\n0 4\n14 51\n1 0\n19 4\n4 4",
"3\n-2 1\n13 27\n6 0",
"6\n13 -1\n0 4\n14 51\n1 0\n19 4\n4 4",
"3\n-2 0\n13 27\n6 0",
"6\n3 -1\n0 4\n14 51\n1 0\n19 4\n4 4",
"3\n-2 0\n15 27\n6 0",
"6\n3 -1\n0 3\n14 51\n1 0\n19 4\n4 4",
"3\n-2 0\n15 23\n6 0",
"6\n3 -1\n0 3\n14 51\n1 0\n19 4\n4 3",
"3\n0 0\n15 23\n6 0",
"6\n3 -1\n1 3\n14 51\n1 0\n19 4\n4 3",
"3\n0 0\n15 26\n6 0",
"6\n3 -1\n1 3\n14 51\n1 1\n19 4\n4 3",
"6\n3 -1\n1 3\n14 45\n1 1\n19 4\n4 3",
"6\n3 -1\n1 3\n14 54\n1 1\n19 4\n4 3",
"3\n0 0\n22 28\n6 1",
"6\n3 -1\n1 3\n14 54\n1 0\n19 4\n4 3",
"3\n0 0\n22 48\n6 1",
"6\n3 -1\n1 5\n14 54\n1 0\n19 4\n4 3",
"3\n-1 0\n22 48\n6 1",
"6\n3 -1\n1 5\n14 54\n1 0\n19 0\n4 3",
"6\n3 -1\n1 5\n14 54\n1 0\n19 0\n4 5",
"3\n-1 0\n25 48\n6 2",
"6\n3 -1\n1 5\n14 54\n1 0\n19 0\n7 5",
"3\n-1 0\n25 48\n11 2",
"6\n3 -1\n1 5\n14 54\n1 1\n19 0\n7 5",
"6\n3 -1\n2 5\n14 54\n1 1\n19 0\n7 5",
"3\n0 0\n25 48\n11 1",
"6\n3 -1\n2 5\n14 54\n1 2\n19 0\n7 5",
"3\n-1 0\n25 50\n11 1",
"6\n3 -1\n4 5\n14 54\n1 2\n19 0\n7 5",
"3\n-1 0\n1 50\n11 1",
"6\n3 -1\n4 5\n14 54\n1 2\n19 0\n4 5",
"3\n-1 0\n1 75\n11 1",
"6\n1 -1\n4 5\n14 54\n1 2\n19 0\n4 5",
"3\n-1 0\n1 29\n11 1",
"3\n-1 0\n1 21\n11 1"
],
"output": [
"8",
"3",
"7\n",
"4\n",
"9\n",
"1\n",
"8\n",
"5\n",
"3\n",
"2\n",
"6\n",
"11\n",
"13\n",
"21\n",
"19\n",
"10\n",
"18\n",
"16\n",
"17\n",
"20\n",
"15\n",
"14\n",
"0\n",
"12\n",
"1\n",
"7\n",
"1\n",
"7\n",
"4\n",
"4\n",
"3\n",
"3\n",
"1\n",
"2\n",
"4\n",
"6\n",
"4\n",
"7\n",
"5\n",
"9\n",
"6\n",
"4\n",
"6\n",
"6\n",
"6\n",
"6\n",
"7\n",
"6\n",
"7\n",
"6\n",
"6\n",
"6\n",
"5\n",
"11\n",
"6\n",
"11\n",
"11\n",
"19\n",
"6\n",
"5\n",
"18\n",
"4\n",
"11\n",
"5\n",
"11\n",
"2\n",
"8\n",
"3\n",
"7\n",
"7\n",
"9\n",
"8\n",
"9\n",
"8\n",
"9\n",
"7\n",
"9\n",
"7\n",
"7\n",
"7\n",
"17\n",
"7\n",
"17\n",
"8\n",
"17\n",
"7\n",
"6\n",
"21\n",
"6\n",
"16\n",
"7\n",
"8\n",
"15\n",
"8\n",
"15\n",
"9\n",
"3\n",
"9\n",
"3\n",
"9\n",
"3\n",
"3\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N towns on a plane. The i-th town is located at the coordinates (x_i,y_i). There may be more than one town at the same coordinates.
You can build a road between two towns at coordinates (a,b) and (c,d) for a cost of min(|a-c|,|b-d|) yen (the currency of Japan). It is not possible to build other types of roads.
Your objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ x_i,y_i ≤ 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.
Examples
Input
3
1 5
3 9
7 8
Output
3
Input
6
8 3
4 9
12 19
18 1
13 5
7 6
Output
8
### Input:
6
8 3
4 9
12 19
18 1
13 5
7 6
### Output:
8
### Input:
3
1 5
3 9
7 8
### Output:
3
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
class UnionFind:
def __init__(self, size):
self.table = [-1 for _ in range(size)]
def find(self, x):
if self.table[x] < 0:
return x
else:
self.table[x] = self.find(self.table[x])
return self.table[x]
def union(self, x, y):
s1 = self.find(x)
s2 = self.find(y)
if s1 != s2:
if self.table[s1] <= self.table[s2]:
self.table[s1] += self.table[s2]
self.table[s2] = s1
else:
self.table[s2] += self.table[s1]
self.table[s1] = s2
return True
return False
def subsetall(self):
a = []
for i in range(len(self.table)):
if self.table[i] < 0:
a.append((i, -self.table[i]))
return a
def main():
N = I()
a = []
b = []
for i in range(N):
x,y = LI()
a.append((x,i))
b.append((y,i))
a.sort()
b.sort()
t = []
for i in range(1,N):
t.append((a[i][0]-a[i-1][0], a[i][1], a[i-1][1]))
t.append((b[i][0]-b[i-1][0], b[i][1], b[i-1][1]))
t.sort()
r = 0
uf = UnionFind(N)
for c,d,e in t:
if uf.union(d,e):
r += c
return r
print(main()) |
p03837 AtCoder Beginner Contest 051 - Candidates of No Shortest Paths_2951 | You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.
The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.
Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).
A connected graph is a graph where there is a path between every pair of different vertices.
Find the number of the edges that are not contained in any shortest path between any pair of different vertices.
Constraints
* 2≤N≤100
* N-1≤M≤min(N(N-1)/2,1000)
* 1≤a_i,b_i≤N
* 1≤c_i≤1000
* c_i is an integer.
* The given graph contains neither self-loops nor double edges.
* The given graph is connected.
Input
The input is given from Standard Input in the following format:
N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Output
Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.
Examples
Input
3 3
1 2 1
1 3 1
2 3 3
Output
1
Input
3 2
1 2 1
2 3 1
Output
0 | N, M = map(int, input().split())
inf = 10**6
abc = []
d = [[inf]*N for i in range(N)]
for i in range(M):
a, b, c = map(int, input().split())
d[a-1][b-1] = c
d[b-1][a-1] = c
abc.append((a-1,b-1,c))
for k in range(N):
for i in range(N):
for j in range(N):
d[i][j] = min(d[i][k]+d[k][j], d[i][j])
ans = 0
for i in range(M):
a, b, c = abc[i]
if d[a][b] < inf and d[a][b] < c:
ans += 1
print(ans) | {
"input": [
"3 3\n1 2 1\n1 3 1\n2 3 3",
"3 2\n1 2 1\n2 3 1",
"3 3\n1 2 2\n1 3 1\n2 3 3",
"4 3\n1 2 1\n1 3 1\n2 3 3",
"3 2\n1 2 2\n2 3 1",
"3 2\n1 3 2\n2 3 1",
"3 2\n1 3 2\n2 0 1",
"3 2\n1 2 2\n2 0 1",
"3 2\n2 2 2\n2 0 1",
"3 2\n1 1 1\n2 3 1",
"3 3\n1 2 2\n1 3 1\n2 3 0",
"3 2\n1 3 2\n2 1 1",
"3 2\n1 2 2\n2 -1 1",
"4 3\n1 2 1\n1 3 1\n2 3 4",
"3 2\n1 3 3\n2 1 1",
"6 2\n1 3 3\n2 1 1",
"3 2\n1 2 1\n2 3 2",
"3 3\n1 1 2\n1 3 1\n2 3 3",
"3 2\n1 2 2\n1 3 1",
"3 2\n1 1 2\n2 3 1",
"3 2\n1 0 2\n2 0 1",
"4 3\n1 3 1\n1 3 1\n2 3 3",
"5 2\n1 2 2\n2 -1 1",
"4 0\n1 2 1\n1 3 1\n2 3 4",
"3 2\n1 3 6\n2 1 1",
"6 2\n0 3 3\n2 1 1",
"3 2\n1 2 1\n2 2 2",
"3 3\n1 1 1\n1 3 1\n2 3 3",
"3 2\n1 1 2\n2 1 1",
"3 0\n1 0 2\n2 0 1",
"5 2\n0 2 2\n2 -1 1",
"4 0\n1 2 1\n1 3 2\n2 3 4",
"3 2\n1 0 6\n2 1 1",
"6 2\n0 0 3\n2 1 1",
"3 3\n1 1 1\n1 3 1\n2 3 2",
"3 2\n1 0 2\n2 1 1",
"3 0\n2 0 2\n2 0 1",
"4 0\n2 2 1\n1 3 2\n2 3 4",
"3 2\n2 0 6\n2 1 1",
"6 2\n0 0 3\n2 1 2",
"3 0\n2 0 2\n2 1 1",
"4 0\n2 2 1\n0 3 2\n2 3 4",
"3 2\n2 0 6\n3 1 1",
"6 2\n0 0 3\n1 1 2",
"3 -1\n2 0 2\n2 1 1",
"4 0\n2 2 1\n0 3 2\n2 0 4",
"3 1\n2 0 6\n3 1 1",
"6 2\n1 0 3\n1 1 2",
"3 -1\n2 0 2\n2 2 1",
"4 0\n2 1 1\n0 3 2\n2 0 4",
"3 1\n2 0 6\n3 1 2",
"9 2\n1 0 3\n1 1 2",
"3 -1\n2 0 2\n4 2 1",
"7 0\n2 1 1\n0 3 2\n2 0 4",
"3 1\n2 1 6\n3 1 2",
"9 2\n1 0 5\n1 1 2",
"3 -1\n2 0 2\n4 2 2",
"7 0\n2 1 1\n0 3 2\n0 0 4",
"3 1\n0 1 6\n3 1 2",
"9 2\n1 0 10\n1 1 2",
"3 -1\n2 0 2\n4 3 2",
"7 0\n2 1 1\n0 3 1\n0 0 4",
"3 1\n0 1 7\n3 1 2",
"9 2\n1 0 10\n1 1 3",
"3 -1\n2 0 2\n5 3 2",
"7 -1\n2 1 1\n0 3 1\n0 0 4",
"3 1\n0 1 14\n3 1 2",
"9 2\n1 0 14\n1 1 3",
"3 -1\n2 -1 2\n5 3 2",
"7 -1\n2 1 0\n0 3 1\n0 0 4",
"3 1\n0 1 23\n3 1 2",
"9 2\n1 0 14\n1 1 2",
"0 -1\n2 -1 2\n5 3 2",
"7 -1\n2 0 1\n0 3 1\n0 0 4",
"3 1\n0 1 23\n3 2 2",
"0 -1\n2 -1 2\n0 3 2",
"14 -1\n2 0 1\n0 3 1\n0 0 4",
"4 1\n0 1 23\n3 2 2",
"1 -1\n2 -1 2\n0 3 2",
"14 0\n2 0 1\n0 3 1\n0 0 4",
"4 1\n0 1 23\n3 4 2",
"1 -1\n2 -2 2\n0 3 2",
"14 0\n2 0 1\n0 3 1\n0 0 5",
"4 2\n0 1 23\n3 4 2",
"1 0\n2 -2 2\n0 3 2",
"14 0\n2 0 1\n0 2 1\n0 0 5",
"14 0\n2 0 1\n0 4 1\n0 0 5",
"23 0\n2 0 1\n0 4 1\n0 0 5",
"23 0\n2 0 1\n0 4 1\n0 0 8",
"4 0\n2 0 1\n0 4 1\n0 0 8",
"4 0\n2 0 0\n0 4 1\n0 0 8",
"7 0\n2 0 0\n0 4 1\n0 0 8",
"7 0\n1 0 0\n0 4 1\n0 0 8",
"7 0\n1 0 0\n-1 4 1\n0 0 8",
"7 0\n1 0 0\n-1 4 1\n0 0 4",
"7 1\n1 0 0\n-1 4 1\n0 0 4",
"7 1\n1 0 0\n-1 8 1\n0 0 4",
"7 1\n1 -1 0\n-1 8 1\n0 0 4",
"7 1\n1 -1 0\n-1 4 1\n0 0 4",
"7 1\n1 -1 0\n-1 4 1\n-1 0 4",
"7 1\n1 -1 0\n-1 4 2\n-1 0 4",
"7 1\n1 -2 0\n-1 4 2\n-1 0 4"
],
"output": [
"1",
"0",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.
The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.
Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).
A connected graph is a graph where there is a path between every pair of different vertices.
Find the number of the edges that are not contained in any shortest path between any pair of different vertices.
Constraints
* 2≤N≤100
* N-1≤M≤min(N(N-1)/2,1000)
* 1≤a_i,b_i≤N
* 1≤c_i≤1000
* c_i is an integer.
* The given graph contains neither self-loops nor double edges.
* The given graph is connected.
Input
The input is given from Standard Input in the following format:
N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Output
Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.
Examples
Input
3 3
1 2 1
1 3 1
2 3 3
Output
1
Input
3 2
1 2 1
2 3 1
Output
0
### Input:
3 3
1 2 1
1 3 1
2 3 3
### Output:
1
### Input:
3 2
1 2 1
2 3 1
### Output:
0
### Code:
N, M = map(int, input().split())
inf = 10**6
abc = []
d = [[inf]*N for i in range(N)]
for i in range(M):
a, b, c = map(int, input().split())
d[a-1][b-1] = c
d[b-1][a-1] = c
abc.append((a-1,b-1,c))
for k in range(N):
for i in range(N):
for j in range(N):
d[i][j] = min(d[i][k]+d[k][j], d[i][j])
ans = 0
for i in range(M):
a, b, c = abc[i]
if d[a][b] < inf and d[a][b] < c:
ans += 1
print(ans) |
p00090 Overlaps of Seals_2957 | Stick n circular stickers with a radius of 1 on a square origami paper with a side length of 10. The stickers can be stacked. Create a program that reads the coordinates of the position where the stickers are to be attached and outputs the number of stickers at the place where the stickers overlap most on the origami paper (assuming that even one sticker "overlaps"). ..
Gives the x and y coordinates with the lower left corner of the origami as the origin. Let's put the sticker with these x and y as the center of the circle. The center of the circle never goes out of the origami. Also, multiple stickers will not be attached at the same coordinates.
Hint
It is a figure with a sticker attached as shown in the input example. The circle represents the sticker, and the number represents the number of lines in the input example. At point (2.3, 4.6), the four stickers on the second, third, sixth, and tenth lines of the input example overlap.
<image>
The distance between the centers of 6 and 9 is 2.01293, so the seals do not overlap. The distance between the centers of 1 and 12 is 1.98231, so the seals overlap.
When two circles are in contact (when the distance between the centers is 2), they are assumed to overlap.
Input
Given multiple datasets. Each dataset is given in the following format:
n
x1, y1
x2, y2
::
xn, yn
The first line gives the number of stickers n (0 ≤ 100). The next n lines give the center coordinates of each seal. xi and yi represent the x and y coordinates of the center of the i-th sticker. Each value is given as a real number, including up to 6 digits after the decimal point.
When n is 0, it is the end of the input. The number of datasets does not exceed 50.
Output
For each data set, output the number of stickers (integer) at the place where the stickers overlap most on the origami paper.
Example
Input
15
3.14979,8.51743
2.39506,3.84915
2.68432,5.39095
5.61904,9.16332
7.85653,4.75593
2.84021,5.41511
1.79500,8.59211
7.55389,8.17604
4.70665,4.66125
1.63470,4.42538
7.34959,4.61981
5.09003,8.11122
5.24373,1.30066
0.13517,1.83659
7.57313,1.58150
0
Output
4 | import itertools
x=[0.]*100;y=[0.]*100
for e in iter(input,'0'):
a=0
n=int(e)
for i in range(n):x[i],y[i]=map(float,input().split(','))
for i,j in itertools.product(range(100),range(100)):
c=0
for k in range(n):
if pow(x[k]-(i/10),2)+pow(y[k]-(j/10),2)<=1.01:c+=1
if c>a:a=c
print(a)
| {
"input": [
"15\n3.14979,8.51743\n2.39506,3.84915\n2.68432,5.39095\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n2.68432,5.39095\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n58093.5,23486.2\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n51948.3,60593.2\n50893.5,23486.2\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n51948.3,60593.2\n50893.5,23486.2\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n01295.8,01597.1\n7.55389,8.17604\n4.70665,4.66124\n83524.4,07436.1\n17916.4,95943.7\n22111.8,30090.5\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.61904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.60904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n4.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.60904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n4.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.60904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n66003.1,37342.5\n0.13517,1.83659\n7.57313,1.58150\n0",
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"15\n4.13979,8.51743\n51948.3,60593.2\n2.68432,5.92185\n5.50904,9.16332\n7.85653,4.74593\n2.84021,5.41511\n11295.8,00597.1\n7.55389,8.16604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30076\n0.13527,1.83659\n7.57313,1.58150\n0",
"15\n4.13979,8.51743\n51948.3,60593.2\n2.68432,5.92085\n23361.5,40905.9\n7.85653,4.74593\n2.84021,5.41511\n11295.8,00597.1\n7.55389,8.16604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30076\n0.13527,1.83659\n7.57313,1.58150\n0",
"15\n4.13979,8.51743\n51948.3,60593.2\n58029.5,23486.2\n9.50904,5.16332\n7.85653,4.74593\n2.84021,5.41511\n11295.8,00597.1\n7.55389,8.16604\n52166.4,56607.4\n1.63470,4.42538\n7.34959,4.61981\n22111.8,30090.5\n5.24373,1.30076\n0.13527,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n2.68432,5.39095\n23361.9,40916.5\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.59211\n7.55389,8.17604\n4.70665,4.66125\n1.62470,4.43538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n3.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.60904,9.16332\n39557.4,35658.7\n2.84021,5.41511\n1.79500,8.59211\n8.55389,8.17604\n4.70665,4.66125\n1.63470,4.42538\n7.34959,4.61981\n5.09003,8.11122\n5.24373,1.30066\n0.13517,1.83659\n7.57313,1.58150\n0",
"15\n4.13979,8.51743\n2.39506,3.84915\n2.68432,5.39085\n5.60904,9.16332\n7.85653,4.75593\n2.84021,5.41511\n1.79500,8.69211\n7.55389,8.17604\n4.70665,4.66125\n83524.4,07436.1\n7.34959,4.61981\n5.09003,8.11122\n66003.1,36342.5\n0.13517,1.83659\n7.57313,1.58150\n0"
],
"output": [
"4",
"4\n",
"3\n",
"2\n",
"1\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"3\n",
"4\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"3\n",
"3\n",
"3\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"4\n",
"4\n",
"3\n",
"3\n",
"4\n",
"4\n",
"4\n",
"4\n",
"2\n",
"4\n",
"3\n",
"4\n",
"3\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"4\n",
"3\n",
"4\n",
"4\n",
"3\n",
"4\n",
"3\n",
"4\n",
"3\n",
"3\n",
"2\n",
"4\n",
"4\n",
"3\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Stick n circular stickers with a radius of 1 on a square origami paper with a side length of 10. The stickers can be stacked. Create a program that reads the coordinates of the position where the stickers are to be attached and outputs the number of stickers at the place where the stickers overlap most on the origami paper (assuming that even one sticker "overlaps"). ..
Gives the x and y coordinates with the lower left corner of the origami as the origin. Let's put the sticker with these x and y as the center of the circle. The center of the circle never goes out of the origami. Also, multiple stickers will not be attached at the same coordinates.
Hint
It is a figure with a sticker attached as shown in the input example. The circle represents the sticker, and the number represents the number of lines in the input example. At point (2.3, 4.6), the four stickers on the second, third, sixth, and tenth lines of the input example overlap.
<image>
The distance between the centers of 6 and 9 is 2.01293, so the seals do not overlap. The distance between the centers of 1 and 12 is 1.98231, so the seals overlap.
When two circles are in contact (when the distance between the centers is 2), they are assumed to overlap.
Input
Given multiple datasets. Each dataset is given in the following format:
n
x1, y1
x2, y2
::
xn, yn
The first line gives the number of stickers n (0 ≤ 100). The next n lines give the center coordinates of each seal. xi and yi represent the x and y coordinates of the center of the i-th sticker. Each value is given as a real number, including up to 6 digits after the decimal point.
When n is 0, it is the end of the input. The number of datasets does not exceed 50.
Output
For each data set, output the number of stickers (integer) at the place where the stickers overlap most on the origami paper.
Example
Input
15
3.14979,8.51743
2.39506,3.84915
2.68432,5.39095
5.61904,9.16332
7.85653,4.75593
2.84021,5.41511
1.79500,8.59211
7.55389,8.17604
4.70665,4.66125
1.63470,4.42538
7.34959,4.61981
5.09003,8.11122
5.24373,1.30066
0.13517,1.83659
7.57313,1.58150
0
Output
4
### Input:
15
3.14979,8.51743
2.39506,3.84915
2.68432,5.39095
5.61904,9.16332
7.85653,4.75593
2.84021,5.41511
1.79500,8.59211
7.55389,8.17604
4.70665,4.66125
1.63470,4.42538
7.34959,4.61981
5.09003,8.11122
5.24373,1.30066
0.13517,1.83659
7.57313,1.58150
0
### Output:
4
### Input:
15
3.13979,8.51743
2.39506,3.84915
2.68432,5.39095
5.61904,9.16332
7.85653,4.75593
2.84021,5.41511
1.79500,8.59211
7.55389,8.17604
4.70665,4.66125
1.63470,4.42538
7.34959,4.61981
5.09003,8.11122
5.24373,1.30066
0.13517,1.83659
7.57313,1.58150
0
### Output:
4
### Code:
import itertools
x=[0.]*100;y=[0.]*100
for e in iter(input,'0'):
a=0
n=int(e)
for i in range(n):x[i],y[i]=map(float,input().split(','))
for i,j in itertools.product(range(100),range(100)):
c=0
for k in range(n):
if pow(x[k]-(i/10),2)+pow(y[k]-(j/10),2)<=1.01:c+=1
if c>a:a=c
print(a)
|
p00222 Prime Quadruplet_2960 | A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 ≤ n ≤ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439 | # AOJ 0222 Prime Quadruplet
# Python3 2018.6.23 bal4u
# From Wekipedia (https://en.wikipedia.org/wiki/Prime_quadruplet)
# All prime quadruplets except {5, 7, 11, 13} are of the form
# {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n.
MAX = 899
diff = (0,3,3,21,22,13,7,39,7,73, \
126,119,88,3,11,66,29,17,53,42, \
101,214,104,298,252,133,255,141,76,91, \
168,81,45,56,203,301,43,66,291,223, \
92,97,442,290,437,281,38,144,549,241, \
29,192,11,518,266,490,122,130,13,329, \
85,209,71,241,290,18,301,52,120,34, \
50,805,276,217,182,53,209,155,77,468, \
448,29,90,85,91,7,146,21,309,234, \
60,213,511,59,273,364,57,77,87,231, \
452,168,154,346,273,588,11,91,322,335, \
140,221,87,442,297,95,321,498,146,182, \
8,38,11,679,111,120,83,36,59,462, \
32,349,448,333,644,63,101,960,161,759, \
255,354,270,52,200,133,112,297,298,27, \
74,577,25,182,280,584,756,266,287,277, \
119,31,561,59,179,630,34,98,1,84, \
217,234,4,48,127,528,679,35,108,15, \
752,60,31,228,559,7,35,56,43,10, \
151,374,297,294,14,60,196,133,18,63, \
63,17,35,290,953,584,66,102,427,4, \
357,507,441,420,802,14,66,171,252,88, \
14,364,32,220,66,256,427,651,52,287, \
987,214,161,319,241,1333,190,325,63,500, \
1026,60,13,112,238,144,137,349,417,32, \
164,196,115,735,200,382,273,104,119,214, \
665,235,297,665,25,34,211,280,542,375, \
188,42,134,573,350,106,17,112,676,1095, \
403,62,193,60,13,116,60,255,609,350, \
7,165,661,25,748,176,10,283,144,987, \
389,59,60,342,112,144,31,98,676,297, \
652,189,56,34,441,50,314,266,29,546, \
297,39,657,46,703,70,270,221,122,767, \
13,134,318,1222,84,650,371,92,164,760, \
318,175,158,679,496,389,273,38,676,270, \
902,228,143,196,18,287,102,409,612,1, \
56,269,311,714,1092,176,34,165,143,438, \
266,249,97,442,105,7,913,81,80,871, \
497,585,574,11,220,94,855,132,473,836, \
301,7,833,63,1145,60,1886,382,111,43, \
111,319,431,108,297,60,878,799,133,472, \
529,420,241,46,231,304,616,1145,595,447, \
589,76,399,865,154,101,119,739,528,673, \
49,994,412,1072,6,25,3,49,126,1079, \
1141,66,220,932,1049,561,692,764,476,248, \
200,1897,658,644,24,399,143,1331,839,1, \
1077,760,11,34,658,36,647,21,528,242, \
98,529,24,1117,192,396,930,224,365,66, \
557,377,757,322,203,335,770,155,97,21, \
665,484,553,321,207,116,574,272,287,253, \
637,259,38,263,62,1268,451,693,756,630, \
357,105,32,581,455,153,540,350,91,210, \
409,270,377,442,490,615,424,52,890,199, \
102,1746,462,749,24,644,540,220,840,1656, \
223,74,434,179,665,923,428,307,875,50, \
2387,276,109,363,529,550,139,798,176,150, \
297,123,66,266,414,17,130,1344,300,1799, \
8,1176,279,351,461,396,112,626,498,931, \
2782,123,1253,780,781,1119,46,39,847,468, \
1037,1144,63,332,294,1082,525,459,220,70, \
231,31,1029,256,290,662,242,98,252,13, \
1008,64,346,1211,119,802,189,272,298,122, \
697,319,195,273,410,1221,365,885,322,52, \
847,165,112,67,812,630,801,87,60,424, \
630,867,231,123,308,396,76,119,60,203, \
17,63,553,931,147,588,127,437,164,43, \
14,371,115,150,354,315,473,3,1221,245, \
36,272,214,24,385,249,182,445,171,35, \
921,300,1558,1250,129,539,476,94,11,227, \
427,151,102,126,2176,71,297,60,413,195, \
190,944,49,554,1102,676,279,78,143,364, \
357,462,1144,1050,218,423,623,364,416,239, \
143,280,248,365,77,77,1529,157,361,514, \
536,31,330,87,193,514,935,227,18,91, \
104,49,133,1149,104,518,396,1015,143,445, \
360,385,680,49,1053,669,647,931,140,231, \
31,1075,483,627,101,1012,714,346,504,60, \
917,1140,1180,98,297,1029,225,1918,406,188, \
368,466,1305,1117,1028,50,150,273,333,101, \
151,146,1100,119,1532,497,487,235,658,322, \
538,210,701,574,136,220,168,105,603,332, \
409,84,81,39,860,309,384,259,266,207, \
872,377,403,248,819,882,931,148,42,371, \
805,325,668,529,409,3151,2016,14,38,1487, \
350,295,266,343,1833,1887,123,370,260,696, \
137,962,410,132,847,1051,426,39,214,546, \
539,493,325,137,112,889,130,237,43,1183, \
118,371,1,580,316,434,2698,53,98,262, \
203,119,31,189,813,119,195,294,1435,1345, \
531,624,210,231,321,553,11,756,1358)
def bsch(x):
l, r = 0, MAX
while l < r:
m = (l + r) >> 1
if tbl[m] == x: return m
if tbl[m] < x: l = m+1
else: r = m
return l-1;
tbl = [0]*MAX
for i in range(1, MAX): tbl[i] = tbl[i-1] + diff[i]
for i in range(MAX): tbl[i] = tbl[i]*30+19
while 1:
n = int(input())
if n == 0: break
if n < 19: print("13")
else: print(tbl[bsch(n)])
| {
"input": [
"13\n14\n15\n16\n17\n18\n19\n20\n10000\n0",
"13\n14\n15\n16\n17\n18\n0\n20\n10000\n0",
"13\n14\n15\n16\n17\n27\n0\n20\n10000\n0",
"13\n14\n27\n16\n17\n27\n0\n-1\n11000\n0",
"13\n14\n15\n16\n17\n18\n19\n20\n00000\n0",
"13\n26\n15\n16\n17\n27\n0\n20\n10000\n0",
"13\n14\n15\n16\n32\n27\n0\n-1\n11000\n0",
"13\n14\n23\n16\n17\n18\n19\n20\n00000\n0",
"13\n19\n15\n16\n17\n18\n0\n20\n10001\n0",
"13\n26\n15\n29\n17\n27\n0\n20\n10000\n0",
"13\n15\n23\n16\n17\n18\n19\n18\n00000\n0",
"13\n14\n15\n16\n17\n18\n19\n20\n10010\n0",
"13\n14\n25\n16\n32\n27\n0\n-1\n11000\n0",
"13\n14\n23\n32\n17\n18\n19\n20\n00000\n0",
"13\n19\n15\n16\n0\n18\n0\n20\n10001\n0",
"13\n15\n23\n16\n17\n18\n19\n18\n00100\n0",
"13\n14\n15\n21\n17\n24\n0\n3\n11000\n0",
"13\n14\n27\n15\n17\n13\n0\n3\n11000\n1",
"13\n14\n23\n32\n17\n31\n19\n20\n00000\n0",
"13\n15\n23\n16\n17\n18\n19\n18\n00110\n0",
"13\n14\n18\n32\n17\n31\n19\n20\n00000\n0",
"13\n19\n29\n16\n0\n18\n0\n20\n10001\n-1",
"13\n14\n18\n32\n17\n31\n13\n46\n00000\n1",
"13\n18\n27\n22\n17\n52\n0\n1\n01110\n0",
"13\n14\n15\n16\n17\n36\n19\n20\n10000\n0",
"13\n0\n15\n16\n17\n27\n0\n3\n11000\n0",
"13\n14\n15\n16\n17\n36\n19\n20\n00000\n0",
"13\n15\n23\n16\n24\n18\n19\n20\n00000\n0",
"13\n26\n27\n16\n17\n27\n0\n3\n11000\n2",
"13\n15\n23\n16\n31\n18\n19\n18\n00000\n0",
"13\n14\n15\n16\n0\n24\n0\n3\n11000\n0",
"13\n14\n15\n16\n27\n36\n19\n20\n10000\n0",
"13\n14\n15\n16\n24\n36\n19\n20\n00000\n0",
"13\n15\n23\n16\n17\n18\n18\n20\n00000\n1",
"13\n28\n23\n16\n24\n18\n19\n20\n00000\n0",
"13\n24\n23\n16\n31\n18\n19\n18\n00000\n0",
"13\n14\n23\n19\n17\n18\n19\n20\n00100\n0",
"13\n22\n23\n16\n17\n18\n0\n18\n00110\n0",
"13\n27\n18\n32\n17\n31\n19\n20\n00000\n-1",
"13\n26\n30\n79\n17\n27\n0\n20\n11000\n1",
"13\n14\n18\n32\n17\n13\n20\n46\n00000\n1",
"13\n14\n15\n25\n27\n36\n19\n20\n10000\n0",
"13\n14\n30\n16\n24\n36\n19\n20\n00000\n0",
"13\n24\n23\n16\n31\n19\n19\n18\n00000\n0",
"13\n14\n15\n0\n24\n27\n0\n0\n11100\n1",
"13\n28\n27\n16\n31\n27\n0\n0\n11000\n0",
"13\n24\n23\n29\n31\n19\n19\n18\n00000\n0",
"13\n17\n17\n16\n17\n0\n0\n-1\n10010\n1",
"13\n19\n15\n20\n0\n24\n0\n20\n10011\n-1",
"13\n22\n18\n32\n17\n13\n20\n46\n00000\n0",
"13\n24\n23\n29\n31\n19\n19\n27\n00000\n0",
"13\n14\n89\n17\n29\n17\n0\n0\n11100\n1",
"13\n28\n27\n16\n31\n135\n0\n0\n11000\n0",
"13\n26\n23\n29\n31\n19\n19\n27\n00100\n0",
"13\n20\n15\n27\n17\n15\n0\n0\n10000\n2",
"13\n26\n23\n29\n31\n17\n19\n27\n00100\n0",
"13\n26\n15\n29\n31\n17\n19\n27\n00100\n0",
"13\n19\n27\n21\n50\n168\n0\n-2\n11000\n-1",
"13\n19\n27\n21\n50\n72\n0\n-2\n11000\n-1",
"13\n23\n15\n0\n0\n76\n1\n0\n10000\n2",
"13\n26\n15\n29\n20\n27\n0\n20\n10000\n0",
"13\n25\n23\n16\n17\n18\n19\n20\n00000\n0",
"13\n14\n15\n31\n17\n36\n19\n20\n10000\n0",
"13\n14\n15\n32\n17\n18\n0\n20\n10000\n-1",
"13\n14\n23\n19\n17\n18\n13\n20\n00000\n0",
"13\n20\n15\n16\n27\n36\n19\n20\n10000\n0",
"13\n14\n27\n28\n31\n27\n0\n0\n11000\n0",
"13\n26\n30\n79\n17\n17\n0\n20\n11000\n1",
"13\n14\n30\n21\n24\n36\n19\n20\n00000\n0",
"13\n14\n155\n15\n17\n27\n0\n3\n10000\n1",
"13\n14\n23\n19\n17\n18\n22\n20\n01100\n0",
"13\n26\n14\n29\n31\n19\n19\n27\n00000\n0",
"13\n61\n23\n0\n0\n25\n0\n26\n10101\n-2",
"13\n14\n19\n0\n6\n40\n1\n0\n10000\n1",
"13\n26\n15\n48\n31\n25\n33\n27\n00100\n0",
"13\n14\n23\n16\n16\n18\n19\n20\n10000\n0",
"13\n25\n23\n16\n17\n18\n19\n20\n10000\n0",
"13\n14\n0\n21\n17\n24\n0\n2\n11000\n0",
"13\n19\n15\n31\n17\n36\n19\n20\n10000\n0",
"13\n20\n29\n16\n27\n36\n19\n20\n10000\n0",
"13\n28\n23\n24\n17\n18\n19\n20\n00100\n0",
"13\n19\n29\n24\n0\n25\n0\n20\n10011\n-1",
"13\n14\n30\n79\n17\n17\n0\n20\n11000\n1",
"13\n14\n18\n32\n32\n13\n20\n46\n00000\n2",
"13\n14\n155\n15\n22\n27\n0\n3\n10000\n1",
"13\n21\n43\n16\n31\n36\n19\n20\n00000\n0",
"13\n22\n18\n32\n17\n13\n20\n76\n00100\n0",
"13\n28\n27\n16\n120\n40\n0\n0\n11000\n0",
"13\n19\n0\n16\n0\n20\n-1\n20\n00001\n-8",
"13\n28\n14\n16\n31\n80\n0\n0\n11000\n1",
"13\n14\n15\n16\n17\n27\n0\n3\n10000\n0",
"13\n14\n15\n16\n17\n27\n0\n3\n11000\n0",
"13\n14\n15\n16\n17\n27\n0\n0\n11000\n0",
"13\n14\n15\n16\n17\n27\n0\n-1\n11000\n0",
"13\n14\n27\n16\n17\n27\n0\n-1\n11000\n1",
"13\n14\n27\n16\n17\n37\n0\n-1\n11000\n1",
"13\n14\n15\n16\n17\n18\n0\n20\n10001\n0",
"13\n14\n15\n16\n17\n27\n0\n3\n11000\n1",
"13\n14\n27\n16\n17\n27\n0\n-1\n10000\n0",
"13\n14\n42\n16\n17\n27\n0\n-1\n11000\n1",
"13\n14\n27\n16\n17\n27\n0\n3\n11000\n1"
],
"output": [
"13\n13\n13\n13\n13\n13\n19\n19\n9439",
"13\n13\n13\n13\n13\n13\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n",
"13\n13\n13\n13\n13\n13\n19\n19\n",
"13\n19\n13\n13\n13\n19\n",
"13\n13\n13\n13\n19\n19\n",
"13\n13\n19\n13\n13\n13\n19\n19\n",
"13\n19\n13\n13\n13\n13\n",
"13\n19\n13\n19\n13\n19\n",
"13\n13\n19\n13\n13\n13\n19\n13\n",
"13\n13\n13\n13\n13\n13\n19\n19\n9439\n",
"13\n13\n19\n13\n19\n19\n",
"13\n13\n19\n19\n13\n13\n19\n19\n",
"13\n19\n13\n13\n",
"13\n13\n19\n13\n13\n13\n19\n13\n19\n",
"13\n13\n13\n19\n13\n19\n",
"13\n13\n19\n13\n13\n13\n",
"13\n13\n19\n19\n13\n19\n19\n19\n",
"13\n13\n19\n13\n13\n13\n19\n13\n109\n",
"13\n13\n13\n19\n13\n19\n19\n19\n",
"13\n19\n19\n13\n",
"13\n13\n13\n19\n13\n19\n13\n19\n",
"13\n13\n19\n19\n13\n19\n",
"13\n13\n13\n13\n13\n19\n19\n19\n9439\n",
"13\n",
"13\n13\n13\n13\n13\n19\n19\n19\n",
"13\n13\n19\n13\n19\n13\n19\n19\n",
"13\n19\n19\n13\n13\n19\n",
"13\n13\n19\n13\n19\n13\n19\n13\n",
"13\n13\n13\n13\n",
"13\n13\n13\n13\n19\n19\n19\n19\n9439\n",
"13\n13\n13\n13\n19\n19\n19\n19\n",
"13\n13\n19\n13\n13\n13\n13\n19\n",
"13\n19\n19\n13\n19\n13\n19\n19\n",
"13\n19\n19\n13\n19\n13\n19\n13\n",
"13\n13\n19\n19\n13\n13\n19\n19\n19\n",
"13\n19\n19\n13\n13\n13\n",
"13\n19\n13\n19\n13\n19\n19\n19\n",
"13\n19\n19\n19\n13\n19\n",
"13\n13\n13\n19\n13\n13\n19\n19\n",
"13\n13\n13\n19\n19\n19\n19\n19\n9439\n",
"13\n13\n19\n13\n19\n19\n19\n19\n",
"13\n19\n19\n13\n19\n19\n19\n13\n",
"13\n13\n13\n",
"13\n19\n19\n13\n19\n19\n",
"13\n19\n19\n19\n19\n19\n19\n13\n",
"13\n13\n13\n13\n13\n",
"13\n19\n13\n19\n",
"13\n19\n13\n19\n13\n13\n19\n19\n",
"13\n19\n19\n19\n19\n19\n19\n19\n",
"13\n13\n19\n13\n19\n13\n",
"13\n19\n19\n13\n19\n109\n",
"13\n19\n19\n19\n19\n19\n19\n19\n19\n",
"13\n19\n13\n19\n13\n13\n",
"13\n19\n19\n19\n19\n13\n19\n19\n19\n",
"13\n19\n13\n19\n19\n13\n19\n19\n19\n",
"13\n19\n19\n19\n19\n109\n",
"13\n19\n19\n19\n19\n19\n",
"13\n19\n13\n",
"13\n19\n13\n19\n19\n19\n",
"13\n19\n19\n13\n13\n13\n19\n19\n",
"13\n13\n13\n19\n13\n19\n19\n19\n9439\n",
"13\n13\n13\n19\n13\n13\n",
"13\n13\n19\n19\n13\n13\n13\n19\n",
"13\n19\n13\n13\n19\n19\n19\n19\n9439\n",
"13\n13\n19\n19\n19\n19\n",
"13\n19\n19\n19\n13\n13\n",
"13\n13\n19\n19\n19\n19\n19\n19\n",
"13\n13\n109\n13\n13\n19\n",
"13\n13\n19\n19\n13\n13\n19\n19\n829\n",
"13\n19\n13\n19\n19\n19\n19\n19\n",
"13\n19\n19\n",
"13\n13\n19\n",
"13\n19\n13\n19\n19\n19\n19\n19\n19\n",
"13\n13\n19\n13\n13\n13\n19\n19\n9439\n",
"13\n19\n19\n13\n13\n13\n19\n19\n9439\n",
"13\n13\n",
"13\n19\n13\n19\n13\n19\n19\n19\n9439\n",
"13\n19\n19\n13\n19\n19\n19\n19\n9439\n",
"13\n19\n19\n19\n13\n13\n19\n19\n19\n",
"13\n19\n19\n19\n",
"13\n13\n19\n19\n13\n13\n",
"13\n13\n13\n19\n19\n13\n19\n19\n",
"13\n13\n109\n13\n19\n19\n",
"13\n19\n19\n13\n19\n19\n19\n19\n",
"13\n19\n13\n19\n13\n13\n19\n19\n19\n",
"13\n19\n19\n13\n109\n19\n",
"13\n19\n",
"13\n19\n13\n13\n19\n19\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n",
"13\n13\n13\n13\n13\n13\n",
"13\n13\n13\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n",
"13\n13\n19\n13\n13\n19\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A set of four prime numbers arranged like (a, a + 2, a + 6, a + 8) is called a quadruplet prime number. Of the four prime numbers that make up a quadruplet prime, the largest number is called the size of the quadruplet prime. For example, the smallest prime quadruplet is a set of (5, 7, 11, 13), which is 13 in size. The next largest prime quadruplet is the set of (11, 13, 17, 19), which is 19 in size.
Create a program that takes the integer n (13 ≤ n ≤ 10,000,000) as input and outputs the maximum size of the quadruplet prime numbers whose size is n or less.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n is given on one row for each dataset.
The number of datasets does not exceed 2000.
Output
Outputs the maximum prime quadruplet size on one line for each input dataset.
Example
Input
13
14
15
16
17
18
19
20
10000
0
Output
13
13
13
13
13
13
19
19
9439
### Input:
13
14
15
16
17
18
19
20
10000
0
### Output:
13
13
13
13
13
13
19
19
9439
### Input:
13
14
15
16
17
18
0
20
10000
0
### Output:
13
13
13
13
13
13
### Code:
# AOJ 0222 Prime Quadruplet
# Python3 2018.6.23 bal4u
# From Wekipedia (https://en.wikipedia.org/wiki/Prime_quadruplet)
# All prime quadruplets except {5, 7, 11, 13} are of the form
# {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n.
MAX = 899
diff = (0,3,3,21,22,13,7,39,7,73, \
126,119,88,3,11,66,29,17,53,42, \
101,214,104,298,252,133,255,141,76,91, \
168,81,45,56,203,301,43,66,291,223, \
92,97,442,290,437,281,38,144,549,241, \
29,192,11,518,266,490,122,130,13,329, \
85,209,71,241,290,18,301,52,120,34, \
50,805,276,217,182,53,209,155,77,468, \
448,29,90,85,91,7,146,21,309,234, \
60,213,511,59,273,364,57,77,87,231, \
452,168,154,346,273,588,11,91,322,335, \
140,221,87,442,297,95,321,498,146,182, \
8,38,11,679,111,120,83,36,59,462, \
32,349,448,333,644,63,101,960,161,759, \
255,354,270,52,200,133,112,297,298,27, \
74,577,25,182,280,584,756,266,287,277, \
119,31,561,59,179,630,34,98,1,84, \
217,234,4,48,127,528,679,35,108,15, \
752,60,31,228,559,7,35,56,43,10, \
151,374,297,294,14,60,196,133,18,63, \
63,17,35,290,953,584,66,102,427,4, \
357,507,441,420,802,14,66,171,252,88, \
14,364,32,220,66,256,427,651,52,287, \
987,214,161,319,241,1333,190,325,63,500, \
1026,60,13,112,238,144,137,349,417,32, \
164,196,115,735,200,382,273,104,119,214, \
665,235,297,665,25,34,211,280,542,375, \
188,42,134,573,350,106,17,112,676,1095, \
403,62,193,60,13,116,60,255,609,350, \
7,165,661,25,748,176,10,283,144,987, \
389,59,60,342,112,144,31,98,676,297, \
652,189,56,34,441,50,314,266,29,546, \
297,39,657,46,703,70,270,221,122,767, \
13,134,318,1222,84,650,371,92,164,760, \
318,175,158,679,496,389,273,38,676,270, \
902,228,143,196,18,287,102,409,612,1, \
56,269,311,714,1092,176,34,165,143,438, \
266,249,97,442,105,7,913,81,80,871, \
497,585,574,11,220,94,855,132,473,836, \
301,7,833,63,1145,60,1886,382,111,43, \
111,319,431,108,297,60,878,799,133,472, \
529,420,241,46,231,304,616,1145,595,447, \
589,76,399,865,154,101,119,739,528,673, \
49,994,412,1072,6,25,3,49,126,1079, \
1141,66,220,932,1049,561,692,764,476,248, \
200,1897,658,644,24,399,143,1331,839,1, \
1077,760,11,34,658,36,647,21,528,242, \
98,529,24,1117,192,396,930,224,365,66, \
557,377,757,322,203,335,770,155,97,21, \
665,484,553,321,207,116,574,272,287,253, \
637,259,38,263,62,1268,451,693,756,630, \
357,105,32,581,455,153,540,350,91,210, \
409,270,377,442,490,615,424,52,890,199, \
102,1746,462,749,24,644,540,220,840,1656, \
223,74,434,179,665,923,428,307,875,50, \
2387,276,109,363,529,550,139,798,176,150, \
297,123,66,266,414,17,130,1344,300,1799, \
8,1176,279,351,461,396,112,626,498,931, \
2782,123,1253,780,781,1119,46,39,847,468, \
1037,1144,63,332,294,1082,525,459,220,70, \
231,31,1029,256,290,662,242,98,252,13, \
1008,64,346,1211,119,802,189,272,298,122, \
697,319,195,273,410,1221,365,885,322,52, \
847,165,112,67,812,630,801,87,60,424, \
630,867,231,123,308,396,76,119,60,203, \
17,63,553,931,147,588,127,437,164,43, \
14,371,115,150,354,315,473,3,1221,245, \
36,272,214,24,385,249,182,445,171,35, \
921,300,1558,1250,129,539,476,94,11,227, \
427,151,102,126,2176,71,297,60,413,195, \
190,944,49,554,1102,676,279,78,143,364, \
357,462,1144,1050,218,423,623,364,416,239, \
143,280,248,365,77,77,1529,157,361,514, \
536,31,330,87,193,514,935,227,18,91, \
104,49,133,1149,104,518,396,1015,143,445, \
360,385,680,49,1053,669,647,931,140,231, \
31,1075,483,627,101,1012,714,346,504,60, \
917,1140,1180,98,297,1029,225,1918,406,188, \
368,466,1305,1117,1028,50,150,273,333,101, \
151,146,1100,119,1532,497,487,235,658,322, \
538,210,701,574,136,220,168,105,603,332, \
409,84,81,39,860,309,384,259,266,207, \
872,377,403,248,819,882,931,148,42,371, \
805,325,668,529,409,3151,2016,14,38,1487, \
350,295,266,343,1833,1887,123,370,260,696, \
137,962,410,132,847,1051,426,39,214,546, \
539,493,325,137,112,889,130,237,43,1183, \
118,371,1,580,316,434,2698,53,98,262, \
203,119,31,189,813,119,195,294,1435,1345, \
531,624,210,231,321,553,11,756,1358)
def bsch(x):
l, r = 0, MAX
while l < r:
m = (l + r) >> 1
if tbl[m] == x: return m
if tbl[m] < x: l = m+1
else: r = m
return l-1;
tbl = [0]*MAX
for i in range(1, MAX): tbl[i] = tbl[i-1] + diff[i]
for i in range(MAX): tbl[i] = tbl[i]*30+19
while 1:
n = int(input())
if n == 0: break
if n < 19: print("13")
else: print(tbl[bsch(n)])
|
p00600 Computation of Minimum Length of Pipeline_2965 | The Aizu Wakamatsu city office decided to lay a hot water pipeline covering the whole area of the city to heat houses. The pipeline starts from some hot springs and connects every district in the city. The pipeline can fork at a hot spring or a district, but no cycle is allowed. The city office wants to minimize the length of pipeline in order to build it at the least possible expense.
Write a program to compute the minimal length of the pipeline. The program reads an input that consists of the following three parts:
Hint
The first line correspondings to the first part: there are three hot springs and five districts. The following three lines are the second part: the distances between a hot spring and a district. For instance, the distance between the first hot spring and the third district is 25. The last four lines are the third part: the distances between two districts. For instance, the distance between the second and the third districts is 9. The second hot spring and the fourth district are not connectable The second and the fifth districts are not connectable, either.
Input
* The first part consists of two positive integers in one line, which represent the number s of hot springs and the number d of districts in the city, respectively.
* The second part consists of s lines: each line contains d non-negative integers. The i-th integer in the j-th line represents the distance between the j-th hot spring and the i-th district if it is non-zero. If zero it means they are not connectable due to an obstacle between them.
* The third part consists of d-1 lines. The i-th line has d - i non-negative integers. The i-th integer in the j-th line represents the distance between the j-th and the (i + j)-th districts if it is non-zero. The meaning of zero is the same as mentioned above.
For the sake of simplicity, you can assume the following:
* The number of hot springs and that of districts do not exceed 50.
* Each distance is no more than 100.
* Each line in the input file contains at most 256 characters.
* Each number is delimited by either whitespace or tab.
The input has several test cases. The input terminate with a line which has two 0. The number of test cases is less than 20.
Output
Output the minimum length of pipeline for each test case.
Example
Input
3 5
12 8 25 19 23
9 13 16 0 17
20 14 16 10 22
17 27 18 16
9 7 0
19 5
21
0 0
Output
38 | while(1):
s,d=[int(x) for x in input().split()]
A=[999 for x in range(d)]
if s==0: break
for j in range(s):
l=[int(x) for x in input().split()]
for i in range(d):
if l[i]!=0:
A[i]=min(A[i], l[i])
B=[[999 for x in range(d)] for y in range(d)]
for j in range(d-1):
l=[int(x) for x in input().split()]
for i in range(d-1-j):
if l[i]!=0:
B[j][i+j+1]=l[i]
B[i+j+1][j]=l[i]
notevaled=[1 for x in range(d)]
ans=0
for i in range(d):
mini=A.index(min(A))
ans+=A[mini]
notevaled[mini]=0
A[mini]=999
for x in range(d):
if notevaled[x]:
A[x]=min( A[x], B[mini][x] )
print(ans)
| {
"input": [
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 44\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 15 70 19 44\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n19 5\n21\n0 0",
"3 5\n12 15 70 19 44\n16 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n5 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 13 16 0 8\n20 8 16 10 22\n17 21 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n20 8 16 10 22\n17 21 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 8\n30 8 16 10 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n30 8 16 10 22\n17 21 18 16\n7 6 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n6 8 44 19 44\n9 13 16 0 17\n20 1 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n20 8 16 10 22\n17 21 19 16\n9 12 0\n19 8\n21\n0 0",
"3 5\n12 8 2 19 44\n5 12 16 0 8\n30 8 16 10 22\n17 21 18 16\n7 6 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 2\n30 8 16 13 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 19 6 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 1 2\n30 8 16 13 22\n17 21 18 10\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 1 19 44\n6 12 16 1 2\n30 8 16 13 22\n17 21 18 10\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 25 56 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n2 4 0\n2 5\n21\n0 0",
"3 5\n22 4 30 19 71\n5 12 11 0 8\n5 8 1 11 19\n17 21 19 16\n9 12 0\n19 3\n6\n0 0",
"3 5\n12 8 30 19 44\n6 5 16 0 3\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 25 19 23\n4 13 16 0 17\n20 14 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n1 8 30 19 44\n6 12 16 0 8\n30 2 16 4 22\n17 21 18 16\n7 12 0\n17 2\n27\n0 0",
"3 5\n12 8 25 56 0\n5 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n2 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 2 6 22\n17 37 18 16\n7 12 0\n40 2\n21\n0 0",
"3 5\n12 13 27 19 23\n0 13 16 0 17\n20 9 16 10 22\n17 26 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 56 0\n5 13 16 0 17\n20 2 16 10 22\n17 27 18 16\n1 7 0\n2 5\n21\n0 0",
"3 5\n12 8 44 19 44\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 70 19 44\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n9 13 16 0 17\n20 8 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n9 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 15 70 19 44\n30 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n20 8 16 10 22\n17 21 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n30 8 16 10 22\n17 21 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 8\n30 8 16 10 22\n17 21 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n22\n0 0",
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 14 16 10 22\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 23\n15 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 33 23\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n19 5\n21\n0 0",
"3 5\n6 8 44 19 44\n9 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 49 19 44\n5 13 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 13 16 0 8\n20 8 16 10 22\n17 32 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n20 8 16 10 22\n17 21 19 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n19 8 16 10 22\n17 21 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 2\n30 8 16 10 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 9 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n17 2\n22\n0 0",
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 14 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 17\n20 14 9 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 23\n15 13 16 0 17\n20 9 16 10 22\n17 26 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 33 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n19 5\n21\n0 0",
"3 5\n12 8 49 19 44\n5 2 16 0 17\n20 8 16 10 22\n17 21 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 12\n5 13 16 0 8\n20 8 16 10 22\n17 32 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 48\n5 12 16 0 8\n19 8 16 10 22\n17 21 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 19 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 15 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n17 2\n27\n0 0",
"3 5\n12 8 25 19 23\n9 13 16 0 17\n20 7 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 29\n20 14 9 10 22\n17 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 19 23\n0 13 16 0 17\n20 9 16 10 22\n17 26 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 33 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n2 5\n21\n0 0",
"3 5\n6 8 26 19 44\n9 13 16 0 17\n20 1 16 10 22\n17 21 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 12\n5 13 16 0 8\n20 8 16 18 22\n17 32 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n5 12 16 0 8\n20 8 16 10 19\n17 21 19 16\n9 12 0\n19 8\n21\n0 0",
"3 5\n12 8 30 19 48\n5 12 16 0 8\n19 8 16 10 22\n17 32 18 16\n7 12 0\n19 5\n21\n0 0",
"3 5\n12 8 2 19 44\n5 12 16 0 8\n30 8 0 10 22\n17 21 18 16\n7 6 0\n19 5\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 2\n30 8 16 13 22\n17 21 18 10\n7 12 0\n19 2\n21\n0 0",
"3 5\n0 8 30 19 44\n6 23 15 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n1 8 30 19 44\n6 12 16 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n17 2\n27\n0 0",
"3 5\n12 8 25 19 33\n9 13 16 0 17\n20 7 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 29\n20 14 9 10 22\n21 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 56 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 7 0\n2 5\n21\n0 0",
"3 5\n12 8 30 19 12\n5 13 16 0 8\n20 8 16 18 22\n17 46 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n12 11 30 19 44\n5 12 16 0 8\n20 8 16 10 19\n17 21 19 16\n9 12 0\n19 8\n21\n0 0",
"3 5\n12 8 30 19 48\n5 12 16 0 8\n19 8 16 10 22\n17 32 18 16\n7 12 0\n19 9\n21\n0 0",
"3 5\n12 8 2 19 44\n5 12 16 0 8\n30 8 0 10 22\n17 21 18 16\n7 6 0\n19 7\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 19 6 22\n17 21 18 16\n7 12 0\n21 2\n21\n0 0",
"3 5\n0 8 30 19 58\n6 23 15 0 8\n30 8 16 4 22\n17 21 18 16\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 25 23 33\n9 13 16 0 17\n20 7 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 15\n20 14 9 10 22\n21 27 18 16\n9 7 0\n19 5\n21\n0 0",
"3 5\n12 8 25 56 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 4 0\n2 5\n21\n0 0",
"3 5\n12 8 30 19 12\n4 13 16 0 8\n20 8 16 18 22\n17 46 18 16\n9 12 0\n19 5\n21\n0 0",
"3 5\n23 11 30 19 44\n5 12 16 0 8\n20 8 16 10 19\n17 21 19 16\n9 12 0\n19 8\n21\n0 0",
"3 5\n12 8 30 19 48\n5 12 16 0 8\n19 0 16 10 22\n17 32 18 16\n7 12 0\n19 9\n21\n0 0",
"3 5\n12 8 2 19 44\n5 12 16 0 8\n30 8 0 10 22\n17 21 18 16\n7 6 0\n19 11\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 19 6 22\n17 37 18 16\n7 12 0\n21 2\n21\n0 0",
"3 5\n0 8 30 19 58\n6 23 15 0 8\n30 8 16 4 22\n17 21 18 32\n7 12 0\n19 2\n21\n0 0",
"3 5\n7 8 25 23 33\n9 13 16 0 17\n20 7 16 10 11\n17 27 18 16\n8 7 0\n19 5\n21\n0 0",
"3 5\n12 8 44 19 44\n17 13 16 0 15\n20 14 9 10 22\n21 27 18 16\n9 1 0\n19 5\n21\n0 0",
"3 5\n0 8 25 56 0\n9 13 16 0 17\n20 9 16 10 22\n17 27 18 16\n1 4 0\n2 5\n21\n0 0",
"3 5\n12 8 30 19 12\n4 13 16 0 8\n20 8 16 18 22\n17 46 18 16\n9 12 0\n19 5\n13\n0 0",
"3 5\n23 11 30 19 44\n5 12 16 0 8\n5 8 16 10 19\n17 21 19 16\n9 12 0\n19 8\n21\n0 0",
"3 5\n12 8 30 19 48\n5 12 16 0 8\n19 0 16 10 22\n17 32 18 21\n7 12 0\n19 9\n21\n0 0",
"3 5\n12 8 1 38 44\n6 12 16 1 2\n30 8 16 13 22\n17 21 18 10\n7 12 0\n19 2\n21\n0 0",
"3 5\n12 8 30 19 44\n6 12 16 0 3\n30 8 19 6 22\n17 37 18 16\n7 12 0\n40 2\n21\n0 0"
],
"output": [
"38",
"38\n",
"40\n",
"30\n",
"43\n",
"34\n",
"37\n",
"36\n",
"35\n",
"33\n",
"27\n",
"41\n",
"31\n",
"22\n",
"28\n",
"39\n",
"25\n",
"29\n",
"24\n",
"18\n",
"17\n",
"26\n",
"19\n",
"20\n",
"32\n",
"16\n",
"21\n",
"23\n",
"42\n",
"15\n",
"38\n",
"38\n",
"38\n",
"38\n",
"38\n",
"43\n",
"34\n",
"36\n",
"35\n",
"36\n",
"27\n",
"27\n",
"37\n",
"41\n",
"30\n",
"35\n",
"37\n",
"36\n",
"36\n",
"35\n",
"27\n",
"27\n",
"27\n",
"37\n",
"41\n",
"41\n",
"30\n",
"31\n",
"36\n",
"35\n",
"22\n",
"27\n",
"27\n",
"36\n",
"41\n",
"41\n",
"25\n",
"28\n",
"38\n",
"39\n",
"35\n",
"25\n",
"29\n",
"27\n",
"22\n",
"36\n",
"41\n",
"25\n",
"38\n",
"39\n",
"38\n",
"27\n",
"24\n",
"27\n",
"36\n",
"41\n",
"25\n",
"37\n",
"39\n",
"38\n",
"28\n",
"24\n",
"27\n",
"34\n",
"35\n",
"25\n",
"37\n",
"39\n",
"38\n",
"17\n",
"24\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The Aizu Wakamatsu city office decided to lay a hot water pipeline covering the whole area of the city to heat houses. The pipeline starts from some hot springs and connects every district in the city. The pipeline can fork at a hot spring or a district, but no cycle is allowed. The city office wants to minimize the length of pipeline in order to build it at the least possible expense.
Write a program to compute the minimal length of the pipeline. The program reads an input that consists of the following three parts:
Hint
The first line correspondings to the first part: there are three hot springs and five districts. The following three lines are the second part: the distances between a hot spring and a district. For instance, the distance between the first hot spring and the third district is 25. The last four lines are the third part: the distances between two districts. For instance, the distance between the second and the third districts is 9. The second hot spring and the fourth district are not connectable The second and the fifth districts are not connectable, either.
Input
* The first part consists of two positive integers in one line, which represent the number s of hot springs and the number d of districts in the city, respectively.
* The second part consists of s lines: each line contains d non-negative integers. The i-th integer in the j-th line represents the distance between the j-th hot spring and the i-th district if it is non-zero. If zero it means they are not connectable due to an obstacle between them.
* The third part consists of d-1 lines. The i-th line has d - i non-negative integers. The i-th integer in the j-th line represents the distance between the j-th and the (i + j)-th districts if it is non-zero. The meaning of zero is the same as mentioned above.
For the sake of simplicity, you can assume the following:
* The number of hot springs and that of districts do not exceed 50.
* Each distance is no more than 100.
* Each line in the input file contains at most 256 characters.
* Each number is delimited by either whitespace or tab.
The input has several test cases. The input terminate with a line which has two 0. The number of test cases is less than 20.
Output
Output the minimum length of pipeline for each test case.
Example
Input
3 5
12 8 25 19 23
9 13 16 0 17
20 14 16 10 22
17 27 18 16
9 7 0
19 5
21
0 0
Output
38
### Input:
3 5
12 8 25 19 23
9 13 16 0 17
20 14 16 10 22
17 27 18 16
9 7 0
19 5
21
0 0
### Output:
38
### Input:
3 5
12 8 25 19 44
9 13 16 0 17
20 14 16 10 22
17 27 18 16
9 7 0
19 5
21
0 0
### Output:
38
### Code:
while(1):
s,d=[int(x) for x in input().split()]
A=[999 for x in range(d)]
if s==0: break
for j in range(s):
l=[int(x) for x in input().split()]
for i in range(d):
if l[i]!=0:
A[i]=min(A[i], l[i])
B=[[999 for x in range(d)] for y in range(d)]
for j in range(d-1):
l=[int(x) for x in input().split()]
for i in range(d-1-j):
if l[i]!=0:
B[j][i+j+1]=l[i]
B[i+j+1][j]=l[i]
notevaled=[1 for x in range(d)]
ans=0
for i in range(d):
mini=A.index(min(A))
ans+=A[mini]
notevaled[mini]=0
A[mini]=999
for x in range(d):
if notevaled[x]:
A[x]=min( A[x], B[mini][x] )
print(ans)
|
p00736 How can I satisfy thee? Let me count the ways..._2969 | Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | class N:
def __init__(self, a):
self.a = a
def __mul__(self, b):
if self.a == 0:
return N(0)
elif self.a == 1:
return N((b.a >= 1) * 1)
else:
return b
def __add__(self, b):
if self.a == 0:
return b
elif self.a == 1:
return N((b.a > 1) + 1)
else:
return N(2)
def __neg__(self):
if self.a == 2:
return N(0)
elif self.a == 1:
return N(1)
else:
return N(2)
while True:
s = input().replace("-", "-").replace("0", "N(0)").replace("1", "N(1)").replace("2", "N(2)")
N(1) + N(2)
if s == ".": break
result = []
for P in map(N, range(3)):
for Q in map(N, range(3)):
for R in map(N, range(3)):
result.append(eval(s).a)
print(result.count(2)) | {
"input": [
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*Q)\n(--R+(P*R))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n1\n2\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-Q)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*P)\n(--R+(P*R))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R+(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P+-P)\n-2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(Q*-P)\n1\n2\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+Q))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--Q+(P*R))\n(Q*-P)\n1\n1\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--P+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---Q))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(Q*-P)\n-1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(P*R))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(Q*-P)\n-1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n0\n-1\n(-1+(((---P+Q)*(--Q+---R))*(-R*-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n2\n1\n(-1+(((---P+R)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n-2\n2\n(-1*(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-Q)\n1\n0\n(-1+(((---P+Q)*(--P+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(P*R))\n(P*-Q)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(Q*-P)\n-1\n2\n(-1+(((---Q+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(Q*P)\n(--R+(P*R))\n(P*-Q)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*Q)\n(--R+(P*R))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*P)\n(--R+(P*R))\n(P*-P)\n0\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n0\n0\n(-1+(((---P+Q)*(--R+---Q))*(-R+-P)))\n.",
"(Q*Q)\n(--R+(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(Q*-P)\n0\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R*(P*R))\n(P*-P)\n0\n-1\n(-1+(((---P+Q)*(--Q+---R))*(-R*-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P+-P)\n0\n2\n(-1+(((---P+Q)*(--Q+---Q))*(-R+-P)))\n.",
"(P+Q)\n(--Q+(P*R))\n(Q*-P)\n1\n0\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n1\n-2\n(-1+(((---P+P)*(--Q+---R))*(-R+-P)))\n.",
"(Q*Q)\n(--R+(P*R))\n(P*-P)\n0\n0\n(-1+(((---P+Q)*(--P+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R*(P*R))\n(P*-P)\n0\n-1\n(-1+(((---P+Q)*(--Q+---Q))*(-R*-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P+-P)\n0\n2\n(-1+(((---P+Q)*(--Q+---P))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(Q*-P)\n1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+Q))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+R))\n(P*-P)\n-2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P+-P)\n1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+R))\n(Q*-P)\n-2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--Q+(P*Q))\n(P*-P)\n2\n2\n(-1+(((---P+R)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--Q+(P*R))\n(P*-P)\n-2\n0\n(-1+(((---P+R)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(Q*-P)\n1\n2\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(P*Q))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(Q*-P)\n0\n-1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*Q)\n-(-R+(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R+(P*R))\n(P*-P)\n1\n-1\n(-0+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-Q)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(Q*Q)\n(--R+(P*R))\n(P+-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(Q*-P)\n1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R+(P*R))\n(P+-P)\n1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R*(P*R))\n(Q*-P)\n1\n-1\n(-1+(((---P+Q)*(--Q+---Q))*(-R*-P)))\n.",
"(P+Q)\n(--R*(P*R))\n(P*-P)\n0\n2\n(-2+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(Q*R))\n(P+-Q)\n2\n-1\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(Q*-P)\n2\n2\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(P*R))\n(P*-Q)\n2\n2\n(-1+(((---P+Q)*(--Q+---R))+(-R+-P)))\n.",
"(P+Q)\n(--R+(P*R))\n(P*-P)\n-1\n-1\n(-1*(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(Q*-P)\n2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R+(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--P+---R))*(-R+-P)))\n.",
"(P+R)\n(--R+(P*R))\n(P*-P)\n1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+P)\n(--R+(P*R))\n(P*-P)\n-1\n-1\n(-1*(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P+-P)\n0\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+Q))\n(P*-P)\n2\n1\n(-1+(((---P+R)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P+R))\n(P*-Q)\n1\n0\n(-1+(((---P+Q)*(--P+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R+(Q*R))\n(Q*-P)\n-1\n2\n(-1+(((---Q+Q)*(--Q+---R))*(-Q+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n2\n-1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n-2\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R+(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n1\n-1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n-1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(Q*P)\n(--R+(P*R))\n(P*-P)\n1\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n-2\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*R))\n(P*-P)\n0\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*P)\n(--R+(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R+(P*Q))\n(P*-P)\n0\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(R*P)\n(--R+(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P+Q)\n(--R+(P*R))\n(P*-P)\n-1\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n-1\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n0\n0\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--Q+(P*R))\n(Q*-P)\n1\n2\n(-1+(((---P+Q)*(--R+---R))*(-R+-P)))\n.",
"(R*P)\n(--R+(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*R)\n(--R*(P*R))\n(P*-P)\n-2\n2\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n.",
"(P*Q)\n(--R*(P*R))\n(P*-P)\n0\n1\n(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))\n."
],
"output": [
"3\n11\n0\n27\n0\n7",
"3\n9\n0\n27\n0\n7\n",
"3\n11\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n11\n0\n0\n27\n7\n",
"9\n9\n0\n27\n0\n7\n",
"3\n11\n0\n0\n27\n8\n",
"3\n9\n0\n27\n0\n5\n",
"3\n9\n0\n0\n27\n7\n",
"9\n9\n0\n0\n0\n7\n",
"15\n9\n0\n0\n0\n7\n",
"3\n3\n0\n0\n0\n7\n",
"3\n3\n0\n0\n27\n7\n",
"3\n3\n18\n0\n0\n7\n",
"3\n11\n0\n27\n0\n7\n",
"3\n11\n3\n0\n27\n8\n",
"3\n19\n0\n27\n0\n7\n",
"3\n11\n3\n0\n0\n8\n",
"3\n9\n0\n0\n0\n5\n",
"3\n11\n0\n27\n27\n7\n",
"3\n9\n0\n0\n27\n5\n",
"3\n3\n0\n0\n27\n8\n",
"3\n9\n3\n0\n0\n7\n",
"3\n9\n0\n0\n0\n19\n",
"3\n9\n3\n0\n27\n5\n",
"3\n3\n0\n0\n0\n3\n",
"3\n11\n0\n27\n0\n5\n",
"3\n3\n0\n0\n27\n0\n",
"3\n9\n3\n0\n0\n5\n",
"3\n9\n3\n0\n0\n19\n",
"3\n9\n3\n0\n27\n6\n",
"3\n9\n3\n27\n0\n19\n",
"3\n9\n0\n27\n27\n7\n",
"9\n9\n0\n27\n0\n19\n",
"9\n9\n0\n0\n27\n7\n",
"3\n3\n0\n0\n0\n5\n",
"9\n9\n0\n0\n27\n5\n",
"3\n3\n3\n0\n27\n7\n",
"15\n3\n0\n0\n0\n3\n",
"3\n3\n18\n0\n27\n8\n",
"15\n11\n3\n0\n0\n8\n",
"3\n3\n0\n0\n0\n8\n",
"9\n9\n0\n0\n0\n5\n",
"15\n3\n0\n0\n0\n2\n",
"3\n3\n18\n0\n27\n11\n",
"3\n11\n3\n0\n0\n7\n",
"3\n19\n0\n0\n0\n7\n",
"3\n15\n0\n0\n0\n7\n",
"3\n9\n18\n0\n27\n7\n",
"3\n15\n3\n0\n0\n7\n",
"3\n9\n0\n27\n27\n5\n",
"3\n11\n0\n0\n0\n5\n",
"3\n9\n3\n0\n27\n8\n",
"3\n11\n0\n0\n0\n19\n",
"3\n3\n3\n0\n0\n7\n",
"9\n3\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n27\n",
"3\n9\n3\n27\n0\n7\n",
"3\n9\n0\n27\n0\n19\n",
"9\n9\n18\n0\n27\n5\n",
"3\n11\n3\n0\n27\n7\n",
"15\n9\n18\n0\n27\n7\n",
"15\n3\n3\n0\n0\n2\n",
"15\n3\n0\n0\n27\n7\n",
"3\n9\n15\n27\n0\n19\n",
"3\n9\n3\n27\n27\n8\n",
"3\n3\n0\n27\n0\n7\n",
"3\n9\n3\n27\n27\n19\n",
"15\n9\n0\n0\n0\n0\n",
"3\n11\n3\n27\n27\n7\n",
"15\n9\n0\n0\n0\n5\n",
"15\n9\n0\n0\n27\n7\n",
"9\n9\n0\n0\n0\n0\n",
"3\n9\n18\n0\n0\n7\n",
"3\n19\n0\n27\n0\n5\n",
"3\n15\n3\n0\n0\n5\n",
"15\n9\n3\n0\n27\n6\n",
"3\n9\n0\n27\n0\n7\n",
"3\n9\n0\n27\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n11\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"3\n3\n0\n0\n0\n7\n",
"3\n3\n0\n0\n0\n7\n",
"3\n9\n0\n0\n0\n7\n",
"9\n9\n0\n0\n0\n7\n",
"3\n11\n0\n0\n27\n7\n",
"3\n9\n0\n0\n0\n7\n",
"15\n9\n0\n0\n0\n7\n",
"3\n3\n0\n0\n27\n7\n",
"3\n3\n0\n0\n0\n7\n",
"3\n11\n3\n0\n27\n8\n",
"3\n9\n0\n0\n0\n7\n",
"3\n3\n0\n0\n27\n7\n",
"3\n3\n0\n0\n0\n7\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7
### Input:
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
### Output:
3
11
0
27
0
7
### Input:
(P*Q)
(--R+(P*R))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
### Output:
3
9
0
27
0
7
### Code:
class N:
def __init__(self, a):
self.a = a
def __mul__(self, b):
if self.a == 0:
return N(0)
elif self.a == 1:
return N((b.a >= 1) * 1)
else:
return b
def __add__(self, b):
if self.a == 0:
return b
elif self.a == 1:
return N((b.a > 1) + 1)
else:
return N(2)
def __neg__(self):
if self.a == 2:
return N(0)
elif self.a == 1:
return N(1)
else:
return N(2)
while True:
s = input().replace("-", "-").replace("0", "N(0)").replace("1", "N(1)").replace("2", "N(2)")
N(1) + N(2)
if s == ".": break
result = []
for P in map(N, range(3)):
for Q in map(N, range(3)):
for R in map(N, range(3)):
result.append(eval(s).a)
print(result.count(2)) |
p00876 Swimming Jam_2972 | Despite urging requests of the townspeople, the municipal office cannot afford to improve many of the apparently deficient city amenities under this recession. The city swimming pool is one of the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under this circumstances, settled usage rules so that the limited facilities can be utilized fully.
Two lanes are to be used for one-way swimming of different directions. Swimmers are requested to start swimming in one of the lanes, from its one end to the other, and then change the lane to swim his/her way back. When he or she reaches the original starting end, he/she should return to his/her initial lane and starts swimming again.
Each swimmer has his/her own natural constant pace. Swimmers, however, are not permitted to pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that might cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the slower swimmer at the slower pace until the end of the lane is reached. Note that the blocking swimmer’s natural pace may be faster than the blocked swimmer; the blocking swimmer might also be blocked by another swimmer ahead, whose natural pace is slower than the blocked swimmer. Blocking would have taken place whether or not a faster swimmer was between them.
Swimmers can change their order if they reach the end of the lane simultaneously. They change their order so that ones with faster natural pace swim in front. When a group of two or more swimmers formed by a congestion reaches the end of the lane, they are considered to reach there simultaneously, and thus change their order there.
The number of swimmers, their natural paces in times to swim from one end to the other, and the numbers of laps they plan to swim are given. Note that here one "lap" means swimming from one end to the other and then swimming back to the original end. Your task is to calculate the time required for all the swimmers to finish their plans. All the swimmers start from the same end of the pool at the same time, the faster swimmers in front.
In solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time required to change the lanes and the order in a group of swimmers at an end of the lanes.
Input
The input is a sequence of datasets. Each dataset is formatted as follows.
n
t1 c1
...
tn cn
n is an integer (1 ≤ n ≤ 50) that represents the number of swimmers. ti and ci are integers (1 ≤ ti ≤ 300, 1 ≤ ci ≤ 250) that represent the natural pace in times to swim from one end to the other and the number of planned laps for the i-th swimmer, respectively. ti and ci are separated by a space.
The end of the input is indicated by a line containing one zero.
Output
For each dataset, output the time required for all the swimmers to finish their plans in a line. No extra characters should occur in the output.
Example
Input
2
10 30
15 20
2
10 240
15 160
3
2 6
7 2
8 2
4
2 4
7 2
8 2
18 1
0
Output
600
4800
36
40 | from collections import deque
while 1:
N = int(input())
if N == 0:
break
T = [0]*N; C = [0]*N
que0 = deque()
que1 = deque()
P = [list(map(int, input().split())) for i in range(N)]
P.sort()
for i in range(N):
t, c = P[i]
que0.append((i, t))
T[i] = t
C[i] = c
INF = 10**18
ans = 0
rest = N
while rest:
t = min(que0[0][1] if que0 else INF, que1[0][1] if que1 else INF)
st0 = []; st1 = []
while que0 and que0[0][1] <= t:
st0.append(que0.popleft()[0])
st0.sort()
for i in st0:
que1.append((i, t+T[i]))
while que1 and que1[0][1] <= t:
st1.append(que1.popleft()[0])
st1.sort()
for i in st1:
if C[i] == 1:
rest -= 1
else:
que0.append((i, t+T[i]))
C[i] -= 1
ans = max(ans, t)
print(ans)
| {
"input": [
"2\n10 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 296\n3\n2 6\n7 3\n4 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 4\n7 2\n8 2\n10 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n0\n2 6\n7 3\n8 2\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 33\n2\n10 240\n15 160\n3\n2 6\n7 3\n4 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n5 1\n0",
"2\n10 30\n15 20\n2\n10 240\n15 160\n3\n4 6\n7 4\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 6\n8 2\n4\n2 4\n7 2\n8 2\n10 1\n0",
"2\n10 44\n15 17\n2\n10 240\n15 160\n0\n2 6\n7 3\n8 2\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n1 30\n15 17\n2\n10 50\n15 160\n3\n2 6\n7 3\n8 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 33\n2\n10 240\n15 160\n3\n2 6\n7 3\n4 4\n4\n2 5\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n5 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 2\n4\n2 4\n13 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 6\n8 2\n4\n2 6\n7 2\n8 2\n10 1\n0",
"2\n3 44\n15 17\n2\n10 240\n15 160\n0\n2 6\n7 3\n8 2\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n1 30\n15 17\n2\n10 50\n15 160\n3\n2 6\n7 3\n8 4\n4\n2 3\n1 2\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 2\n4\n2 4\n13 2\n8 2\n28 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 10\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n3 6\n7 6\n8 2\n4\n2 6\n7 2\n8 2\n10 2\n0",
"2\n12 30\n15 33\n2\n10 240\n15 41\n3\n2 6\n1 3\n4 4\n4\n2 5\n1 2\n8 2\n18 1\n0",
"2\n12 30\n15 20\n2\n20 240\n15 160\n3\n2 10\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n5 30\n15 20\n0\n10 240\n20 160\n5\n2 6\n7 2\n8 1\n4\n2 4\n13 2\n8 2\n28 1\n0",
"2\n9 30\n15 9\n0\n10 240\n20 160\n5\n2 6\n0 1\n8 0\n4\n2 0\n1 1\n8 2\n28 1\n0",
"2\n12 30\n15 9\n0\n2 255\n23 160\n5\n2 6\n0 1\n8 0\n4\n4 0\n1 1\n8 2\n28 1\n0",
"2\n10 30\n15 20\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 4\n13 2\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 11\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 48\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 36\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n14 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n4 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 296\n3\n2 6\n7 3\n4 4\n4\n2 4\n1 2\n8 2\n6 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 6\n2 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n3\n2 6\n7 2\n8 2\n4\n3 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n4\n10 50\n15 160\n3\n2 6\n7 3\n8 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 33\n2\n10 240\n15 160\n3\n4 6\n7 3\n4 4\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n20 240\n15 160\n3\n2 6\n7 2\n3 2\n4\n2 4\n7 2\n8 2\n5 1\n0",
"2\n10 30\n15 20\n2\n10 240\n23 160\n3\n4 6\n7 4\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n5 30\n15 30\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n9 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n4\n2 4\n7 1\n8 2\n5 1\n0",
"2\n1 30\n15 17\n2\n10 50\n15 160\n3\n2 6\n7 3\n8 4\n4\n3 4\n1 2\n8 2\n18 1\n0",
"2\n5 30\n9 20\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 2\n4\n2 4\n13 2\n8 2\n18 1\n0",
"2\n12 30\n15 33\n2\n10 240\n15 160\n3\n2 6\n7 3\n4 4\n4\n2 5\n1 2\n8 2\n8 1\n0",
"2\n10 30\n15 20\n2\n20 180\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n5\n2 6\n7 1\n8 2\n4\n2 4\n13 2\n8 2\n28 1\n0",
"2\n10 30\n15 20\n2\n5 240\n15 160\n3\n2 10\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n5\n2 6\n7 2\n8 1\n4\n2 4\n13 2\n8 2\n12 1\n0",
"2\n12 30\n15 33\n2\n10 240\n15 41\n3\n2 6\n1 3\n4 4\n4\n2 5\n1 2\n8 2\n6 1\n0",
"2\n1 71\n15 17\n2\n10 240\n15 160\n0\n0 6\n7 3\n8 0\n2\n2 4\n1 3\n8 0\n18 1\n-1",
"2\n18 30\n15 20\n0\n10 240\n20 160\n5\n2 6\n7 1\n8 0\n4\n2 1\n1 1\n8 2\n28 1\n0",
"2\n1 12\n15 17\n2\n3 240\n14 160\n0\n0 3\n7 3\n8 1\n2\n2 4\n1 3\n8 0\n18 1\n-1",
"2\n6 30\n15 9\n0\n2 240\n20 160\n5\n2 6\n0 1\n8 0\n4\n4 0\n1 1\n8 2\n28 1\n0",
"2\n10 30\n15 28\n2\n10 240\n15 155\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 48\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n10 36\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 7\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n6 30\n15 20\n2\n10 240\n15 160\n3\n4 6\n7 4\n8 2\n4\n2 4\n7 3\n8 2\n18 1\n0",
"2\n5 30\n15 20\n2\n10 240\n20 160\n3\n4 6\n7 2\n8 2\n4\n3 4\n7 2\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n0\n2 4\n12 1\n8 2\n18 1\n0",
"2\n10 30\n15 17\n2\n10 240\n15 160\n5\n2 6\n7 6\n8 2\n4\n2 4\n7 2\n2 2\n10 1\n0",
"2\n10 30\n15 20\n2\n13 180\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n10 30\n15 20\n2\n5 240\n15 160\n3\n2 10\n4 2\n8 2\n4\n2 4\n7 2\n8 2\n8 1\n0",
"2\n5 30\n15 1\n0\n10 240\n20 160\n5\n2 1\n7 1\n8 0\n4\n2 1\n1 2\n8 2\n28 1\n0",
"2\n1 12\n15 17\n2\n10 240\n18 160\n0\n0 6\n7 3\n8 1\n2\n2 4\n1 3\n8 0\n18 1\n-1",
"2\n10 30\n15 28\n2\n10 240\n15 155\n3\n2 6\n7 2\n8 1\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n5 30\n15 32\n2\n10 25\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 1\n0",
"2\n10 4\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 1\n7 2\n8 2\n18 1\n0",
"2\n10 48\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n10 36\n15 17\n2\n10 240\n28 160\n3\n2 6\n7 3\n8 7\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 20\n2\n5 240\n15 160\n3\n2 10\n4 2\n8 2\n4\n2 4\n7 2\n2 2\n8 1\n0",
"2\n5 30\n24 20\n0\n11 240\n20 160\n5\n2 11\n7 2\n8 0\n4\n2 1\n13 2\n8 2\n28 1\n0",
"2\n1 61\n15 17\n2\n10 240\n15 160\n0\n0 6\n7 3\n13 0\n2\n2 4\n1 3\n8 4\n18 1\n0",
"2\n1 81\n15 17\n2\n10 240\n15 160\n0\n0 6\n7 3\n8 0\n4\n2 4\n1 3\n8 0\n7 1\n0",
"2\n9 30\n19 20\n0\n10 240\n20 160\n5\n2 6\n7 1\n8 0\n4\n4 2\n1 2\n8 2\n28 1\n0",
"2\n9 30\n24 9\n0\n2 56\n23 160\n5\n2 6\n0 1\n8 0\n4\n4 0\n0 1\n8 2\n28 1\n0",
"2\n5 30\n15 32\n2\n10 25\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n10 4\n15 17\n2\n10 240\n15 160\n3\n2 6\n7 4\n8 2\n4\n2 1\n7 2\n8 2\n28 1\n0",
"2\n14 30\n15 17\n2\n10 142\n15 160\n3\n4 6\n7 3\n4 1\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 30\n15 21\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n0\n2 4\n12 1\n8 3\n18 1\n0",
"2\n10 30\n15 20\n2\n10 240\n23 160\n3\n4 7\n7 4\n9 2\n4\n2 4\n7 4\n8 2\n18 2\n0",
"2\n10 52\n15 20\n2\n5 240\n15 160\n3\n2 10\n4 2\n8 2\n4\n2 4\n7 2\n2 2\n8 1\n0",
"2\n5 30\n15 6\n2\n5 240\n20 160\n5\n1 6\n7 2\n8 1\n4\n2 4\n13 2\n8 2\n12 1\n0",
"2\n5 30\n15 17\n0\n10 240\n20 160\n7\n2 6\n7 4\n8 1\n4\n0 1\n1 2\n8 2\n28 1\n-1",
"2\n9 30\n26 20\n0\n10 152\n20 160\n5\n2 6\n4 1\n8 0\n4\n2 0\n0 1\n8 2\n31 1\n0",
"2\n16 50\n15 9\n0\n0 255\n23 160\n5\n2 6\n0 1\n8 0\n4\n4 -1\n1 1\n8 2\n28 1\n0",
"2\n10 30\n15 32\n2\n10 64\n15 160\n0\n2 6\n7 4\n8 2\n4\n2 4\n13 2\n8 2\n18 0\n0",
"2\n5 30\n15 45\n2\n10 25\n15 160\n3\n2 5\n7 2\n8 2\n4\n2 4\n7 2\n8 2\n18 2\n0",
"2\n10 8\n15 17\n2\n10 240\n28 160\n3\n2 6\n7 5\n8 7\n4\n2 4\n1 2\n8 2\n18 1\n0",
"2\n10 45\n15 21\n2\n10 240\n15 160\n3\n2 6\n7 3\n8 2\n0\n2 4\n12 1\n8 3\n18 1\n0",
"2\n10 24\n15 17\n2\n10 240\n7 160\n3\n2 6\n7 6\n8 2\n4\n2 7\n3 2\n8 2\n10 1\n0",
"2\n5 30\n15 6\n2\n5 240\n20 160\n0\n1 6\n7 2\n8 1\n4\n2 4\n13 2\n8 2\n12 1\n0",
"2\n1 12\n15 17\n2\n10 240\n14 308\n0\n0 3\n7 3\n8 -1\n2\n0 4\n2 3\n12 0\n18 1\n-1",
"2\n9 11\n15 9\n0\n2 255\n23 207\n5\n0 6\n0 1\n8 -1\n5\n4 0\n1 1\n8 2\n28 1\n0",
"2\n16 36\n15 9\n0\n0 255\n23 160\n5\n2 6\n0 1\n8 0\n4\n4 -1\n1 1\n8 2\n28 1\n0",
"2\n10 30\n15 28\n2\n10 240\n15 155\n3\n2 6\n2 2\n8 1\n4\n2 4\n5 2\n8 2\n18 1\n0",
"2\n10 30\n15 28\n2\n10 64\n15 160\n0\n2 6\n7 4\n8 2\n4\n2 4\n13 2\n8 2\n18 0\n0"
],
"output": [
"600\n4800\n36\n40",
"600\n4800\n56\n40\n",
"600\n4800\n36\n40\n",
"600\n4800\n42\n40\n",
"600\n4800\n64\n40\n",
"600\n8880\n42\n40\n",
"600\n9600\n36\n40\n",
"600\n6400\n36\n40\n",
"600\n4800\n56\n32\n",
"600\n4800\n",
"990\n4800\n42\n40\n",
"600\n9600\n36\n32\n",
"600\n4800\n56\n72\n",
"600\n6400\n57\n36\n",
"600\n4800\n84\n32\n",
"880\n4800\n",
"510\n4800\n64\n40\n",
"990\n4800\n42\n44\n",
"600\n9600\n32\n32\n",
"600\n6400\n105\n36\n",
"600\n4800\n84\n40\n",
"510\n4800\n",
"510\n4800\n64\n36\n",
"600\n6400\n105\n56\n",
"600\n9600\n52\n32\n",
"600\n4800\n84\n44\n",
"990\n4800\n32\n44\n",
"720\n9600\n52\n32\n",
"600\n",
"540\n",
"720\n",
"600\n4800\n56\n52\n",
"600\n4800\n32\n40\n",
"510\n4800\n56\n40\n",
"960\n4800\n42\n40\n",
"720\n4800\n64\n40\n",
"840\n4800\n42\n40\n",
"600\n8880\n42\n32\n",
"600\n9600\n32\n40\n",
"600\n6400\n36\n42\n",
"600\n4800\n64\n36\n",
"990\n4800\n50\n40\n",
"600\n9600\n28\n32\n",
"600\n7360\n56\n72\n",
"900\n6400\n57\n36\n",
"600\n4800\n42\n32\n",
"510\n4800\n64\n42\n",
"360\n6400\n105\n36\n",
"990\n4800\n42\n32\n",
"600\n7200\n32\n32\n",
"600\n6400\n104\n56\n",
"600\n4800\n52\n32\n",
"600\n6400\n105\n32\n",
"990\n4800\n32\n32\n",
"550\n4800\n",
"1080\n",
"510\n4480\n",
"414\n",
"840\n4800\n36\n40\n",
"960\n4800\n42\n72\n",
"720\n4800\n112\n40\n",
"600\n4800\n56\n50\n",
"600\n6400\n49\n42\n",
"600\n4800\n42\n",
"600\n4800\n84\n20\n",
"600\n4800\n32\n32\n",
"600\n4800\n48\n32\n",
"300\n",
"510\n5760\n",
"840\n4800\n32\n40\n",
"960\n4800\n32\n40\n",
"510\n4800\n56\n36\n",
"960\n4800\n36\n72\n",
"720\n8960\n112\n40\n",
"600\n4800\n48\n28\n",
"960\n",
"530\n4800\n",
"570\n4800\n",
"760\n",
"648\n",
"960\n4800\n32\n72\n",
"510\n4800\n56\n56\n",
"840\n4800\n50\n40\n",
"630\n4800\n42\n",
"600\n7360\n61\n72\n",
"1040\n4800\n48\n28\n",
"300\n6400\n105\n32\n",
"510\n",
"1040\n",
"1600\n",
"960\n4800\n",
"1350\n4800\n32\n72\n",
"510\n8960\n112\n40\n",
"900\n4800\n42\n",
"510\n4800\n84\n40\n",
"300\n6400\n",
"510\n8624\n",
"270\n",
"1152\n",
"840\n4800\n28\n40\n",
"840\n4800\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Despite urging requests of the townspeople, the municipal office cannot afford to improve many of the apparently deficient city amenities under this recession. The city swimming pool is one of the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under this circumstances, settled usage rules so that the limited facilities can be utilized fully.
Two lanes are to be used for one-way swimming of different directions. Swimmers are requested to start swimming in one of the lanes, from its one end to the other, and then change the lane to swim his/her way back. When he or she reaches the original starting end, he/she should return to his/her initial lane and starts swimming again.
Each swimmer has his/her own natural constant pace. Swimmers, however, are not permitted to pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that might cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the slower swimmer at the slower pace until the end of the lane is reached. Note that the blocking swimmer’s natural pace may be faster than the blocked swimmer; the blocking swimmer might also be blocked by another swimmer ahead, whose natural pace is slower than the blocked swimmer. Blocking would have taken place whether or not a faster swimmer was between them.
Swimmers can change their order if they reach the end of the lane simultaneously. They change their order so that ones with faster natural pace swim in front. When a group of two or more swimmers formed by a congestion reaches the end of the lane, they are considered to reach there simultaneously, and thus change their order there.
The number of swimmers, their natural paces in times to swim from one end to the other, and the numbers of laps they plan to swim are given. Note that here one "lap" means swimming from one end to the other and then swimming back to the original end. Your task is to calculate the time required for all the swimmers to finish their plans. All the swimmers start from the same end of the pool at the same time, the faster swimmers in front.
In solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time required to change the lanes and the order in a group of swimmers at an end of the lanes.
Input
The input is a sequence of datasets. Each dataset is formatted as follows.
n
t1 c1
...
tn cn
n is an integer (1 ≤ n ≤ 50) that represents the number of swimmers. ti and ci are integers (1 ≤ ti ≤ 300, 1 ≤ ci ≤ 250) that represent the natural pace in times to swim from one end to the other and the number of planned laps for the i-th swimmer, respectively. ti and ci are separated by a space.
The end of the input is indicated by a line containing one zero.
Output
For each dataset, output the time required for all the swimmers to finish their plans in a line. No extra characters should occur in the output.
Example
Input
2
10 30
15 20
2
10 240
15 160
3
2 6
7 2
8 2
4
2 4
7 2
8 2
18 1
0
Output
600
4800
36
40
### Input:
2
10 30
15 20
2
10 240
15 160
3
2 6
7 2
8 2
4
2 4
7 2
8 2
18 1
0
### Output:
600
4800
36
40
### Input:
2
10 30
15 20
2
10 240
15 160
3
2 6
7 4
8 2
4
2 4
7 2
8 2
18 1
0
### Output:
600
4800
56
40
### Code:
from collections import deque
while 1:
N = int(input())
if N == 0:
break
T = [0]*N; C = [0]*N
que0 = deque()
que1 = deque()
P = [list(map(int, input().split())) for i in range(N)]
P.sort()
for i in range(N):
t, c = P[i]
que0.append((i, t))
T[i] = t
C[i] = c
INF = 10**18
ans = 0
rest = N
while rest:
t = min(que0[0][1] if que0 else INF, que1[0][1] if que1 else INF)
st0 = []; st1 = []
while que0 and que0[0][1] <= t:
st0.append(que0.popleft()[0])
st0.sort()
for i in st0:
que1.append((i, t+T[i]))
while que1 and que1[0][1] <= t:
st1.append(que1.popleft()[0])
st1.sort()
for i in st1:
if C[i] == 1:
rest -= 1
else:
que0.append((i, t+T[i]))
C[i] -= 1
ans = max(ans, t)
print(ans)
|
p01139 Surrounding Area_2978 | Surrounding Area
Land fence
English text is not available in this practice contest.
Two real estate agents were boarding a passenger ship to the southern island. Blue sky, refreshing breeze ... The two enjoyed a voyage with other passengers. However, one day a tornado suddenly sank a passenger ship. The other passengers were rescued by the rescue team, but somehow only these two were overlooked. After a few days of drifting, they landed on an uninhabited island. This uninhabited island was rectangular and was divided into grids as shown in the figure below.
Shape of uninhabited island
Figure C-1: Shape of uninhabited island
They were so greedy that they were thinking of selling the land on this uninhabited island rather than calling for help. And they did not split the land in half, but began to scramble for the land. They each began to enclose what they wanted to land on one with black stakes and the other with white stakes. All stakes were struck in the center of the grid, and no stakes were struck in one grid. After a while, both were exhausted and stopped hitting the stakes.
Your job is to write a program to find the area of land surrounded by black and white stakes. However, it is intuitive that the grid (i, j) is surrounded by black stakes. It means that. To be exact, it is defined as follows.
> Define a grid "extended adjacent" to the black stake as follows: The same applies to white stakes.
>
> * If there are no stakes in grid (i, j) and there are black stakes in any of the grids adjacent to grid (i, j), then grid (i, j) extends adjacent to the black stakes. doing.
>
> * If there are no stakes in grid (i, j) and any of the grids adjacent to grid (i, j) are extended adjacent to black stakes, then grid (i, j) is a black stake. It is adjacent to the stake. This rule is applied recursively.
>
>
>
> At this time, when the grid (i, j) is extended adjacent to the black stake and not adjacent to the white stake, and only then, the grid (i, j) is surrounded by the black stake. It is said that there is. Conversely, when the grid (i, j) is extended adjacent to the white stake and not adjacent to the black stake, and only then, the grid (i, j) is surrounded by the white stake. It is said that there is.
Input
The input consists of multiple datasets. Each data set has the following structure.
> w h
> a1,1 a2,1 a3,1 ... aw,1
> a1,2 a2,2 a3,2 ... aw, 2
> ...
> a1, h a2, h a3, h ... aw, h
w is the width of the land and h is the height of the land. These satisfy 1 ≤ w and h ≤ 50. Each ai, j is one half-width character representing the state of the grid (i, j), "` B` "is struck with a black stake, and" `W`" is struck with a white stake. "`.` "(Period) indicates that none of the stakes have been struck.
w = h = 0 represents the end of the input and is not included in the dataset.
Output
For each dataset, print the size of the land surrounded by the black stakes and the size of the land surrounded by the white stakes on one line, separated by a single space.
Sample Input
10 10
..... W ....
.... W.W ...
... W ... W ..
.... W ... W.
..... W ... W
...... W.W.
BBB .... W ..
..B..BBBBB
..B .... B ....
..B..B..W.
5 3
... B.
... BB
.....
1 1
..
0 0
Output for the Sample Input
6 21
12 0
0 0
Example
Input
10 10
.....W....
....W.W...
...W...W..
....W...W.
.....W...W
......W.W.
BBB....W..
..B..BBBBB
..B..B....
..B..B..W.
5 3
...B.
...BB
.....
1 1
.
0 0
Output
6 21
12 0
0 0 | #!/usr/bin/env python
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**6)
def dfs(x, y, symbol,land):
if land[y][x] != '.':
return ([land[y][x]] if not str(land[y][x]).isnumeric() else False), 0
land[y][x] = symbol
count = 1
dxdy = [(1,0),(-1,0),(0,1),(0,-1)]
owner_list = []
for dx,dy in dxdy:
if 0 <= x + dx < len(land[0]) and 0 <= y + dy < len(land):
ret,c = dfs(x + dx, y + dy, symbol,land)
count += c
if ret is not False:
owner_list += ret
return (list(set(owner_list)), count)
while True:
w,h = map(int,input().split())
if w == 0 and h == 0:
break
land = [list(input()) for i in range(0,h)]
symbol = 0
count_dict = {'W' :0, 'B' :0}
for y in range(h):
for x in range(w):
if land[y][x] == '.':
ret, count = dfs(x,y,symbol,land)
if len(ret) == 1:
count_dict[ret[0]] += count
symbol += 1
print(count_dict['B'],count_dict['W']) | {
"input": [
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n...B.B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n...B.B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\n..W....BBB\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n...B.B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n.....WW...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..V.\n2 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..BB.BB.BB\n....B..B..\n...B.B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n.WB..B....\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"1 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\n..W....BBB\n..B..BBBBB\n..B./A....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W/\nWW........\n......W.W.\nBB....BW..\nBBBBB..B..\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n.BB..B.BBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW....-\n...WW.....\n....W...W.\n.....W...W\n.W.W......\n..W....BBB\n..B..BBBBB\n..B..B../.\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\nW...W.....\n.W.W......\nBBC....W..\n..B..BBBBA\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"8 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..V.\n2 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n1 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"8 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\nB....BBBBB\n..B..B....\n..B..B..V.\n2 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\nWW........\n......W.W.\nBB....BW..\n..B..BBBBB\n..B..B....\n..B..B..W.\n2 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W..-.\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n...W....W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n3 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\nWW........\n......W.W.\nBB....BW..\n..B..BBBBB\n..B..B....\n..B..B..W.\n2 3\n...B.\nBB...\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n3 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"1 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..V.\n2 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"1 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n.BB..B.BBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\nW.....W...\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B..W.\n3 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n.W...W....\nW...W.....\n.W.W......\nBBC....W..\n..B..BBBBA\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n1 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"3 10\n.....W....\n...WW.....\n...WW.....\n....W...W-\n....-W..-W\n......W.W.\nBBB....W..\n..B..BBCBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n../.W...W.\n.....W...W\n..../.W.W.\nBBB....W..\nBBBBB..B..\n..B..B../.\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n.W......W.\n.....W...W\n......W.W.\n..W....BBB\nBB.BB..B.B\n..B..B....\n..B..B..W.\n3 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"8 10\n.....W.../\n....W.W...\n.....WW...\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\nB....BBBBB\n..B..B....\n..B..B..W.\n2 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\nBBBBB..B..\n..B..B....\n..W..B..B.\n5 3\n...B.\nBB...\n.....\n1 1\n.\n0 0",
"3 10\n.....W....\n....W.W...\n...W...X..\n....W...W.\nWW........\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n3 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\n..W....BBB\n..B..BBBBC\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"8 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n1 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\nWW........\n......W.W.\nBB....BW..\n..B..BBBBB\n..B..B....\n..B..B..W.\n3 3\n...B.\nBB...\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\n.....W...W\n......W.W.\nBBB....W./\n..B..BBBBB\n..B..B....\n.W..B..B..\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n.W...W....\nW...W.....\n.W.W......\n..W....CBB\n..B..BBBBA\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n..W......W\n......W.W.\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B/.W.\n4 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n.W......W.\n.....W...W\n......W.W.\n..W....BBB\nBB.BB..B.B\n..B..B....\n..B..B..W.\n3 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"8 10\n.....W.../\n....W.W...\n.....WW...\n....W...W-\nW...W.....\n......W.W.\nBBB....W..\nB....BBBBB\n..B..B....\n..B..B..W.\n4 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n.....WW...\n...WW.....\n....W...W.\n../..W...W\n......W.W.\nBBB....W..\nB.B...BBBB\n....B..B..\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n.W...W....\n..W......W\n......W.W.\n..W....BBB\n..B..BBBBB\n....B..B..\n.W..B..B..\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....WW....\n.....W...W\n......W.W.\nBBB....W./\n..B..BBBBB\n..B..B....\n.W..B..B..\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W-\nW...W../..\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B.-\n..B..B..W.\n4 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n....-W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.W.......W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBA\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n...B.B..W.\n5 3\n...B.\nBB...\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n....-W...W\n..-...W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n......W..W\n......W.W.\n..W....BBB\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n......W..W\n......W.W.\n..W....BBB\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\nB....\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n..BB.\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\n.....W...W\n....W.W...\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n../..W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B../.\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W-\n....-W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\nWW........\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n....W.W...\n...WW.....\n....X...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBA\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..V.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n..BB.\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n../..W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B../.\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.../.\n...WW.....\n....W...W-\n....-W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W....\n....W.W...\n...WW.....\n....X...W.\nW...W.....\n......W.W.\nBBB....W..\n..B.BBBB.B\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n.W...W....\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n..BB.\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...W.....W\n...WW.....\n....W...W.\n../..W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.../.\n...WW.....\n....W...W-\n....-W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..BW...\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n.W...W....\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W-\n5 3\n.B...\n..BB.\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n.....W...W\n......W.W.\n..W....BBB\n..B..BBBBC\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"10 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\nW...W.....\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n...B.B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n....-W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n..B/.B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n....-W...W\n..-...W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nB..B.\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n......W..W\n......W.W.\n..W....BBB\n..B..BBBAB\n....B..B..\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0",
"4 10\n.....W.../\n....W.W...\n...WW.....\n....W...W.\nW...W.....\n......W.W.\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n..W...W...\n....W...W.\n......W..W\n......W.W.\n..W....BBB\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\nB....\n...BB\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW.....\n...WW.....\n....W...W.\n.....W...W\n......W.W.\nBBB....W..\n..B..BBBBB\n....B..B..\n..B..B..W.\n5 3\n.B...\nBB...\n.....\n1 1\n.\n0 0",
"2 10\n.....W....\n...WW....-\n...WW.....\n....W...W.\n.....W...W\n.W.W......\nBBB....W..\n..B..BBBBB\n..B..B../.\n..B..B..W.\n5 3\n...B.\n...BB\n.....\n1 1\n.\n0 0",
"6 10\n.....W....\n....W.W...\n...W...W..\n....W...W.\nWW........\n......W.W.\nBBB....W..\n..B..BBBBB\n..B..B....\n..B..B..W.\n5 3\n.B...\n...BB\n.....\n1 1\n.\n0 0"
],
"output": [
"6 21\n12 0\n0 0",
"6 21\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"7 21\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"0 0\n12 0\n0 0\n",
"7 0\n12 0\n0 0\n",
"1 0\n12 0\n0 0\n",
"1 21\n12 0\n0 0\n",
"6 19\n12 0\n0 0\n",
"6 0\n5 0\n0 0\n",
"10 21\n12 0\n0 0\n",
"12 0\n12 0\n0 0\n",
"0 9\n12 0\n0 0\n",
"8 0\n12 0\n0 0\n",
"6 4\n12 0\n0 0\n",
"5 0\n12 0\n0 0\n",
"0 19\n12 0\n0 0\n",
"6 9\n12 0\n0 0\n",
"10 0\n5 0\n0 0\n",
"6 4\n0 0\n0 0\n",
"4 0\n5 0\n0 0\n",
"6 0\n0 0\n0 0\n",
"18 0\n8 0\n0 0\n",
"6 0\n4 0\n0 0\n",
"6 10\n12 0\n0 0\n",
"6 0\n8 0\n0 0\n",
"9 0\n12 0\n0 0\n",
"0 0\n5 0\n0 0\n",
"3 4\n12 0\n0 0\n",
"0 0\n6 0\n0 0\n",
"6 8\n12 0\n0 0\n",
"6 21\n0 0\n0 0\n",
"24 0\n12 0\n0 0\n",
"16 0\n12 0\n0 0\n",
"8 0\n8 0\n0 0\n",
"4 1\n5 0\n0 0\n",
"0 21\n12 0\n0 0\n",
"7 0\n0 0\n0 0\n",
"0 4\n12 0\n0 0\n",
"10 13\n0 0\n0 0\n",
"6 0\n7 0\n0 0\n",
"1 4\n12 0\n0 0\n",
"0 17\n12 0\n0 0\n",
"0 0\n10 0\n0 0\n",
"8 0\n6 0\n0 0\n",
"4 1\n10 0\n0 0\n",
"17 0\n12 0\n0 0\n",
"2 0\n12 0\n0 0\n",
"1 3\n12 0\n0 0\n",
"6 0\n10 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 21\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"7 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"1 0\n12 0\n0 0\n",
"0 0\n12 0\n0 0\n",
"1 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 21\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"0 0\n12 0\n0 0\n",
"7 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"1 0\n12 0\n0 0\n",
"0 0\n12 0\n0 0\n",
"0 0\n12 0\n0 0\n",
"18 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n",
"6 0\n12 0\n0 0\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Surrounding Area
Land fence
English text is not available in this practice contest.
Two real estate agents were boarding a passenger ship to the southern island. Blue sky, refreshing breeze ... The two enjoyed a voyage with other passengers. However, one day a tornado suddenly sank a passenger ship. The other passengers were rescued by the rescue team, but somehow only these two were overlooked. After a few days of drifting, they landed on an uninhabited island. This uninhabited island was rectangular and was divided into grids as shown in the figure below.
Shape of uninhabited island
Figure C-1: Shape of uninhabited island
They were so greedy that they were thinking of selling the land on this uninhabited island rather than calling for help. And they did not split the land in half, but began to scramble for the land. They each began to enclose what they wanted to land on one with black stakes and the other with white stakes. All stakes were struck in the center of the grid, and no stakes were struck in one grid. After a while, both were exhausted and stopped hitting the stakes.
Your job is to write a program to find the area of land surrounded by black and white stakes. However, it is intuitive that the grid (i, j) is surrounded by black stakes. It means that. To be exact, it is defined as follows.
> Define a grid "extended adjacent" to the black stake as follows: The same applies to white stakes.
>
> * If there are no stakes in grid (i, j) and there are black stakes in any of the grids adjacent to grid (i, j), then grid (i, j) extends adjacent to the black stakes. doing.
>
> * If there are no stakes in grid (i, j) and any of the grids adjacent to grid (i, j) are extended adjacent to black stakes, then grid (i, j) is a black stake. It is adjacent to the stake. This rule is applied recursively.
>
>
>
> At this time, when the grid (i, j) is extended adjacent to the black stake and not adjacent to the white stake, and only then, the grid (i, j) is surrounded by the black stake. It is said that there is. Conversely, when the grid (i, j) is extended adjacent to the white stake and not adjacent to the black stake, and only then, the grid (i, j) is surrounded by the white stake. It is said that there is.
Input
The input consists of multiple datasets. Each data set has the following structure.
> w h
> a1,1 a2,1 a3,1 ... aw,1
> a1,2 a2,2 a3,2 ... aw, 2
> ...
> a1, h a2, h a3, h ... aw, h
w is the width of the land and h is the height of the land. These satisfy 1 ≤ w and h ≤ 50. Each ai, j is one half-width character representing the state of the grid (i, j), "` B` "is struck with a black stake, and" `W`" is struck with a white stake. "`.` "(Period) indicates that none of the stakes have been struck.
w = h = 0 represents the end of the input and is not included in the dataset.
Output
For each dataset, print the size of the land surrounded by the black stakes and the size of the land surrounded by the white stakes on one line, separated by a single space.
Sample Input
10 10
..... W ....
.... W.W ...
... W ... W ..
.... W ... W.
..... W ... W
...... W.W.
BBB .... W ..
..B..BBBBB
..B .... B ....
..B..B..W.
5 3
... B.
... BB
.....
1 1
..
0 0
Output for the Sample Input
6 21
12 0
0 0
Example
Input
10 10
.....W....
....W.W...
...W...W..
....W...W.
.....W...W
......W.W.
BBB....W..
..B..BBBBB
..B..B....
..B..B..W.
5 3
...B.
...BB
.....
1 1
.
0 0
Output
6 21
12 0
0 0
### Input:
10 10
.....W....
....W.W...
...W...W..
....W...W.
.....W...W
......W.W.
BBB....W..
..B..BBBBB
..B..B....
..B..B..W.
5 3
...B.
...BB
.....
1 1
.
0 0
### Output:
6 21
12 0
0 0
### Input:
10 10
.....W....
....W.W...
...W...W..
....W...W.
.....W...W
......W.W.
BBB....W..
..B..BBBBB
..B..B....
..B..B..W.
5 3
.B...
...BB
.....
1 1
.
0 0
### Output:
6 21
12 0
0 0
### Code:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**6)
def dfs(x, y, symbol,land):
if land[y][x] != '.':
return ([land[y][x]] if not str(land[y][x]).isnumeric() else False), 0
land[y][x] = symbol
count = 1
dxdy = [(1,0),(-1,0),(0,1),(0,-1)]
owner_list = []
for dx,dy in dxdy:
if 0 <= x + dx < len(land[0]) and 0 <= y + dy < len(land):
ret,c = dfs(x + dx, y + dy, symbol,land)
count += c
if ret is not False:
owner_list += ret
return (list(set(owner_list)), count)
while True:
w,h = map(int,input().split())
if w == 0 and h == 0:
break
land = [list(input()) for i in range(0,h)]
symbol = 0
count_dict = {'W' :0, 'B' :0}
for y in range(h):
for x in range(w):
if land[y][x] == '.':
ret, count = dfs(x,y,symbol,land)
if len(ret) == 1:
count_dict[ret[0]] += count
symbol += 1
print(count_dict['B'],count_dict['W']) |
p01278 Voronoi Island_2981 | Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved in territorial disputes. The residents of the island were despaired of the disputes.
One day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the island such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi Division today.
Actually, there are many aspects of whether the method is fair. According to one historian, the clever lord suggested the method because he could gain broader area than other lords.
Your task is to write a program to calculate the size of the area each lord can gain. You may assume that Voronoi Island has a convex shape.
Input
The input consists of multiple datasets. Each dataset has the following format:
N M
Ix1 Iy1
Ix2 Iy2
...
IxN IyN
Cx1 Cy1
Cx2 Cy2
...
CxM CyM
N is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ixi, Iyi) denotes the coordinate of the i-th vertex; (Cxi, Cyi ) denotes the coordinate of the castle of the i-the lord.
The input meets the following constraints: 3 ≤ N ≤ 10, 2 ≤ M ≤ 10, -100 ≤ Ixi, Iyi, Cxi, Cyi ≤ 100. The vertices are given counterclockwise. All the coordinates are integers.
The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.
Output
For each dataset, print the area gained by each liege lord with an absolute error of at most 10-4 . You may output any number of digits after the decimal point. The order of the output areas must match that of the lords in the input.
Example
Input
3 3
0 0
8 0
0 8
2 2
4 2
2 4
0 0
Output
9.0
11.5
11.5 | import sys
readline = sys.stdin.readline
write = sys.stdout.write
def cross3(O, A, B):
ox, oy = O; ax, ay = A; bx, by = B
return (ax - ox) * (by - oy) - (bx - ox) * (ay - oy)
def cross_point(p0, p1, q0, q1):
x0, y0 = p0; x1, y1 = p1
x2, y2 = q0; x3, y3 = q1
dx0 = x1 - x0; dy0 = y1 - y0
dx1 = x3 - x2; dy1 = y3 - y2
s = (y0-y2)*dx1 - (x0-x2)*dy1
sm = dx0*dy1 - dy0*dx1
if -EPS < sm < EPS:
return None
return x0 + s*dx0/sm, y0 + s*dy0/sm
EPS = 1e-9
def convex_cut(P, line):
q0, q1 = line
N = len(P)
Q = []
for i in range(N):
p0 = P[i-1]; p1 = P[i]
cv0 = cross3(q0, q1, p0)
cv1 = cross3(q0, q1, p1)
if cv0 * cv1 < EPS:
v = cross_point(q0, q1, p0, p1)
if v is not None:
Q.append(v)
if cv1 > -EPS:
Q.append(p1)
return Q
def polygon_area(P):
s = 0
N = len(P)
for i in range(N):
p0 = P[i-1]; p1 = P[i]
s += p0[0]*p1[1] - p0[1]*p1[0]
return abs(s) / 2
def solve():
N, M = map(int, input().split())
if N == M == 0:
return False
P = [list(map(int, readline().split())) for i in range(N)]
Q = [list(map(int, readline().split())) for i in range(M)]
for i in range(M):
x0, y0 = Q[i]
P0 = P
for j in range(M):
if i == j:
continue
x1, y1 = Q[j]
ax = (x0 + x1) / 2; ay = (y0 + y1) / 2
q0 = (ax, ay)
q1 = (ax - (y1 - y0), ay + (x1 - x0))
P0 = convex_cut(P0, (q0, q1))
write("%.16f\n" % polygon_area(P0))
return True
while solve():
...
| {
"input": [
"3 3\n0 0\n8 0\n0 8\n2 2\n4 2\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 8\n2 2\n4 2\n2 4\n0 0",
"3 3\n0 0\n8 -1\n-1 8\n2 2\n4 2\n2 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n4 0\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 2\n2 2\n4 2\n2 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n7 0\n2 4\n0 0",
"3 3\n0 0\n14 0\n0 8\n2 2\n7 0\n2 4\n0 0",
"3 3\n0 0\n14 0\n0 8\n1 2\n7 0\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 2\n2 2\n3 2\n2 7\n0 0",
"3 3\n0 0\n14 0\n0 8\n1 0\n7 0\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n0 0\n14 0\n0 8\n1 0\n7 1\n2 4\n0 0",
"3 3\n0 0\n10 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n2 3\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n4 3\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n1 3\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 0\n0 2\n1 3\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n0 2\n1 3\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n0 2\n1 3\n6 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n0 2\n1 5\n6 0\n2 7\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n4 4\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 8\n2 2\n4 2\n4 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n4 -1\n2 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n7 1\n2 4\n0 0",
"3 3\n0 -1\n8 -1\n0 2\n2 2\n4 2\n2 6\n0 0",
"3 3\n0 0\n11 0\n0 8\n2 2\n7 0\n2 4\n0 0",
"3 3\n0 0\n3 -1\n0 2\n2 2\n4 2\n2 7\n0 0",
"3 3\n0 0\n16 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n0 0\n14 1\n0 8\n1 0\n7 1\n2 4\n0 0",
"3 3\n0 0\n7 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -2\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n2 3\n3 1\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 4\n1 3\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n0 2\n1 5\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n1 2\n1 5\n6 0\n2 7\n0 0",
"3 3\n0 0\n8 -1\n0 8\n2 2\n4 0\n4 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 4\n4 -1\n2 4\n0 0",
"3 3\n0 0\n8 0\n0 1\n2 2\n7 1\n2 4\n0 0",
"3 3\n0 -1\n8 -1\n0 2\n1 2\n4 2\n2 6\n0 0",
"3 3\n0 0\n7 -1\n0 2\n2 2\n3 1\n2 7\n0 0",
"3 3\n1 0\n10 -2\n0 2\n2 2\n0 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 4\n1 0\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n1 2\n1 5\n3 0\n2 7\n0 0",
"3 3\n0 0\n8 1\n0 8\n2 4\n4 -1\n2 4\n0 0",
"3 3\n0 0\n16 -1\n0 2\n1 2\n3 0\n2 13\n0 0",
"3 3\n0 0\n7 -1\n0 2\n2 4\n3 1\n2 7\n0 0",
"3 3\n2 0\n10 -2\n0 2\n2 2\n0 0\n2 7\n0 0",
"3 3\n2 0\n10 -1\n0 4\n1 0\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n1 2\n0 5\n6 0\n4 7\n0 0",
"3 3\n0 0\n16 -1\n0 2\n1 2\n3 -1\n2 13\n0 0",
"3 3\n0 0\n7 -1\n0 3\n2 4\n3 1\n2 7\n0 0",
"3 3\n2 0\n10 -2\n-1 2\n2 2\n0 0\n2 7\n0 0",
"3 3\n2 0\n10 -1\n0 4\n1 -1\n3 0\n2 7\n0 0",
"3 3\n0 1\n10 0\n1 2\n0 5\n3 0\n2 7\n0 0",
"3 3\n0 0\n7 -1\n0 3\n4 4\n3 1\n2 7\n0 0",
"3 3\n0 0\n10 0\n1 2\n0 5\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n1 2\n0 1\n6 0\n4 7\n0 0",
"3 3\n4 0\n10 -2\n-1 2\n2 2\n0 0\n3 7\n0 0",
"3 3\n4 0\n10 -2\n-1 2\n2 2\n-1 0\n3 7\n0 0",
"3 3\n1 1\n10 0\n1 3\n0 1\n6 0\n1 7\n0 0",
"3 3\n0 0\n10 0\n1 2\n-1 1\n3 1\n2 7\n0 0",
"3 3\n0 0\n10 0\n1 2\n-1 1\n3 0\n2 10\n0 0",
"3 3\n1 0\n10 0\n1 2\n-1 1\n0 0\n4 10\n0 0",
"3 3\n1 0\n10 0\n1 2\n0 1\n0 0\n4 10\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n4 2\n2 0\n0 0",
"3 3\n0 0\n8 -1\n0 16\n2 2\n4 2\n2 4\n0 0",
"3 3\n0 0\n8 -1\n-1 8\n2 2\n4 2\n2 7\n0 0",
"3 3\n0 0\n8 -1\n0 2\n2 4\n4 2\n2 6\n0 0",
"3 3\n0 0\n14 0\n0 8\n2 2\n8 0\n2 4\n0 0",
"3 3\n0 0\n14 0\n0 8\n1 2\n4 0\n2 4\n0 0",
"3 3\n0 0\n14 0\n0 8\n1 0\n7 0\n2 2\n0 0",
"3 3\n0 0\n8 -1\n0 2\n2 2\n6 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n2 2\n6 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n-1 2\n2 3\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n4 3\n2 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n1 3\n3 1\n2 7\n0 0",
"3 3\n1 0\n10 0\n0 2\n2 3\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n0 2\n1 8\n6 0\n2 7\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n2 4\n2 4\n0 0",
"3 3\n0 0\n8 -1\n0 8\n3 2\n4 2\n4 4\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n4 -1\n2 0\n0 0",
"3 3\n0 0\n8 0\n0 8\n2 2\n7 1\n2 7\n0 0",
"3 3\n0 0\n11 0\n0 8\n2 2\n7 0\n0 4\n0 0",
"3 3\n0 0\n3 -1\n0 2\n1 2\n4 2\n2 7\n0 0",
"3 3\n0 0\n30 -1\n0 2\n2 2\n3 0\n2 7\n0 0",
"3 3\n0 0\n14 1\n0 8\n1 0\n7 1\n1 4\n0 0",
"3 3\n1 0\n10 -2\n0 2\n0 2\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 2\n2 3\n1 1\n2 7\n0 0",
"3 3\n1 0\n10 -1\n0 4\n1 1\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 -1\n0 2\n1 5\n3 0\n2 7\n0 0",
"3 3\n1 0\n10 0\n1 2\n1 5\n6 0\n2 7\n0 0",
"3 3\n0 0\n8 0\n0 1\n2 2\n8 1\n2 4\n0 0",
"3 3\n0 -1\n8 -1\n1 2\n1 2\n4 2\n2 6\n0 0",
"3 3\n0 0\n16 0\n0 2\n2 2\n3 0\n2 13\n0 0",
"3 3\n0 0\n7 -1\n0 2\n2 2\n3 2\n2 7\n0 0",
"3 3\n1 1\n10 -1\n0 4\n1 0\n3 0\n2 7\n0 0",
"3 3\n1 2\n10 0\n1 2\n1 5\n3 0\n2 7\n0 0",
"3 3\n1 1\n10 0\n1 2\n1 5\n7 0\n4 7\n0 0",
"3 3\n0 0\n8 1\n0 8\n2 8\n4 -1\n2 4\n0 0",
"3 3\n0 0\n16 -1\n0 2\n1 2\n2 0\n2 13\n0 0"
],
"output": [
"9.0\n11.5\n11.5",
"9.562500\n11.878676\n10.558824\n",
"10.125000\n10.687500\n10.687500\n",
"10.500000\n9.000000\n12.500000\n",
"4.875000\n3.125000\n0.000000\n",
"14.067857\n5.432143\n12.500000\n",
"14.100000\n22.358824\n19.541176\n",
"10.913690\n23.529062\n21.557248\n",
"4.218750\n3.781250\n0.000000\n",
"7.500000\n23.402574\n25.097426\n",
"2.842857\n5.157143\n0.000000\n",
"7.454257\n24.979282\n23.566460\n",
"3.111979\n6.888021\n0.000000\n",
"2.151563\n6.348438\n0.000000\n",
"1.022556\n7.477444\n0.000000\n",
"0.000000\n8.500000\n0.000000\n",
"1.108297\n7.391703\n0.000000\n",
"1.308894\n7.691106\n0.000000\n",
"0.921245\n3.078755\n0.000000\n",
"1.962798\n2.037202\n0.000000\n",
"1.300000\n2.700000\n0.000000\n",
"13.500000\n8.000000\n10.500000\n",
"14.062500\n11.326389\n6.611111\n",
"12.887500\n6.612500\n12.500000\n",
"13.500000\n6.012500\n12.487500\n",
"7.312500\n4.687500\n0.000000\n",
"14.100000\n13.282759\n16.617241\n",
"3.000000\n0.000000\n0.000000\n",
"3.626263\n12.373737\n0.000000\n",
"6.865777\n24.323082\n24.811141\n",
"2.677350\n4.322650\n0.000000\n",
"1.800000\n6.200000\n0.000000\n",
"0.664062\n7.835938\n0.000000\n",
"4.723214\n12.776786\n0.000000\n",
"0.042857\n3.957143\n0.000000\n",
"1.186364\n3.313636\n0.000000\n",
"14.222222\n9.777778\n8.000000\n",
"21.175000\n10.825000\n21.175000\n",
"3.119512\n0.880488\n0.000000\n",
"6.328125\n5.671875\n0.000000\n",
"2.712500\n4.287500\n0.000000\n",
"6.857143\n1.142857\n0.000000\n",
"4.951852\n12.444444\n0.103704\n",
"0.000000\n4.500000\n0.000000\n",
"23.250980\n8.749020\n23.250980\n",
"3.318885\n12.681115\n0.000000\n",
"0.072917\n6.927083\n0.000000\n",
"6.000000\n0.000000\n0.000000\n",
"2.907692\n12.000000\n0.092308\n",
"0.960242\n3.539758\n0.000000\n",
"4.222997\n11.777003\n0.000000\n",
"0.982456\n9.517544\n0.000000\n",
"4.285714\n0.714286\n0.000000\n",
"0.000000\n14.600000\n0.400000\n",
"0.000000\n5.500000\n0.000000\n",
"0.000000\n10.500000\n0.000000\n",
"0.000000\n10.000000\n0.000000\n",
"1.860998\n2.639002\n0.000000\n",
"0.952381\n0.047619\n0.000000\n",
"0.977273\n0.022727\n0.000000\n",
"3.814593\n5.185407\n0.000000\n",
"1.000000\n9.000000\n0.000000\n",
"1.235197\n8.764803\n0.000000\n",
"0.000000\n9.000000\n0.000000\n",
"5.062500\n3.937500\n0.000000\n",
"16.500000\n12.000000\n3.500000\n",
"9.562500\n17.977500\n36.460000\n",
"15.203125\n10.937500\n5.359375\n",
"1.454545\n6.545455\n0.000000\n",
"15.500000\n20.591954\n19.908046\n",
"8.041667\n26.989583\n20.968750\n",
"3.062500\n22.793023\n30.144477\n",
"5.523220\n2.476780\n0.000000\n",
"4.687643\n3.812357\n0.000000\n",
"1.250000\n6.750000\n0.000000\n",
"2.176515\n6.323485\n0.000000\n",
"0.871795\n7.628205\n0.000000\n",
"1.285714\n7.714286\n0.000000\n",
"0.000000\n3.796296\n0.203704\n",
"19.500000\n12.500000\n12.500000\n",
"14.328125\n9.623264\n8.048611\n",
"22.387500\n6.112500\n3.500000\n",
"19.858333\n6.016667\n6.125000\n",
"20.167680\n13.411268\n10.421053\n",
"2.916667\n0.083333\n0.000000\n",
"4.160156\n25.839844\n0.000000\n",
"7.244853\n26.367647\n22.387500\n",
"1.270677\n6.729323\n0.000000\n",
"1.897321\n6.602679\n0.000000\n",
"6.217105\n11.282895\n0.000000\n",
"0.032143\n3.467857\n0.000000\n",
"1.636364\n7.363636\n0.000000\n",
"3.353316\n0.646684\n0.000000\n",
"5.517857\n6.482143\n0.000000\n",
"3.987500\n12.012500\n0.000000\n",
"4.107143\n2.892857\n0.000000\n",
"3.511111\n8.888889\n0.100000\n",
"0.000000\n0.000000\n0.000000\n",
"1.696736\n2.803264\n0.000000\n",
"2.285714\n8.749020\n20.965266\n",
"2.227273\n13.772727\n0.000000\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved in territorial disputes. The residents of the island were despaired of the disputes.
One day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the island such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi Division today.
Actually, there are many aspects of whether the method is fair. According to one historian, the clever lord suggested the method because he could gain broader area than other lords.
Your task is to write a program to calculate the size of the area each lord can gain. You may assume that Voronoi Island has a convex shape.
Input
The input consists of multiple datasets. Each dataset has the following format:
N M
Ix1 Iy1
Ix2 Iy2
...
IxN IyN
Cx1 Cy1
Cx2 Cy2
...
CxM CyM
N is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ixi, Iyi) denotes the coordinate of the i-th vertex; (Cxi, Cyi ) denotes the coordinate of the castle of the i-the lord.
The input meets the following constraints: 3 ≤ N ≤ 10, 2 ≤ M ≤ 10, -100 ≤ Ixi, Iyi, Cxi, Cyi ≤ 100. The vertices are given counterclockwise. All the coordinates are integers.
The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.
Output
For each dataset, print the area gained by each liege lord with an absolute error of at most 10-4 . You may output any number of digits after the decimal point. The order of the output areas must match that of the lords in the input.
Example
Input
3 3
0 0
8 0
0 8
2 2
4 2
2 4
0 0
Output
9.0
11.5
11.5
### Input:
3 3
0 0
8 0
0 8
2 2
4 2
2 4
0 0
### Output:
9.0
11.5
11.5
### Input:
3 3
0 0
8 -1
0 8
2 2
4 2
2 4
0 0
### Output:
9.562500
11.878676
10.558824
### Code:
import sys
readline = sys.stdin.readline
write = sys.stdout.write
def cross3(O, A, B):
ox, oy = O; ax, ay = A; bx, by = B
return (ax - ox) * (by - oy) - (bx - ox) * (ay - oy)
def cross_point(p0, p1, q0, q1):
x0, y0 = p0; x1, y1 = p1
x2, y2 = q0; x3, y3 = q1
dx0 = x1 - x0; dy0 = y1 - y0
dx1 = x3 - x2; dy1 = y3 - y2
s = (y0-y2)*dx1 - (x0-x2)*dy1
sm = dx0*dy1 - dy0*dx1
if -EPS < sm < EPS:
return None
return x0 + s*dx0/sm, y0 + s*dy0/sm
EPS = 1e-9
def convex_cut(P, line):
q0, q1 = line
N = len(P)
Q = []
for i in range(N):
p0 = P[i-1]; p1 = P[i]
cv0 = cross3(q0, q1, p0)
cv1 = cross3(q0, q1, p1)
if cv0 * cv1 < EPS:
v = cross_point(q0, q1, p0, p1)
if v is not None:
Q.append(v)
if cv1 > -EPS:
Q.append(p1)
return Q
def polygon_area(P):
s = 0
N = len(P)
for i in range(N):
p0 = P[i-1]; p1 = P[i]
s += p0[0]*p1[1] - p0[1]*p1[0]
return abs(s) / 2
def solve():
N, M = map(int, input().split())
if N == M == 0:
return False
P = [list(map(int, readline().split())) for i in range(N)]
Q = [list(map(int, readline().split())) for i in range(M)]
for i in range(M):
x0, y0 = Q[i]
P0 = P
for j in range(M):
if i == j:
continue
x1, y1 = Q[j]
ax = (x0 + x1) / 2; ay = (y0 + y1) / 2
q0 = (ax, ay)
q1 = (ax - (y1 - y0), ay + (x1 - x0))
P0 = convex_cut(P0, (q0, q1))
write("%.16f\n" % polygon_area(P0))
return True
while solve():
...
|
p01448 A Way to Invite Friends_2985 | From tomorrow, the long-awaited summer vacation will begin. So I decided to invite my friends to go out to the sea.
However, many of my friends are shy. They would hate it if they knew that too many people would come with them.
Besides, many of my friends want to stand out. They will probably hate it if they know that not many people come with them.
Also, some of my friends are always shy, though they always want to stand out. They will surely hate if too many or too few people come with them.
This kind of thing should be more fun to do in large numbers. That's why I want to invite as many friends as possible. However, it is not good to force a friend you dislike.
How many friends can I invite up to?
I'm not very good at this kind of problem that seems to use my head. So I have a request for you. If you don't mind, could you solve this problem for me? No, I'm not overdoing it. But if I'm slacking off, I'm very happy.
Input
N
a1 b1
a2 b2
..
..
..
aN bN
The integer N (1 ≤ N ≤ 100,000) is written on the first line of the input. This represents the number of friends.
On the following N lines, the integer ai and the integer bi (2 ≤ ai ≤ bi ≤ 100,001) are written separated by blanks. The integers ai and bi written on the 1 + i line indicate that the i-th friend does not want to go to the sea unless the number of people going to the sea is ai or more and bi or less. Note that the number of people going to the sea includes "I".
Output
Output the maximum number of friends you can invite to the sea so that no friends dislike it.
Examples
Input
4
2 5
4 7
2 4
3 6
Output
3
Input
5
8 100001
7 100001
12 100001
8 100001
3 100001
Output
0
Input
6
2 9
4 8
6 7
6 6
5 7
2 100001
Output
5 | n = int(input())
l = [0 for i in range(n+2)]
for i in range(n):
[a,b] = list(map(int,input().split()))
if a <= n+1:
l[a] += 1
if b+1 <= n+1:
l[b+1] -= 1
ans = 0
for i in range(n+2):
if i != 0:
l[i] = l[i-1] + l[i]
if l[i] >= i-1:
ans = i-1
print(ans) | {
"input": [
"5\n8 100001\n7 100001\n12 100001\n8 100001\n3 100001",
"4\n2 5\n4 7\n2 4\n3 6",
"6\n2 9\n4 8\n6 7\n6 6\n5 7\n2 100001",
"5\n8 100001\n14 100001\n12 100001\n8 100001\n3 100001",
"4\n2 5\n4 7\n2 4\n5 6",
"6\n2 9\n4 8\n6 7\n6 6\n5 4\n2 100001",
"4\n2 1\n4 7\n2 4\n5 6",
"5\n8 100001\n7 100001\n12 100001\n3 100001\n3 100001",
"6\n2 9\n2 8\n6 7\n6 6\n5 4\n2 100001",
"6\n4 9\n2 8\n6 7\n6 6\n5 4\n2 100001",
"5\n6 100001\n7 100001\n12 100001\n8 100001\n3 100001",
"4\n2 2\n4 7\n2 4\n3 6",
"4\n2 6\n4 7\n2 4\n5 6",
"6\n2 16\n4 8\n6 7\n6 6\n5 4\n2 100001",
"6\n2 9\n2 8\n6 7\n11 6\n5 4\n2 100001",
"4\n2 0\n4 7\n2 4\n3 6",
"4\n2 10\n4 7\n2 4\n5 6",
"6\n2 16\n4 16\n6 7\n6 6\n5 4\n2 100001",
"6\n2 9\n2 8\n6 7\n11 6\n7 4\n2 100001",
"4\n4 0\n4 7\n2 4\n3 6",
"6\n2 9\n2 8\n6 8\n11 6\n7 4\n2 100001",
"5\n8 100001\n14 100001\n12 100000\n8 100001\n3 100001",
"4\n2 5\n4 7\n2 4\n6 6",
"5\n6 100001\n7 100001\n12 100001\n14 100001\n3 100001",
"4\n2 4\n4 7\n2 4\n3 6",
"6\n2 16\n4 8\n6 7\n6 6\n5 4\n4 100001",
"6\n2 9\n2 8\n10 7\n11 6\n7 4\n2 100001",
"4\n4 0\n4 7\n4 4\n3 6",
"6\n2 9\n2 4\n6 8\n11 6\n7 4\n2 100001",
"5\n8 100001\n14 100001\n12 100000\n11 100001\n3 100001",
"5\n5 100001\n7 100001\n12 100001\n14 100001\n3 100001",
"4\n2 4\n4 13\n2 4\n3 6",
"6\n2 16\n4 8\n6 7\n6 6\n5 4\n4 100000",
"6\n2 9\n2 8\n10 7\n11 6\n8 4\n2 100001",
"6\n2 9\n2 4\n6 8\n11 12\n7 4\n2 100001",
"5\n8 100001\n14 100001\n13 100000\n11 100001\n3 100001",
"6\n4 9\n2 8\n10 7\n11 6\n8 4\n2 100001",
"5\n8 100001\n7 100001\n12 100001\n8 100001\n2 100001",
"6\n2 9\n4 8\n6 7\n6 6\n5 11\n2 100001",
"5\n8 100001\n14 100001\n12 100001\n8 100001\n5 100001",
"6\n2 9\n4 8\n6 7\n6 6\n5 4\n2 100000",
"6\n2 9\n2 8\n2 7\n6 6\n5 4\n2 100001",
"5\n6 100001\n5 100001\n12 100001\n8 100001\n3 100001",
"4\n2 2\n4 7\n2 7\n3 6",
"6\n2 16\n4 8\n6 7\n6 6\n2 4\n2 100001",
"4\n2 0\n4 4\n2 4\n3 6",
"6\n2 6\n4 16\n6 7\n6 6\n5 4\n2 100001",
"6\n2 9\n2 8\n6 9\n11 6\n7 4\n2 100001",
"4\n2 1\n4 6\n2 4\n5 6",
"5\n8 100001\n14 100001\n17 100000\n8 100001\n3 100001",
"5\n6 100001\n7 100001\n12 100001\n14 100001\n5 100001",
"6\n2 32\n4 8\n6 7\n6 6\n5 4\n4 100001",
"6\n2 9\n2 4\n10 7\n11 6\n7 4\n2 100001",
"5\n5 100001\n7 100001\n13 100001\n14 100001\n3 100001",
"6\n2 9\n2 4\n6 8\n13 12\n7 4\n2 100001",
"5\n8 000001\n14 100001\n13 100000\n11 100001\n3 100001",
"5\n8 100001\n7 100000\n12 100001\n8 100001\n2 100001",
"6\n0 9\n4 8\n6 7\n6 6\n5 11\n2 100001",
"6\n2 9\n2 8\n2 7\n6 6\n5 8\n2 100001",
"4\n2 1\n4 6\n2 1\n5 6",
"5\n8 100001\n14 100001\n17 100000\n8 100001\n3 100000",
"5\n5 100001\n7 100001\n13 000001\n14 100001\n3 100001",
"6\n2 9\n2 4\n3 8\n13 12\n7 4\n2 100001",
"6\n0 9\n4 8\n6 7\n6 6\n5 7\n2 100001",
"6\n2 9\n4 8\n2 7\n6 6\n5 8\n2 100001",
"4\n2 1\n5 6\n2 1\n5 6",
"5\n5 100001\n7 100001\n13 000001\n24 100001\n3 100001",
"6\n2 9\n2 4\n3 8\n12 12\n7 4\n2 100001",
"5\n5 100001\n7 100001\n13 000001\n24 100000\n3 100001",
"6\n2 9\n2 4\n3 8\n12 12\n7 4\n4 100001",
"5\n5 100001\n7 100001\n13 000001\n16 100000\n3 100001",
"6\n2 9\n4 8\n6 13\n6 6\n5 7\n2 100001",
"6\n2 9\n2 8\n11 7\n6 6\n5 4\n2 100001",
"5\n6 100001\n7 100001\n12 100001\n13 100001\n3 100001",
"6\n2 9\n4 8\n6 7\n11 6\n5 4\n2 100001",
"4\n2 0\n4 7\n2 4\n1 6",
"6\n2 16\n4 16\n6 7\n6 11\n5 4\n2 100001",
"6\n2 9\n2 8\n11 7\n11 6\n7 4\n2 100001",
"4\n2 1\n4 9\n2 4\n5 6",
"5\n8 100001\n14 100001\n12 100000\n13 100001\n3 100001",
"5\n6 100001\n7 100001\n12 100000\n14 100001\n3 100001",
"6\n4 16\n4 8\n6 7\n6 6\n5 4\n4 100001",
"6\n2 9\n2 8\n10 7\n11 6\n1 4\n2 100001",
"4\n4 0\n4 7\n4 4\n3 9",
"5\n8 100001\n14 100001\n20 100000\n11 100001\n3 100001",
"5\n5 100001\n7 100001\n12 100001\n14 100001\n3 100000",
"6\n2 16\n4 8\n12 7\n6 6\n5 4\n4 100000",
"6\n2 11\n2 8\n10 7\n11 6\n8 4\n2 100001",
"6\n2 9\n2 4\n6 8\n11 12\n11 4\n2 100001",
"5\n8 100001\n7 100001\n12 100001\n7 100001\n2 100001",
"5\n8 100001\n14 100001\n22 100001\n8 100001\n5 100001",
"6\n2 9\n4 8\n6 7\n6 6\n4 4\n2 100000",
"5\n10 100001\n5 100001\n12 100001\n8 100001\n3 100001",
"4\n2 2\n4 7\n4 7\n3 6",
"6\n2 6\n4 8\n6 7\n6 6\n2 4\n2 100001",
"4\n2 0\n4 6\n2 4\n3 6",
"6\n2 6\n4 16\n9 7\n6 6\n5 4\n2 100001",
"5\n8 100000\n14 100001\n17 100000\n8 100001\n3 100001",
"6\n2 9\n2 4\n10 7\n11 4\n7 4\n2 100001",
"6\n2 4\n2 4\n6 8\n13 12\n7 4\n2 100001",
"5\n8 000001\n22 100001\n13 100000\n11 100001\n3 100001",
"6\n0 8\n4 8\n6 7\n6 6\n5 11\n2 100001",
"6\n2 9\n2 8\n2 4\n6 6\n5 8\n2 100001"
],
"output": [
"0",
"3",
"5",
"0\n",
"3\n",
"5\n",
"1\n",
"2\n",
"5\n",
"5\n",
"0\n",
"3\n",
"3\n",
"5\n",
"3\n",
"3\n",
"3\n",
"5\n",
"3\n",
"3\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"5\n",
"3\n",
"3\n",
"3\n",
"0\n",
"0\n",
"3\n",
"5\n",
"3\n",
"3\n",
"0\n",
"3\n",
"1\n",
"5\n",
"0\n",
"5\n",
"5\n",
"0\n",
"3\n",
"5\n",
"3\n",
"5\n",
"3\n",
"1\n",
"0\n",
"0\n",
"5\n",
"3\n",
"0\n",
"3\n",
"0\n",
"1\n",
"5\n",
"5\n",
"0\n",
"0\n",
"0\n",
"3\n",
"5\n",
"5\n",
"0\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"5\n",
"3\n",
"0\n",
"3\n",
"3\n",
"5\n",
"3\n",
"1\n",
"0\n",
"0\n",
"5\n",
"3\n",
"3\n",
"0\n",
"0\n",
"3\n",
"3\n",
"3\n",
"1\n",
"0\n",
"5\n",
"0\n",
"3\n",
"5\n",
"3\n",
"3\n",
"0\n",
"3\n",
"3\n",
"0\n",
"5\n",
"5\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
From tomorrow, the long-awaited summer vacation will begin. So I decided to invite my friends to go out to the sea.
However, many of my friends are shy. They would hate it if they knew that too many people would come with them.
Besides, many of my friends want to stand out. They will probably hate it if they know that not many people come with them.
Also, some of my friends are always shy, though they always want to stand out. They will surely hate if too many or too few people come with them.
This kind of thing should be more fun to do in large numbers. That's why I want to invite as many friends as possible. However, it is not good to force a friend you dislike.
How many friends can I invite up to?
I'm not very good at this kind of problem that seems to use my head. So I have a request for you. If you don't mind, could you solve this problem for me? No, I'm not overdoing it. But if I'm slacking off, I'm very happy.
Input
N
a1 b1
a2 b2
..
..
..
aN bN
The integer N (1 ≤ N ≤ 100,000) is written on the first line of the input. This represents the number of friends.
On the following N lines, the integer ai and the integer bi (2 ≤ ai ≤ bi ≤ 100,001) are written separated by blanks. The integers ai and bi written on the 1 + i line indicate that the i-th friend does not want to go to the sea unless the number of people going to the sea is ai or more and bi or less. Note that the number of people going to the sea includes "I".
Output
Output the maximum number of friends you can invite to the sea so that no friends dislike it.
Examples
Input
4
2 5
4 7
2 4
3 6
Output
3
Input
5
8 100001
7 100001
12 100001
8 100001
3 100001
Output
0
Input
6
2 9
4 8
6 7
6 6
5 7
2 100001
Output
5
### Input:
5
8 100001
7 100001
12 100001
8 100001
3 100001
### Output:
0
### Input:
4
2 5
4 7
2 4
3 6
### Output:
3
### Code:
n = int(input())
l = [0 for i in range(n+2)]
for i in range(n):
[a,b] = list(map(int,input().split()))
if a <= n+1:
l[a] += 1
if b+1 <= n+1:
l[b+1] -= 1
ans = 0
for i in range(n+2):
if i != 0:
l[i] = l[i-1] + l[i]
if l[i] >= i-1:
ans = i-1
print(ans) |
p01754 Dinner_2989 | In the spring of 2014, a student successfully passed the university and started living alone. The problem here is what to do with the supper. He decided to plan a supper for the next N days.
He wants to maximize the total happiness he gets in N days. Of course, the more delicious or favorite you eat, the higher your happiness.
His dinner options are two, either head to a nearby dining room or cook for himself.
The happiness you get in the cafeteria depends on the menu of the day. The menu changes daily, but there is only one type every day, and all the menus for N days have already been released. So he knows all the information that if you go to the cafeteria on day i (1 ≤ i ≤ N) you will get the happiness of Ci.
The happiness obtained by self-catering is the self-catering power at the start of self-catering multiplied by a constant P. The initial value of self-catering power is Q, which is -1 if you go to the restaurant every day, +1 if you cook yourself, and fluctuates at the end of the meal of the day.
Find the maximum sum of happiness for him.
Constraints
* 1 ≤ N ≤ 500,000
* 0 ≤ P ≤ 500,000
* | Q | ≤ 500,000
* | Ci | ≤ 500,000
Input
The input is given in the following format as N + 1 line.
N P Q
C1
C2
::
CN
* The first line is given three integers N, P, and Q, which are the number of days, the constant for calculating the happiness of self-catering, and the initial value of self-catering power.
* From the 2nd line to the N + 1st line, one integer is given, and the i + 1st line gives the happiness obtained when going to the cafeteria on the i day.
Output
Output the maximum value of happiness that can be taken in one line.
Examples
Input
1 1 1
2
Output
2
Input
3 2 1
3
3
3
Output
12
Input
3 1 -1
2
-3
2
Output
2
Input
3 1 -10
-10
-10
-10
Output
-27 | tmp = list(map(int,input().split()))
n,p,q = tmp[0],tmp[1],tmp[2]
cs = []
for i in range(n):
cs.append(int(input()))
ans = [sum(cs)]
difs = [p * (q-i) - cs[i] for i in range(n)]
difs.sort(reverse = True)
for i in range(n):
ans.append(ans[-1] + 2 * i * p + difs[i])
print(max(ans))
| {
"input": [
"1 1 1\n2",
"3 2 1\n3\n3\n3",
"3 1 -1\n2\n-3\n2",
"3 1 -10\n-10\n-10\n-10",
"1 0 1\n2",
"3 2 0\n3\n3\n3",
"3 1 -10\n-19\n-10\n-10",
"0 0 1\n2",
"3 2 0\n5\n3\n3",
"2 1 -10\n-19\n-10\n-10",
"3 2 1\n5\n3\n3",
"1 0 0\n4",
"3 2 0\n1\n3\n6",
"2 1 -10\n-35\n-3\n-10",
"2 1 -10\n-35\n-1\n-10",
"2 1 -6\n-35\n-1\n-10",
"2 1 -7\n-34\n-1\n-10",
"2 1 -5\n-34\n-1\n-10",
"1 1 -5\n-34\n-1\n-10",
"1 1 -10\n-34\n-2\n-10",
"1 1 -3\n-64\n-2\n-10",
"1 1 -1\n-64\n-3\n-12",
"2 1 0\n-77\n-2\n-33",
"2 1 1\n-77\n-2\n-33",
"2 2 1\n-13\n2\n0",
"3 3 1\n3\n3\n3",
"3 1 -19\n-19\n-10\n-10",
"2 1 -8\n-34\n-1\n-10",
"1 1 -17\n-34\n-2\n-10",
"1 1 -2\n-64\n-3\n-10",
"2 1 2\n-77\n-1\n-57",
"3 1 -10\n-10\n-8\n0",
"3 1 -19\n-19\n-10\n-18",
"2 -1 -10\n-35\n-5\n-10",
"2 2 0\n3\n4\n2",
"2 1 -13\n-34\n-1\n-10",
"1 4 2\n-47\n-1\n-84",
"2 8 1\n-13\n0\n0",
"3 6 1\n3\n3\n4",
"2 2 -10\n-35\n-9\n-7",
"3 2 1\n0\n10\n4",
"2 13 1\n-23\n0\n0",
"3 2 1\n0\n10\n0",
"2 2 -10\n-14\n-9\n-7",
"3 3 2\n1\n2\n0",
"1 1 -4\n-47\n-1\n-10",
"2 2 -10\n-14\n-6\n-7",
"3 1 -27\n-19\n0\n-18",
"2 1 -10\n-14\n-6\n-7",
"3 -1 -15\n-55\n-1\n-18",
"3 1 -27\n-38\n0\n-18",
"3 1 -1\n2\n-2\n2",
"1 1 2\n2",
"2 0 -10\n-19\n-10\n-10",
"1 1 0\n2",
"3 2 1\n1\n3\n3",
"2 1 -10\n-35\n-10\n-10",
"1 0 0\n2",
"3 2 1\n1\n3\n6",
"2 0 -10\n-35\n-10\n-10",
"2 0 -10\n-35\n-3\n-10",
"1 1 0\n4",
"0 2 0\n1\n3\n6",
"0 1 0\n4",
"0 2 0\n2\n3\n6",
"0 1 0\n7",
"0 2 0\n2\n3\n2",
"0 2 0\n3\n3\n2",
"2 1 -6\n-57\n-1\n-10",
"0 2 0\n3\n4\n2",
"2 1 -6\n-66\n-1\n-10",
"0 2 1\n3\n4\n2",
"2 1 -6\n-100\n-1\n-10",
"2 1 -6\n-34\n-1\n-10",
"1 1 -5\n-34\n-2\n-10",
"1 1 -10\n-64\n-2\n-10",
"1 1 -3\n-64\n-4\n-10",
"1 1 -3\n-64\n-3\n-10",
"1 1 -3\n-64\n-3\n-6",
"1 1 -3\n-64\n-3\n-12",
"0 1 -3\n-64\n-3\n-12",
"1 1 -1\n-34\n-3\n-12",
"1 1 -1\n-34\n-3\n-20",
"1 1 -1\n-34\n-3\n-33",
"1 1 0\n-34\n-3\n-33",
"1 1 0\n-34\n-2\n-33",
"1 1 0\n-65\n-2\n-33",
"1 1 0\n-77\n-2\n-33",
"2 1 1\n-77\n-4\n-33",
"2 1 1\n-77\n-4\n-57",
"2 1 1\n-77\n-1\n-57",
"2 1 0\n-77\n-1\n-57",
"1 1 1\n-77\n-1\n-57",
"1 1 1\n-77\n-1\n-84",
"1 1 1\n-47\n-1\n-84",
"1 1 2\n-47\n-1\n-84",
"1 0 2\n-47\n-1\n-84",
"1 0 2\n-47\n-1\n-16",
"1 0 2\n-47\n0\n-16",
"1 0 3\n-47\n0\n-16",
"1 0 3\n-47\n0\n0",
"1 0 3\n-5\n0\n0",
"2 0 3\n-5\n0\n0",
"2 0 3\n-10\n0\n0"
],
"output": [
"2",
"12",
"2",
"-27",
"2\n",
"9\n",
"-27\n",
"0\n",
"11\n",
"-19\n",
"12\n",
"4\n",
"10\n",
"-13\n",
"-11\n",
"-7\n",
"-8\n",
"-6\n",
"-5\n",
"-10\n",
"-3\n",
"-1\n",
"1\n",
"3\n",
"6\n",
"18\n",
"-39\n",
"-9\n",
"-17\n",
"-2\n",
"5\n",
"-18\n",
"-47\n",
"19\n",
"7\n",
"-14\n",
"8\n",
"24\n",
"36\n",
"-29\n",
"16\n",
"39\n",
"14\n",
"-23\n",
"27\n",
"-4\n",
"-20\n",
"-37\n",
"-16\n",
"42\n",
"-45\n",
"2\n",
"2\n",
"0\n",
"2\n",
"12\n",
"-19\n",
"2\n",
"12\n",
"0\n",
"0\n",
"4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"-7\n",
"0\n",
"-7\n",
"0\n",
"-7\n",
"-7\n",
"-5\n",
"-10\n",
"-3\n",
"-3\n",
"-3\n",
"-3\n",
"0\n",
"-1\n",
"-1\n",
"-1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"3\n",
"3\n",
"3\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In the spring of 2014, a student successfully passed the university and started living alone. The problem here is what to do with the supper. He decided to plan a supper for the next N days.
He wants to maximize the total happiness he gets in N days. Of course, the more delicious or favorite you eat, the higher your happiness.
His dinner options are two, either head to a nearby dining room or cook for himself.
The happiness you get in the cafeteria depends on the menu of the day. The menu changes daily, but there is only one type every day, and all the menus for N days have already been released. So he knows all the information that if you go to the cafeteria on day i (1 ≤ i ≤ N) you will get the happiness of Ci.
The happiness obtained by self-catering is the self-catering power at the start of self-catering multiplied by a constant P. The initial value of self-catering power is Q, which is -1 if you go to the restaurant every day, +1 if you cook yourself, and fluctuates at the end of the meal of the day.
Find the maximum sum of happiness for him.
Constraints
* 1 ≤ N ≤ 500,000
* 0 ≤ P ≤ 500,000
* | Q | ≤ 500,000
* | Ci | ≤ 500,000
Input
The input is given in the following format as N + 1 line.
N P Q
C1
C2
::
CN
* The first line is given three integers N, P, and Q, which are the number of days, the constant for calculating the happiness of self-catering, and the initial value of self-catering power.
* From the 2nd line to the N + 1st line, one integer is given, and the i + 1st line gives the happiness obtained when going to the cafeteria on the i day.
Output
Output the maximum value of happiness that can be taken in one line.
Examples
Input
1 1 1
2
Output
2
Input
3 2 1
3
3
3
Output
12
Input
3 1 -1
2
-3
2
Output
2
Input
3 1 -10
-10
-10
-10
Output
-27
### Input:
1 1 1
2
### Output:
2
### Input:
3 2 1
3
3
3
### Output:
12
### Code:
tmp = list(map(int,input().split()))
n,p,q = tmp[0],tmp[1],tmp[2]
cs = []
for i in range(n):
cs.append(int(input()))
ans = [sum(cs)]
difs = [p * (q-i) - cs[i] for i in range(n)]
difs.sort(reverse = True)
for i in range(n):
ans.append(ans[-1] + 2 * i * p + difs[i])
print(max(ans))
|
p02031 Parentheses Number_2994 | B: Parentheses Number
problem
Define the correct parenthesis string as follows:
* The empty string is the correct parenthesis string
* For the correct parenthesis string S, `(` S `)` is the correct parenthesis string
* For correct parentheses S, T ST is the correct parentheses
Here, the permutations are associated with the correct parentheses according to the following rules.
* When the i-th closing brace corresponds to the j-th opening brace, the i-th value in the sequence is j.
Given a permutation of length n, P = (p_1, p_2, $ \ ldots $, p_n), restore the corresponding parenthesis string.
However, if the parenthesis string corresponding to the permutation does not exist, output `: (`.
Input format
n
p_1 p_2 $ \ ldots $ p_n
The number of permutations n is given in the first row.
Permutations p_1, p_2, $ \ ldots $, p_i, $ \ ldots $, p_n are given in the second row, separated by blanks.
Constraint
* 1 \ leq n \ leq 10 ^ 5
* 1 \ leq p_i \ leq n
* All inputs are integers.
* P = (p_1, p_2, $ \ ldots $, p_n) is a permutation.
Output format
Output the parenthesized string corresponding to the permutation.
Print `: (` if such a parenthesis string does not exist.
Input example 1
2
twenty one
Output example 1
(())
Input example 2
Ten
1 2 3 4 5 6 7 8 9 10
Output example 2
() () () () () () () () () ()
Input example 3
3
3 1 2
Output example 3
:(
Example
Input
2
2 1
Output
(()) | n = int(input())
a = list(map(int,input().split()))
cnt = 0
ans = ''
st = list()
for x in a:
while cnt < x:
ans += '('
cnt += 1
st.append(cnt)
if st[-1] == x:
st.pop()
ans += ')'
else:
ans = ':('
break
print(ans)
| {
"input": [
"2\n2 1",
"2\n1 2",
"2\n2 -2",
"2\n2 -4",
"2\n2 -3",
"2\n2 -6",
"2\n2 -11",
"2\n2 -5",
"2\n2 -10",
"2\n2 -7",
"2\n2 -13",
"2\n2 -16",
"2\n2 -25",
"2\n2 -20",
"2\n2 -14",
"2\n2 -12",
"2\n2 -15",
"2\n2 -36",
"2\n2 -17",
"2\n2 -23",
"2\n2 -22",
"2\n2 -61",
"2\n2 -49",
"2\n2 -30",
"2\n2 -34",
"2\n2 -44",
"2\n2 -55",
"2\n2 -56",
"2\n2 -40",
"2\n2 -92",
"2\n2 -24",
"2\n2 -57",
"2\n2 -85",
"2\n2 -60",
"2\n2 -45",
"2\n2 -29",
"2\n2 -83",
"2\n2 -43",
"2\n2 -21",
"2\n2 -53",
"2\n2 -72",
"2\n2 -87",
"2\n2 -107",
"2\n2 -93",
"2\n2 -27",
"2\n2 -187",
"2\n2 -32",
"2\n2 -19",
"2\n2 -35",
"2\n2 -42",
"2\n2 -26",
"2\n2 -38",
"2\n2 -74",
"2\n2 -64",
"2\n2 -41",
"2\n2 -155",
"2\n2 -48",
"2\n2 -142",
"2\n2 -86",
"2\n2 -58",
"2\n2 -46",
"2\n2 -100",
"2\n2 -125",
"2\n2 -31",
"2\n2 -59",
"2\n2 -149",
"2\n2 -47",
"2\n2 -33",
"2\n2 -39",
"2\n2 -67",
"2\n2 -131",
"2\n2 -156",
"2\n2 -81",
"2\n2 -148",
"2\n2 -232",
"2\n2 -109",
"2\n2 -78",
"2\n2 -18",
"2\n2 -50",
"2\n2 -52",
"2\n2 -75",
"2\n2 -54",
"2\n2 -108",
"2\n2 -84",
"2\n2 -162",
"2\n2 -62",
"2\n2 -213",
"2\n2 -113",
"2\n2 -69",
"2\n2 -110",
"2\n2 -228",
"2\n2 -197",
"2\n2 -209",
"2\n2 -135",
"2\n2 -122",
"2\n2 -176",
"2\n2 -102",
"2\n2 -375",
"2\n2 -348",
"2\n2 -338",
"2\n2 -317"
],
"output": [
"(())",
"()()\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n",
":(\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
B: Parentheses Number
problem
Define the correct parenthesis string as follows:
* The empty string is the correct parenthesis string
* For the correct parenthesis string S, `(` S `)` is the correct parenthesis string
* For correct parentheses S, T ST is the correct parentheses
Here, the permutations are associated with the correct parentheses according to the following rules.
* When the i-th closing brace corresponds to the j-th opening brace, the i-th value in the sequence is j.
Given a permutation of length n, P = (p_1, p_2, $ \ ldots $, p_n), restore the corresponding parenthesis string.
However, if the parenthesis string corresponding to the permutation does not exist, output `: (`.
Input format
n
p_1 p_2 $ \ ldots $ p_n
The number of permutations n is given in the first row.
Permutations p_1, p_2, $ \ ldots $, p_i, $ \ ldots $, p_n are given in the second row, separated by blanks.
Constraint
* 1 \ leq n \ leq 10 ^ 5
* 1 \ leq p_i \ leq n
* All inputs are integers.
* P = (p_1, p_2, $ \ ldots $, p_n) is a permutation.
Output format
Output the parenthesized string corresponding to the permutation.
Print `: (` if such a parenthesis string does not exist.
Input example 1
2
twenty one
Output example 1
(())
Input example 2
Ten
1 2 3 4 5 6 7 8 9 10
Output example 2
() () () () () () () () () ()
Input example 3
3
3 1 2
Output example 3
:(
Example
Input
2
2 1
Output
(())
### Input:
2
2 1
### Output:
(())
### Input:
2
1 2
### Output:
()()
### Code:
n = int(input())
a = list(map(int,input().split()))
cnt = 0
ans = ''
st = list()
for x in a:
while cnt < x:
ans += '('
cnt += 1
st.append(cnt)
if st[-1] == x:
st.pop()
ans += ')'
else:
ans = ':('
break
print(ans)
|
p02174 Power Subsequences_2997 | Problem
Define a function $ f $ that starts with $ 1 $ and takes a sequence of finite lengths as an argument as follows.
$ \ displaystyle f (\\ {a_1, a_2, \ ldots, a_n \\}) = \ sum_ {i = 1} ^ n {a_i} ^ i $
Given a sequence of length $ N $, $ X = \\ {x_1, x_2, \ ldots, x_N \\} $, $ f (X) for all subsequences $ X'$ except empty columns. ') Find $ and output the sum of them divided by $ 998244353 $. However, the subsequence subsequences shall be renumbered starting from $ 1 $ while maintaining the relative order in the original sequence. Also, even if two subsequences are the same as columns, if they are taken out at different positions, they shall be counted separately.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 10 ^ 6 $
* $ 1 \ leq x_i \ leq 10 ^ 6 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ x_1 $ $ \ ldots $ $ x_N $
The first line is given the length $ N $. In the second row, the elements of the sequence $ X $ are given, separated by blanks.
Output
Find $ f (X') $ for all subsequences $ X'$ except empty columns, and divide the sum by $ 998244353 $ to output the remainder.
Examples
Input
3
1 2 3
Output
64
Input
5
100 200 300 400 500
Output
935740429 | #!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 998244353
def solve():
n = I()
x = LI()
ans = 0
for i in range(n):
xi = x[i]
ans += pow(2,n-i-1,mod)*xi*pow(xi+1,i,mod)
if ans >= mod:
ans %= mod
print(ans)
return
if __name__ == "__main__":
solve()
| {
"input": [
"5\n100 200 300 400 500",
"3\n1 2 3",
"5\n100 325 300 400 500",
"3\n1 4 3",
"5\n101 325 300 400 500",
"3\n2 4 3",
"5\n101 325 404 400 500",
"3\n3 4 3",
"5\n101 608 404 400 500",
"3\n4 4 3",
"5\n101 608 404 772 500",
"3\n4 4 1",
"5\n101 608 404 1494 500",
"3\n6 4 1",
"5\n001 608 404 1494 500",
"3\n6 6 1",
"5\n001 608 404 1494 525",
"3\n6 0 1",
"5\n001 608 404 900 525",
"3\n6 0 0",
"5\n000 608 404 900 525",
"5\n000 608 68 900 525",
"5\n000 980 68 900 525",
"3\n3 -2 0",
"5\n001 980 68 900 525",
"5\n011 980 68 900 525",
"3\n3 -1 -1",
"5\n011 1286 68 900 525",
"3\n0 -2 0",
"5\n011 1286 68 900 676",
"3\n0 -1 0",
"5\n011 1286 14 900 676",
"5\n010 1286 14 900 676",
"3\n1 -1 1",
"5\n010 1286 14 279 676",
"5\n011 1286 14 279 676",
"5\n011 1286 14 279 180",
"5\n011 1286 14 279 239",
"5\n010 1286 14 279 239",
"5\n010 1286 14 299 239",
"5\n010 1286 1 299 239",
"5\n010 1286 1 299 228",
"5\n010 1286 0 299 228",
"5\n010 1286 1 347 228",
"5\n010 1778 1 347 228",
"3\n-1 0 0",
"5\n010 536 1 347 228",
"5\n010 536 1 315 228",
"5\n010 536 2 315 228",
"3\n-1 -1 2",
"5\n011 536 2 315 228",
"3\n-1 -1 3",
"5\n011 616 2 315 228",
"5\n011 616 4 315 228",
"5\n011 616 4 315 343",
"5\n011 229 4 315 343",
"5\n011 115 4 315 343",
"3\n-4 -2 -1",
"5\n011 115 2 315 343",
"3\n-8 -2 -1",
"5\n011 115 2 315 110",
"3\n-6 -2 -1",
"5\n011 115 2 315 111",
"3\n-6 0 -1",
"5\n001 115 2 315 111",
"5\n001 115 2 280 111",
"5\n001 181 2 280 111",
"5\n001 181 2 280 011",
"5\n001 181 2 280 010",
"5\n001 181 2 280 110",
"5\n001 174 2 280 110",
"3\n-3 1 -1",
"5\n001 174 2 196 110",
"5\n001 174 0 196 110",
"3\n-12 2 -1",
"5\n011 174 0 196 110",
"3\n-24 2 -1",
"5\n111 174 0 196 110",
"3\n-24 1 -1",
"5\n111 174 0 34 110",
"3\n-15 1 -1",
"5\n101 174 0 34 110",
"3\n-27 1 -1",
"5\n101 174 -1 34 100",
"3\n-27 2 0",
"5\n101 54 -1 34 100",
"5\n101 29 -1 34 100",
"3\n-34 2 1",
"5\n101 29 -2 34 100",
"3\n-34 2 2",
"5\n101 29 -2 49 100",
"3\n-34 1 2",
"5\n101 29 -4 49 100",
"3\n-34 1 0",
"5\n101 29 -7 49 100",
"3\n-38 1 0",
"5\n101 29 -7 49 101",
"3\n-72 1 0",
"5\n101 4 -7 49 101",
"3\n-28 1 0",
"5\n101 4 -7 90 101",
"5\n101 1 -7 90 101"
],
"output": [
"935740429",
"64",
"936266429\n",
"92\n",
"936266445\n",
"96\n",
"94365292\n",
"100\n",
"96479868\n",
"104\n",
"831789230\n",
"60\n",
"969227571\n",
"68\n",
"969225971\n",
"112\n",
"44089359\n",
"28\n",
"387891758\n",
"24\n",
"387891742\n",
"124122334\n",
"128851198\n",
"16\n",
"128851214\n",
"128851374\n",
"12\n",
"134400990\n",
"4\n",
"914383624\n",
"0\n",
"913101232\n",
"913101216\n",
"8\n",
"290580434\n",
"290580450\n",
"813338847\n",
"622160914\n",
"622160898\n",
"525967486\n",
"525954902\n",
"303211168\n",
"303211152\n",
"428103827\n",
"440167667\n",
"-4\n",
"417165827\n",
"32628236\n",
"32628292\n",
"14\n",
"32628308\n",
"44\n",
"33366228\n",
"33366556\n",
"533155617\n",
"530536401\n",
"530221761\n",
"-12\n",
"530221433\n",
"-28\n",
"641417250\n",
"-20\n",
"410463283\n",
"-24\n",
"410463123\n",
"942388427\n",
"942545243\n",
"446862444\n",
"446780758\n",
"175254857\n",
"175234921\n",
"-8\n",
"729361707\n",
"729361635\n",
"-36\n",
"729361795\n",
"-84\n",
"729363395\n",
"-92\n",
"730025738\n",
"-56\n",
"730025578\n",
"-104\n",
"426757286\n",
"-96\n",
"426537446\n",
"426520646\n",
"-120\n",
"426520638\n",
"-106\n",
"435855138\n",
"-114\n",
"435855002\n",
"-132\n",
"435854138\n",
"-148\n",
"962378854\n",
"-284\n",
"962372054\n",
"-108\n",
"87520481\n",
"87520337\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem
Define a function $ f $ that starts with $ 1 $ and takes a sequence of finite lengths as an argument as follows.
$ \ displaystyle f (\\ {a_1, a_2, \ ldots, a_n \\}) = \ sum_ {i = 1} ^ n {a_i} ^ i $
Given a sequence of length $ N $, $ X = \\ {x_1, x_2, \ ldots, x_N \\} $, $ f (X) for all subsequences $ X'$ except empty columns. ') Find $ and output the sum of them divided by $ 998244353 $. However, the subsequence subsequences shall be renumbered starting from $ 1 $ while maintaining the relative order in the original sequence. Also, even if two subsequences are the same as columns, if they are taken out at different positions, they shall be counted separately.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 10 ^ 6 $
* $ 1 \ leq x_i \ leq 10 ^ 6 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ x_1 $ $ \ ldots $ $ x_N $
The first line is given the length $ N $. In the second row, the elements of the sequence $ X $ are given, separated by blanks.
Output
Find $ f (X') $ for all subsequences $ X'$ except empty columns, and divide the sum by $ 998244353 $ to output the remainder.
Examples
Input
3
1 2 3
Output
64
Input
5
100 200 300 400 500
Output
935740429
### Input:
5
100 200 300 400 500
### Output:
935740429
### Input:
3
1 2 3
### Output:
64
### Code:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 998244353
def solve():
n = I()
x = LI()
ans = 0
for i in range(n):
xi = x[i]
ans += pow(2,n-i-1,mod)*xi*pow(xi+1,i,mod)
if ans >= mod:
ans %= mod
print(ans)
return
if __name__ == "__main__":
solve()
|
p02317 Longest Increasing Subsequence_3000 | For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1 | N = int(input())
A = [int(input()) for _ in range(N)]
from bisect import bisect_left, bisect_right, bisect, insort_left, insort_right, insort
def solve(N,A):
lis = []
for i in range(N):
ind = bisect_left(lis,A[i])
if ind == len(lis):
lis.append(A[i])
else:
lis[ind] = A[i]
ans = len(lis)
return ans
print(solve(N,A))
| {
"input": [
"5\n5\n1\n3\n2\n4",
"3\n1\n1\n1",
"5\n5\n1\n3\n2\n6",
"3\n1\n1\n2",
"3\n1\n1\n0",
"5\n0\n2\n1\n2\n11",
"5\n5\n1\n3\n1\n6",
"3\n0\n1\n2",
"5\n5\n1\n2\n1\n6",
"3\n0\n2\n2",
"5\n5\n1\n2\n0\n6",
"5\n5\n1\n2\n-1\n6",
"5\n5\n1\n2\n-1\n10",
"5\n5\n1\n0\n-1\n10",
"5\n5\n1\n0\n0\n10",
"5\n5\n1\n0\n-1\n11",
"5\n5\n1\n0\n0\n11",
"5\n5\n1\n1\n0\n11",
"5\n5\n2\n1\n0\n11",
"5\n8\n2\n1\n0\n11",
"5\n8\n1\n1\n0\n11",
"5\n8\n1\n0\n0\n11",
"5\n2\n1\n0\n0\n11",
"5\n2\n1\n0\n1\n11",
"5\n5\n1\n0\n2\n4",
"3\n1\n2\n1",
"5\n5\n1\n3\n2\n8",
"5\n5\n1\n1\n1\n6",
"3\n0\n1\n3",
"5\n5\n1\n4\n0\n6",
"3\n0\n3\n2",
"5\n5\n0\n2\n0\n6",
"5\n5\n1\n1\n-1\n6",
"5\n5\n2\n2\n-1\n6",
"5\n5\n1\n0\n0\n16",
"5\n8\n1\n0\n-1\n11",
"5\n5\n1\n0\n0\n13",
"5\n5\n1\n1\n0\n2",
"5\n0\n2\n1\n0\n11",
"5\n8\n2\n1\n1\n11",
"5\n8\n1\n1\n1\n11",
"5\n8\n1\n0\n1\n11",
"5\n2\n1\n1\n0\n11",
"5\n2\n1\n0\n1\n19",
"5\n5\n2\n0\n2\n4",
"3\n1\n2\n0",
"5\n9\n1\n3\n2\n8",
"3\n1\n0\n0",
"5\n5\n1\n0\n1\n6",
"3\n0\n1\n1",
"5\n8\n1\n4\n0\n6",
"3\n0\n3\n3",
"5\n5\n0\n2\n-1\n6",
"5\n5\n0\n1\n-1\n6",
"5\n1\n2\n2\n-1\n6",
"5\n5\n1\n0\n0\n23",
"5\n8\n2\n0\n-1\n11",
"5\n5\n1\n0\n0\n24",
"5\n5\n0\n1\n0\n2",
"5\n0\n2\n1\n1\n11",
"5\n8\n2\n1\n1\n4",
"5\n11\n1\n1\n0\n11",
"5\n14\n1\n0\n1\n11",
"5\n2\n1\n1\n0\n15",
"5\n2\n1\n0\n0\n19",
"5\n5\n2\n0\n2\n6",
"3\n2\n0\n0",
"5\n9\n1\n6\n2\n8",
"3\n1\n0\n-1",
"3\n1\n1\n4",
"5\n11\n1\n4\n0\n6",
"5\n1\n2\n2\n-1\n5",
"5\n5\n1\n0\n0\n1",
"5\n8\n2\n0\n0\n11",
"5\n5\n1\n0\n0\n42",
"5\n5\n0\n1\n-1\n2",
"5\n1\n2\n1\n1\n11",
"5\n6\n2\n1\n1\n4",
"5\n11\n0\n1\n0\n11",
"5\n14\n1\n0\n0\n11",
"5\n2\n1\n1\n-1\n15",
"5\n1\n1\n0\n0\n19",
"5\n9\n2\n0\n2\n6",
"3\n2\n0\n1",
"5\n9\n1\n0\n2\n8",
"3\n1\n-1\n-1",
"3\n1\n1\n3",
"5\n11\n1\n3\n0\n6",
"5\n1\n2\n2\n-2\n5",
"5\n3\n1\n0\n0\n1",
"5\n14\n2\n0\n0\n11",
"5\n5\n1\n0\n0\n29",
"5\n5\n0\n1\n-1\n3",
"5\n6\n4\n1\n1\n4",
"5\n11\n0\n1\n1\n11",
"5\n14\n1\n0\n0\n1",
"5\n1\n1\n1\n-1\n15",
"5\n1\n1\n0\n0\n8",
"5\n9\n4\n0\n2\n6",
"3\n2\n0\n2",
"5\n9\n1\n0\n2\n12",
"3\n0\n-1\n-1"
],
"output": [
"3",
"1",
"3\n",
"2\n",
"1\n",
"4\n",
"3\n",
"3\n",
"3\n",
"2\n",
"3\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"3\n",
"2\n",
"3\n",
"3\n",
"2\n",
"3\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"2\n",
"3\n",
"2\n",
"3\n",
"3\n",
"2\n",
"3\n",
"1\n",
"3\n",
"2\n",
"3\n",
"2\n",
"3\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"2\n",
"3\n",
"2\n",
"2\n",
"3\n",
"1\n",
"3\n",
"1\n",
"2\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n",
"2\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
### Input:
5
5
1
3
2
4
### Output:
3
### Input:
3
1
1
1
### Output:
1
### Code:
N = int(input())
A = [int(input()) for _ in range(N)]
from bisect import bisect_left, bisect_right, bisect, insort_left, insort_right, insort
def solve(N,A):
lis = []
for i in range(N):
ind = bisect_left(lis,A[i])
if ind == len(lis):
lis.append(A[i])
else:
lis[ind] = A[i]
ans = len(lis)
return ans
print(solve(N,A))
|
p02462 Multi-Map_3003 | For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that multiple elements can have equivalent keys.
* insert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.
* get($key$): Print all values with the specified $key$.
* delete($key$): Delete all elements with the specified $key$.
* dump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.
Constraints
* $1 \leq q \leq 200,000$
* $1 \leq x \leq 1,000,000,000$
* $1 \leq $ length of $key$ $ \leq 20$
* $key$ consists of lower-case letters
* $L \leq R$ in lexicographic order
* The total number of elements printed by get operations does not exceed $500,000$
* The total number of elements printed by dump operations does not exceed $500,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $key$ $x$
or
1 $key$
or
2 $key$
or
3 $L$ $R$
where the first digits 0, 1, 2 and 3 represent insert, get, delete and dump operations.
Output
For each get operation, print the corresponding values in the order of insertions.
For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements in ascending order of the keys, in case of a tie, in the order of insertions.
Example
Input
10
0 blue 6
0 red 1
0 blue 4
0 white 5
1 red
1 blue
2 red
1 black
1 red
3 w z
Output
1
6
4
white 5 | # -*- coding: utf-8 -*-
"""
Dictionary - Multi-Map
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_8_D&lang=jp
"""
from bisect import insort, bisect_right, bisect_left
class Multi_map:
def __init__(self):
self.mm = dict()
self.lr = []
def insert(self, x, y):
if x in self.mm:
self.mm[x].append(y)
else:
self.mm[x] = [y]
insort(self.lr, x)
def get(self, x):
if x in self.mm and self.mm[x] != []:
print(*self.mm[x], sep='\n')
def delete(self, x):
if x in self.mm:
self.mm[x] = []
def dump(self, l, r):
lb = bisect_left(self.lr, l)
ub = bisect_right(self.lr, r)
for i in range(lb, ub):
k = self.lr[i]
for v in self.mm[k]:
print(f'{k} {v}')
mm = Multi_map()
for _ in range(int(input())):
op, x, y = (input() + ' 1').split()[:3]
if op == '0':
mm.insert(x, int(y))
elif op == '1':
mm.get(x)
elif op == '2':
mm.delete(x)
else:
mm.dump(x, y)
| {
"input": [
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n2 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 xhite 5\n1 red\n2 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n2 blue\n2 sed\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 wihte 5\n1 red\n2 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 hwite 10\n1 red\n2 blue\n2 sed\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 wihte 5\n1 rfd\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 elub 4\n0 white 5\n1 red\n1 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 2\n0 blue 4\n0 white 10\n1 red\n2 blue\n2 sed\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 elub 4\n0 white 5\n1 erd\n1 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 0\n0 eulb 4\n0 xhite 5\n1 red\n2 blue\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 2\n0 blue 4\n0 white 10\n1 der\n2 blue\n2 sed\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 6\n0 whhte 5\n1 rfd\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 4\n0 white 5\n1 erd\n1 blue\n1 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 0\n0 eukb 4\n0 xhite 5\n1 rde\n2 blue\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 3\n0 white 5\n1 erd\n1 blue\n1 red\n1 black\n2 red\n3 w z",
"10\n0 beul 6\n0 der 1\n0 bule 6\n0 whhte 5\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 0\n0 eulb 4\n0 etiwi 10\n1 red\n2 blue\n1 des\n1 kcalb\n1 der\n6 w z",
"10\n0 beul 6\n0 der 1\n0 cule 6\n0 whhte 9\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 der 1\n0 cule 6\n0 xhhte 9\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 cule 6\n0 xhhte 9\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 rdd\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 2\n1 red\n2 blue\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n2 red\n2 blue\n2 qed\n2 black\n1 der\n3 v z",
"10\n0 blue 11\n0 red 2\n0 elub 4\n0 white 5\n1 erd\n1 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 alue 6\n0 red 1\n0 alue 4\n0 white 3\n1 red\n2 bluf\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 2\n0 whitd 5\n1 erd\n1 blue\n1 red\n1 black\n2 red\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 6\n0 xhhte 3\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 0\n0 white 10\n1 red\n1 blue\n2 red\n1 black\n2 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 vhite 5\n1 red\n2 blue\n2 rec\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 2\n0 blue 4\n0 ethiw 5\n1 red\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 whjte 10\n1 dre\n2 blue\n2 sed\n1 black\n1 red\n3 w z",
"10\n0 blue 11\n0 red 2\n0 elub 4\n0 white 5\n1 erd\n1 blue\n2 red\n1 black\n0 red\n3 w z",
"10\n0 alue 6\n0 red 1\n0 alue 4\n0 white 3\n1 rde\n2 bluf\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 3\n0 white 5\n1 erd\n1 alue\n1 red\n2 black\n1 red\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 6\n0 xhhte 2\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 9\n0 xhhtf 9\n1 rcf\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 4\n0 wihte 3\n2 rgd\n1 eulb\n2 sde\n2 black\n1 der\n3 w z",
"10\n0 bkue 6\n0 red 0\n0 eukb 4\n0 xhite 7\n1 rde\n2 blue\n2 red\n1 black\n1 der\n3 w {",
"10\n0 blue 6\n0 red 2\n0 elub 3\n0 white 5\n1 erd\n1 alue\n1 red\n2 black\n1 rfd\n3 w z",
"10\n0 blue 6\n0 der 1\n0 eulb 4\n0 etiwi 10\n1 red\n1 blue\n1 des\n2 kcalb\n1 der\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 6\n0 xhhte 1\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 8\n2 red\n2 blue\n1 qdd\n2 black\n1 der\n3 v z",
"10\n0 bkue 6\n0 red 0\n0 eukb 4\n0 xhite 12\n1 rde\n2 blue\n2 red\n1 black\n1 der\n3 w {",
"10\n0 blue 12\n0 red 2\n0 elub 3\n0 white 5\n1 erd\n1 blue\n1 rde\n1 black\n2 dre\n3 w z",
"10\n0 blue 6\n0 der 1\n0 eulb 4\n0 etiwi 10\n1 red\n1 blue\n1 des\n2 kcalb\n2 der\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 6\n0 xhhue 1\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blud 6\n0 red 1\n0 blue 4\n0 white 6\n2 red\n2 blue\n2 qed\n2 bladk\n2 der\n3 w z",
"10\n0 blue 12\n0 red 2\n0 elub 3\n0 white 4\n1 erd\n1 blue\n1 rde\n1 calck\n2 dre\n3 w z",
"10\n0 blue 1\n0 red -1\n0 eubl 10\n0 iwite 10\n1 red\n2 blue\n1 des\n1 balck\n1 der\n6 w z",
"10\n0 blue 1\n0 red -2\n0 eubl 10\n0 iwite 10\n1 red\n2 blue\n1 des\n1 balck\n1 der\n6 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 white 5\n1 red\n1 blue\n2 red\n0 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 whitd 10\n1 der\n2 blue\n2 sed\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 6\n0 whhte 5\n1 rfd\n1 blue\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 9\n0 red 2\n0 elub 4\n0 white 5\n1 erd\n1 blue\n1 red\n1 black\n1 red\n3 w z",
"10\n0 beul 6\n0 der 1\n0 bule 6\n0 whthe 5\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 der 1\n0 cule 6\n0 wthhe 9\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 cer 1\n0 eluc 6\n0 xihte 9\n1 rfd\n2 eulb\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n1 blue\n2 red\n1 black\n2 red\n3 x z",
"10\n0 blue 6\n0 red 1\n0 clue 4\n0 wgite 10\n1 red\n2 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 elub 3\n0 white 5\n1 red\n1 blue\n2 rfd\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 4\n0 xihte 5\n2 rgd\n1 eulb\n2 sed\n2 black\n1 der\n3 w z",
"10\n0 beul 6\n0 red 1\n0 bule 6\n0 xhhte 5\n1 rfd\n2 eulb\n2 red\n2 blakc\n1 der\n3 w z",
"10\n0 blue 12\n0 red 2\n0 elub 3\n0 white 5\n1 erd\n1 blue\n1 red\n2 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 2\n0 whitd 5\n1 erd\n2 blue\n1 red\n1 black\n2 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 0\n0 wihte 10\n1 red\n1 blue\n2 red\n1 black\n2 red\n3 w z",
"10\n0 blue 6\n0 red 2\n0 blue 4\n0 wihte 5\n1 red\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 aeul 6\n0 red 1\n0 bmue 4\n0 white 8\n1 red\n2 bluf\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 11\n0 red 2\n0 elub 4\n0 white 5\n1 erd\n1 blue\n1 red\n1 black\n0 red\n3 w z",
"10\n0 blue 6\n0 red 0\n0 eukb 4\n0 xhite 5\n1 red\n2 blue\n1 red\n2 black\n1 der\n3 w y",
"10\n0 blue 6\n0 red 1\n0 bule 6\n0 whhtd 5\n1 rfd\n2 eulb\n2 red\n2 black\n1 fer\n3 w z",
"10\n0 blue 6\n0 red 2\n0 elub 2\n0 whitd 5\n1 erd\n1 blue\n1 red\n1 blacj\n0 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 4\n0 wihte 4\n2 rgd\n1 eulb\n2 sde\n2 black\n1 der\n3 w z",
"10\n0 bkue 6\n0 red 0\n0 eukb 4\n0 xhite 4\n1 rde\n2 blue\n2 red\n1 black\n1 der\n3 w {",
"10\n0 blue 6\n0 der 1\n0 eulb 4\n0 etiwi 10\n1 red\n1 eulb\n1 des\n2 kcalb\n1 der\n3 w z",
"10\n0 eulb 6\n0 red 1\n0 blue 4\n0 white 0\n1 red\n2 bmuf\n2 des\n1 black\n1 der\n3 w z",
"10\n0 blue 3\n0 red 0\n0 blue 4\n0 white 5\n1 red\n2 alud\n1 red\n0 black\n0 red\n3 w z",
"10\n0 blue 6\n0 red 4\n0 eulb 1\n0 euiwi 10\n1 red\n2 blue\n1 des\n0 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 0\n0 white 9\n1 red\n1 blue\n2 red\n1 black\n2 red\n0 w z",
"10\n0 blue 6\n0 red 3\n0 elub 3\n0 white 5\n1 erd\n1 alue\n1 red\n0 bldak\n1 rfd\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 white 5\n1 red\n2 blue\n2 red\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n2 blue\n2 sed\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 wihte 5\n1 red\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 4\n0 wihte 5\n1 rfd\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 bule 4\n0 wihte 5\n2 rfd\n1 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 red\n1 black\n0 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 bluf\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 red\n1 blue\n2 red\n2 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 white 5\n1 red\n2 blue\n2 red\n0 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 5\n1 red\n2 blue\n2 qed\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 eulb 4\n0 xhite 5\n1 red\n2 blue\n2 red\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 etihw 5\n1 red\n2 eulb\n2 red\n2 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 white 10\n1 der\n2 blue\n2 sed\n1 black\n1 red\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 wihte 5\n1 red\n1 eulb\n2 red\n2 black\n0 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 hwite 10\n1 red\n2 blue\n1 sed\n1 black\n1 der\n3 w z",
"10\n0 blue 6\n0 red 1\n0 blue 4\n0 wihte 5\n1 qfd\n1 eulb\n2 red\n2 black\n1 der\n3 w z"
],
"output": [
"1\n6\n4\nwhite 5",
"1\nwhite 5\n",
"1\n6\n4\nwhite 10\n",
"1\nwhite 10\n",
"1\nxhite 5\n",
"1\n1\nwhite 10\n",
"1\nwihte 5\n",
"1\n",
"wihte 5\n",
"1\n6\nwhite 5\n",
"2\nwhite 10\n",
"6\nwhite 5\n",
"0\nxhite 5\n",
"white 10\n",
"whhte 5\n",
"6\n2\n2\nwhite 5\n",
"xhite 5\n",
"6\n2\nwhite 5\n",
"1\nwhhte 5\n",
"0\n",
"1\nwhhte 9\n",
"1\nxhhte 9\n",
"xhhte 9\n",
"1\n1\nwhite 5\n",
"1\nwhite 2\n",
"white 5\n",
"11\nwhite 5\n",
"1\nwhite 3\n",
"6\n2\nwhitd 5\n",
"xhhte 3\n",
"1\n6\n0\nwhite 10\n",
"1\n1\n",
"2\n",
"1\nwhjte 10\n",
"11\n",
"white 3\n",
"2\n2\nwhite 5\n",
"xhhte 2\n",
"xhhtf 9\n",
"wihte 3\n",
"xhite 7\n",
"2\nwhite 5\n",
"6\n1\n",
"xhhte 1\n",
"white 8\n",
"xhite 12\n",
"12\nwhite 5\n",
"6\n",
"xhhue 1\n",
"white 6\n",
"12\nwhite 4\n",
"-1\n",
"-2\n",
"1\n6\n",
"1\nwhitd 10\n",
"6\nwhhte 5\n",
"9\n2\n2\nwhite 5\n",
"1\nwhthe 5\n",
"1\nwthhe 9\n",
"xihte 9\n",
"1\n6\n4\n",
"1\nwgite 10\n",
"1\n6\n1\nwhite 5\n",
"xihte 5\n",
"xhhte 5\n",
"12\n2\n2\nwhite 5\n",
"2\nwhitd 5\n",
"1\n6\n0\nwihte 10\n",
"2\nwihte 5\n",
"1\nwhite 8\n",
"11\n2\n",
"0\n0\nxhite 5\n",
"whhtd 5\n",
"6\n2\n",
"wihte 4\n",
"xhite 4\n",
"4\n1\n",
"1\nwhite 0\n",
"0\n0\n",
"4\n",
"1\n6\n0\n",
"3\n",
"1\nwhite 5\n",
"1\nwhite 5\n",
"1\nwhite 5\n",
"1\nwhite 5\n",
"1\nwhite 10\n",
"1\nwihte 5\n",
"wihte 5\n",
"wihte 5\n",
"1\n",
"1\nwhite 5\n",
"1\n6\n4\nwhite 10\n",
"1\n",
"1\nwhite 5\n",
"1\nxhite 5\n",
"1\n",
"1\nwhite 10\n",
"1\n",
"1\n",
"wihte 5\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For a dictionary $M$ that stores elements formed by a pair of a string key and an integer value, perform a sequence of the following operations. Note that multiple elements can have equivalent keys.
* insert($key$, $x$): Insert an element formed by a pair of $key$ and $x$ to $M$.
* get($key$): Print all values with the specified $key$.
* delete($key$): Delete all elements with the specified $key$.
* dump($L$, $R$): Print all elements formed by a pair of the key and the value such that the key is greater than or equal to $L$ and less than or equal to $R$ in lexicographic order.
Constraints
* $1 \leq q \leq 200,000$
* $1 \leq x \leq 1,000,000,000$
* $1 \leq $ length of $key$ $ \leq 20$
* $key$ consists of lower-case letters
* $L \leq R$ in lexicographic order
* The total number of elements printed by get operations does not exceed $500,000$
* The total number of elements printed by dump operations does not exceed $500,000$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given by
0 $key$ $x$
or
1 $key$
or
2 $key$
or
3 $L$ $R$
where the first digits 0, 1, 2 and 3 represent insert, get, delete and dump operations.
Output
For each get operation, print the corresponding values in the order of insertions.
For each dump operation, print the corresponding elements formed by a pair of the key and the value. For the dump operation, print the elements in ascending order of the keys, in case of a tie, in the order of insertions.
Example
Input
10
0 blue 6
0 red 1
0 blue 4
0 white 5
1 red
1 blue
2 red
1 black
1 red
3 w z
Output
1
6
4
white 5
### Input:
10
0 blue 6
0 red 1
0 blue 4
0 white 5
1 red
1 blue
2 red
1 black
1 red
3 w z
### Output:
1
6
4
white 5
### Input:
10
0 blue 6
0 red 1
0 blue 4
0 white 5
1 red
2 blue
2 red
1 black
1 red
3 w z
### Output:
1
white 5
### Code:
# -*- coding: utf-8 -*-
"""
Dictionary - Multi-Map
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_8_D&lang=jp
"""
from bisect import insort, bisect_right, bisect_left
class Multi_map:
def __init__(self):
self.mm = dict()
self.lr = []
def insert(self, x, y):
if x in self.mm:
self.mm[x].append(y)
else:
self.mm[x] = [y]
insort(self.lr, x)
def get(self, x):
if x in self.mm and self.mm[x] != []:
print(*self.mm[x], sep='\n')
def delete(self, x):
if x in self.mm:
self.mm[x] = []
def dump(self, l, r):
lb = bisect_left(self.lr, l)
ub = bisect_right(self.lr, r)
for i in range(lb, ub):
k = self.lr[i]
for v in self.mm[k]:
print(f'{k} {v}')
mm = Multi_map()
for _ in range(int(input())):
op, x, y = (input() + ' 1').split()[:3]
if op == '0':
mm.insert(x, int(y))
elif op == '1':
mm.get(x)
elif op == '2':
mm.delete(x)
else:
mm.dump(x, y)
|
1003_E. Tree Constructing_3013 | You are given three integers n, d and k.
Your task is to construct an undirected tree on n vertices with diameter d and degree of each vertex at most k, or say that it is impossible.
An undirected tree is a connected undirected graph with n - 1 edges.
Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree.
Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex u it is the number of edges (u, v) that belong to the tree, where v is any other vertex of a tree).
Input
The first line of the input contains three integers n, d and k (1 ≤ n, d, k ≤ 4 ⋅ 10^5).
Output
If there is no tree satisfying the conditions above, print only one word "NO" (without quotes).
Otherwise in the first line print "YES" (without quotes), and then print n - 1 lines describing edges of a tree satisfying the conditions above. Vertices of the tree must be numbered from 1 to n. You can print edges and vertices connected by an edge in any order. If there are multiple answers, print any of them.1
Examples
Input
6 3 3
Output
YES
3 1
4 1
1 2
5 2
2 6
Input
6 2 3
Output
NO
Input
10 4 3
Output
YES
2 9
2 10
10 3
3 1
6 10
8 2
4 3
5 6
6 7
Input
8 5 3
Output
YES
2 5
7 2
3 7
3 1
1 6
8 7
4 3 | def main():
n, d, k = map(int, input().split())
r, odd = divmod(d, 2)
k -= 1
cap = d + 1 if k == 1 else 1
if k > 1:
cap = 2 * (k ** (r + 1) - 1) // (k - 1) if odd else 1 + (k + 1) * (k ** r - 1) // (k - 1)
if n == 1 or k < 1 < n - 1 or k == 1 and d != n - 1 or d >= n or k > 1 and not d < n <= cap:
print('NO')
return
def dfs(parent, depth):
stack = []
for _ in range(k - 1):
child = rest.pop()
res.append('%s %s' % (parent, child))
if depth:
stack.append((child, depth))
while stack:
parent, depth = stack.pop()
depth -= 1
for _ in range(k):
child = rest.pop()
res.append('%s %s' % (parent, child))
if depth:
stack.append((child, depth))
res = ['YES']
for pc in enumerate(range(2, d + 2), 1):
res.append('%d %d' % pc)
rest = list(range(n, d + 1, -1))
try:
for p in range(r + 1, r + odd + 2):
dfs(p, r - 1)
for de, p, q in zip(range(r - 2, -1, -1), range(r, 1, -1), range(r + odd + 2, d + 1)):
dfs(p, de)
dfs(q, de)
except IndexError:
pass
print('\n'.join(res))
if __name__ == '__main__':
main()
| {
"input": [
"8 5 3\n",
"6 3 3\n",
"10 4 3\n",
"6 2 3\n",
"400000 3 199999\n",
"20 6 3\n",
"5 5 3\n",
"2 3 1\n",
"10 9 1\n",
"7 5 2\n",
"2 1 4\n",
"3 2 1\n",
"1 1 1\n",
"2 2 1\n",
"2 3 3\n",
"6 4 2\n",
"7 4 3\n",
"2 10 1\n",
"6 5 3\n",
"15 5 3\n",
"5 4 2\n",
"6 5 2\n",
"5 4 3\n",
"2 1 3\n",
"2 1 15\n",
"2 1 2\n",
"400000 2 399998\n",
"2 1 1\n",
"14 5 3\n",
"6 4 3\n",
"2 11 1\n",
"4 3 1\n",
"6 5 1\n",
"9 8 1\n",
"22 6 3\n",
"5 5 2\n",
"4 543 7\n",
"7 5 3\n",
"8 3 3\n",
"3 1 1\n",
"400000 400000 400000\n",
"21 6 3\n",
"3 1 3\n",
"7 4 2\n",
"7 6 1\n",
"6 3 3\n",
"5 4 1\n",
"26 5 4\n",
"200000 100000 2\n",
"20 6 0\n",
"10 9 2\n",
"6 4 4\n",
"2 1 5\n",
"9 8 2\n",
"10 5 3\n",
"6 3 6\n",
"8 5 6\n",
"12 5 3\n",
"3 2 3\n",
"12 7 3\n",
"5 5 0\n",
"2 3 0\n",
"7 8 2\n",
"2 2 4\n",
"0 2 1\n",
"1 1 2\n",
"2 2 0\n",
"2 3 5\n",
"12 4 3\n",
"2 10 2\n",
"6 7 3\n",
"15 4 3\n",
"7 5 1\n",
"10 4 0\n",
"1 1 3\n",
"0 1 15\n",
"400000 2 274303\n",
"14 3 3\n",
"7 2 3\n",
"0 11 1\n",
"6 3 1\n",
"37 6 3\n",
"8 5 2\n",
"4 814 7\n",
"8 3 0\n",
"0 2 2\n",
"39 6 3\n",
"3 0 3\n",
"7 0 2\n",
"7 3 1\n",
"1 4 1\n",
"26 5 2\n",
"200000 101000 2\n",
"2 4 3\n",
"23 6 0\n",
"5 5 1\n",
"10 10 2\n",
"7 16 2\n",
"2 3 2\n",
"0 4 1\n",
"4 1 2\n",
"1 3 5\n",
"6 4 0\n",
"3 10 2\n"
],
"output": [
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n3 8\n",
"YES\n1 2\n2 3\n3 4\n2 5\n3 6\n",
"YES\n1 2\n2 3\n3 4\n4 5\n2 6\n3 7\n7 8\n7 9\n4 10\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n2 8\n3 9\n9 10\n9 11\n4 12\n12 13\n13 14\n13 15\n12 16\n16 17\n16 18\n5 19\n19 20\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1 2\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n2 6\n3 7\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n",
"YES\n1 2\n2 3\n3 4\n4 5\n",
"YES\n1 2\n",
"YES\n1 2\n",
"YES\n1 2\n",
"NO\n",
"YES\n1 2\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n3 8\n8 9\n8 10\n4 11\n11 12\n11 13\n5 14\n",
"YES\n1 2\n2 3\n3 4\n4 5\n2 6\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n2 8\n3 9\n9 10\n9 11\n4 12\n12 13\n13 14\n13 15\n12 16\n16 17\n16 18\n5 19\n19 20\n19 21\n6 22\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n2 8\n3 9\n9 10\n9 11\n4 12\n12 13\n13 14\n13 15\n12 16\n16 17\n16 18\n5 19\n19 20\n19 21\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n2 5\n3 6\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n2 8\n3 9\n9 10\n9 11\n9 12\n3 13\n13 14\n13 15\n13 16\n4 17\n17 18\n17 19\n17 20\n4 21\n21 22\n21 23\n21 24\n5 25\n5 26\n",
"NO\n",
"NO\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 9\n9 10\n",
"YES\n1 2\n2 3\n3 4\n4 5\n2 6\n",
"YES\n1 2\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n8 9\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n3 8\n8 9\n8 10\n",
"YES\n1 2\n2 3\n3 4\n2 5\n2 6\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n2 8\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n2 7\n3 8\n8 9\n8 10\n4 11\n11 12\n",
"YES\n1 2\n2 3\n",
"YES\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n7 8\n2 9\n3 10\n10 11\n10 12\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given three integers n, d and k.
Your task is to construct an undirected tree on n vertices with diameter d and degree of each vertex at most k, or say that it is impossible.
An undirected tree is a connected undirected graph with n - 1 edges.
Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree.
Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex u it is the number of edges (u, v) that belong to the tree, where v is any other vertex of a tree).
Input
The first line of the input contains three integers n, d and k (1 ≤ n, d, k ≤ 4 ⋅ 10^5).
Output
If there is no tree satisfying the conditions above, print only one word "NO" (without quotes).
Otherwise in the first line print "YES" (without quotes), and then print n - 1 lines describing edges of a tree satisfying the conditions above. Vertices of the tree must be numbered from 1 to n. You can print edges and vertices connected by an edge in any order. If there are multiple answers, print any of them.1
Examples
Input
6 3 3
Output
YES
3 1
4 1
1 2
5 2
2 6
Input
6 2 3
Output
NO
Input
10 4 3
Output
YES
2 9
2 10
10 3
3 1
6 10
8 2
4 3
5 6
6 7
Input
8 5 3
Output
YES
2 5
7 2
3 7
3 1
1 6
8 7
4 3
### Input:
8 5 3
### Output:
YES
1 2
2 3
3 4
4 5
5 6
2 7
3 8
### Input:
6 3 3
### Output:
YES
1 2
2 3
3 4
2 5
3 6
### Code:
def main():
n, d, k = map(int, input().split())
r, odd = divmod(d, 2)
k -= 1
cap = d + 1 if k == 1 else 1
if k > 1:
cap = 2 * (k ** (r + 1) - 1) // (k - 1) if odd else 1 + (k + 1) * (k ** r - 1) // (k - 1)
if n == 1 or k < 1 < n - 1 or k == 1 and d != n - 1 or d >= n or k > 1 and not d < n <= cap:
print('NO')
return
def dfs(parent, depth):
stack = []
for _ in range(k - 1):
child = rest.pop()
res.append('%s %s' % (parent, child))
if depth:
stack.append((child, depth))
while stack:
parent, depth = stack.pop()
depth -= 1
for _ in range(k):
child = rest.pop()
res.append('%s %s' % (parent, child))
if depth:
stack.append((child, depth))
res = ['YES']
for pc in enumerate(range(2, d + 2), 1):
res.append('%d %d' % pc)
rest = list(range(n, d + 1, -1))
try:
for p in range(r + 1, r + odd + 2):
dfs(p, r - 1)
for de, p, q in zip(range(r - 2, -1, -1), range(r, 1, -1), range(r + odd + 2, d + 1)):
dfs(p, de)
dfs(q, de)
except IndexError:
pass
print('\n'.join(res))
if __name__ == '__main__':
main()
|
1070_D. Garbage Disposal_3020 | Enough is enough. Too many times it happened that Vasya forgot to dispose of garbage and his apartment stank afterwards. Now he wants to create a garbage disposal plan and stick to it.
For each of next n days Vasya knows a_i — number of units of garbage he will produce on the i-th day. Each unit of garbage must be disposed of either on the day it was produced or on the next day. Vasya disposes of garbage by putting it inside a bag and dropping the bag into a garbage container. Each bag can contain up to k units of garbage. It is allowed to compose and drop multiple bags into a garbage container in a single day.
Being economical, Vasya wants to use as few bags as possible. You are to compute the minimum number of bags Vasya needs to dispose of all of his garbage for the given n days. No garbage should be left after the n-th day.
Input
The first line of the input contains two integers n and k (1 ≤ n ≤ 2⋅10^5, 1 ≤ k ≤ 10^9) — number of days to consider and bag's capacity. The second line contains n space separated integers a_i (0 ≤ a_i ≤ 10^9) — the number of units of garbage produced on the i-th day.
Output
Output a single integer — the minimum number of bags Vasya needs to dispose of all garbage. Each unit of garbage should be disposed on the day it was produced or on the next day. No garbage can be left after the n-th day. In a day it is allowed to compose and drop multiple bags.
Examples
Input
3 2
3 2 1
Output
3
Input
5 1
1000000000 1000000000 1000000000 1000000000 1000000000
Output
5000000000
Input
3 2
1 0 1
Output
2
Input
4 4
2 8 4 1
Output
4 | import sys
n, k = tuple(int(i) for i in sys.stdin.readline().split())
a = tuple(int(i) for i in sys.stdin.readline().split())
assert len(a) == n
bags = 0
r = 0
for ai in a:
leftovers = (r > 0)
q, r = divmod(ai + r, k)
if q == 0:
if leftovers:
bags += 1
r = 0
else:
bags += q
if r > 0:
bags += 1
print(bags)
| {
"input": [
"3 2\n1 0 1\n",
"4 4\n2 8 4 1\n",
"3 2\n3 2 1\n",
"5 1\n1000000000 1000000000 1000000000 1000000000 1000000000\n",
"3 10\n5 5 0\n",
"1 1\n1\n",
"4 4\n3 6 2 3\n",
"1 10\n1\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 17 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 5 2 17 4 7 9 11 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 12 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 6 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"5 2\n3 1 0 3 1\n",
"3 10\n0 5 5\n",
"161 5\n17 0 3 8 4 8 8 14 15 7 5 17 2 5 7 1 3 16 5 13 6 15 12 15 18 1 0 13 19 18 4 11 13 7 7 1 3 15 15 10 4 14 3 3 10 10 12 1 2 14 4 1 8 19 0 11 2 11 16 7 4 4 17 16 9 17 6 10 5 16 4 6 7 0 1 9 10 15 12 19 17 5 4 4 16 19 7 9 17 11 1 0 0 13 14 4 15 10 4 7 15 13 6 3 8 14 15 13 19 17 7 19 10 5 10 17 16 2 5 9 16 16 9 3 6 8 19 0 1 18 6 17 3 17 6 12 6 16 6 6 3 14 5 16 15 9 0 12 10 5 4 8 16 15 11 14 6 13 6 3 1\n",
"2 3\n2 7\n",
"1 10\n0\n",
"7 16\n44 3 9 12 3 1 24\n",
"1 1\n10\n",
"1 10\n2\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 10 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 0 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 6 16 13 5 5 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 5 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"1 1\n0\n",
"3 2\n1 0 0\n",
"110 2\n6 14 13 14 2 17 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 11 15 0 19 19 19 15 19 1 18 4 16 4 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 15 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 4 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 5 14 12 13 17 3 12 6 8 18 14 17 2 14 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 4 3 5 17 4 3 3 14 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 11 18 11 15\n",
"3 2\n0 0 1\n",
"4 5\n5 5 5 5\n",
"3 10\n5 0 5\n",
"3 6\n2 3 3\n",
"3 10\n2 5 0\n",
"1 1\n2\n",
"4 2\n3 6 2 3\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 17 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 5 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 12 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 6 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"5 2\n3 1 0 5 1\n",
"1 12\n0\n",
"7 13\n44 3 9 12 3 1 24\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 10 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 0 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 6 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 5 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 11 15 0 19 19 19 15 19 1 18 4 16 4 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 15 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 4 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 14 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 4 3 5 17 4 3 3 14 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 11 18 11 15\n",
"3 1\n3 2 1\n",
"5 1\n1010000000 1000000000 1000000000 1000000000 1000000000\n",
"4 2\n3 12 2 3\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 17 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 5 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 12 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 10 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 0 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 6 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 11 15 0 19 19 19 15 19 1 18 4 16 4 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 4 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 14 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 14 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 11 18 11 15\n",
"3 1\n6 2 1\n",
"5 1\n0010000000 1000000000 1000000000 1000000000 1000000000\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 17 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 5 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 10 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 0 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 19 19 15 19 1 18 4 16 4 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 4 8 8 4 19 19 17 11\n",
"5 1\n0010000000 1000000000 1000000000 1000000000 1000001000\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 5 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 0 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 14 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"5 1\n0010100000 1000000000 1000000000 1000000000 1000001000\n",
"4 2\n0 0 2 3\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 4 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 19 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"5 1\n0010100000 1000000000 1100000000 1000000000 1000001000\n",
"4 2\n0 0 4 3\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 8 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 1 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 19 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 2 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"5 1\n0010100000 1000100000 1100000000 1000000000 1000001000\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 3 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 7 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 1 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 10 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 22 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 2 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"5 1\n0010100000 1000100000 1100000000 1000000010 1000001000\n",
"110 2\n6 14 13 14 2 18 2 11 4 9 17 1 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 10 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 8 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 22 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 2 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"5 1\n0010100000 1000100000 1100000000 1000000011 1000001000\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 3 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 28 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 7 9 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 11 6 2 17 18 3 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 0 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 8 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 9 17 1 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 10 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 11 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 8 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 22 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 2 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 21 3 1 14 18 11 15\n",
"5 1\n0010100000 1000100000 1100000000 1000000011 1000101000\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 11 6 2 17 18 3 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 0 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 8 6 5 17 6 1 5 11 12 4 8 14 3 2 18 18 10\n",
"110 2\n6 14 13 14 2 18 2 11 4 9 17 1 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 10 19 15 19 1 18 4 16 3 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 11 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 25 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"159 2\n14 7 11 8 0 5 16 0 8 17 8 10 7 12 7 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 22 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 2 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 21 3 1 14 18 11 15\n",
"5 1\n0010100000 1000100000 1100000000 1000000011 1000101100\n",
"1 6\n1\n",
"1 10\n3\n",
"3 12\n5 0 5\n",
"3 6\n2 5 3\n",
"4 4\n2 8 8 1\n",
"3 17\n2 5 0\n",
"1 2\n2\n",
"1 11\n1\n",
"5 2\n3 1 0 7 1\n",
"1 10\n4\n",
"4 4\n0 8 8 1\n",
"3 17\n2 6 0\n",
"1 4\n2\n",
"4 2\n0 12 2 3\n",
"5 2\n4 1 0 7 1\n",
"1 10\n6\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 14 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 14 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"4 4\n1 8 8 1\n",
"3 1\n5 2 1\n",
"3 17\n2 9 0\n",
"1 4\n3\n",
"4 2\n0 5 2 3\n",
"5 2\n4 1 0 4 1\n",
"1 19\n6\n",
"110 2\n6 14 13 14 2 18 2 11 4 16 17 4 14 9 2 10 5 10 13 8 14 11 7 14 12 10 6 15 0 19 19 19 15 19 1 18 4 16 4 13 2 18 0 11 17 14 9 1 11 16 9 14 1 8 16 9 8 17 10 16 6 18 8 3 18 14 15 15 1 23 14 14 6 11 11 8 9 7 13 14 19 14 17 3 10 13 19 0 13 6 17 6 4 6 16 15 10 3 18 10 18 4 0 8 8 4 19 19 17 11\n",
"4 4\n1 8 8 2\n",
"3 17\n3 9 0\n",
"5 2\n4 1 0 4 0\n",
"1 7\n6\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 9 6 2 17 18 2 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 10 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"159 2\n14 7 11 8 0 5 16 0 4 17 8 10 7 12 6 0 15 4 12 15 10 8 9 13 5 11 2 8 1 1 1 8 17 10 15 15 4 6 4 9 11 11 18 11 5 10 14 8 19 18 2 14 14 18 1 7 14 12 4 6 9 3 19 10 6 19 16 1 3 14 12 13 17 3 12 6 8 18 14 17 2 24 2 3 4 7 0 11 0 13 12 13 0 18 18 6 4 8 12 13 2 3 1 1 8 1 3 14 3 17 1 18 12 14 2 3 5 17 4 3 3 5 7 1 13 10 6 4 12 3 4 11 3 13 4 3 18 10 15 12 0 19 19 6 18 17 7 1 11 18 12 13 13 3 1 14 18 11 15\n",
"3 17\n3 9 1\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 3 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 13 5 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"1 12\n6\n",
"4 1\n0 0 4 3\n",
"1 12\n12\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 11 6 2 17 18 2 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 6 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 8 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 3 0 18 2 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 17 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 7 9 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"1 12\n16\n",
"136 2\n11 13 12 17 7 16 15 2 19 12 17 10 4 17 1 6 14 3 9 6 6 13 14 1 15 15 2 14 9 2 18 9 0 3 8 4 3 11 10 8 11 6 2 17 18 2 5 1 6 15 7 12 11 9 8 16 5 18 13 5 19 7 18 19 14 10 17 17 13 0 9 10 12 6 1 3 14 15 3 7 18 5 7 14 3 2 9 14 11 4 15 3 18 9 15 12 16 13 5 6 0 19 1 5 14 19 11 16 12 4 15 19 1 14 5 16 18 4 17 8 6 5 17 6 1 5 11 12 4 8 14 3 17 18 18 10\n",
"1 12\n1\n",
"185 2\n0 14 2 11 5 17 9 11 8 12 8 17 3 0 4 15 4 17 8 1 2 10 8 0 8 16 1 7 10 3 0 18 3 15 2 1 4 1 10 11 6 10 19 5 5 18 2 1 15 17 0 4 12 19 12 8 11 4 7 15 13 0 9 6 2 6 7 2 17 4 7 9 0 17 1 13 4 6 4 10 1 14 0 13 17 16 10 5 7 19 19 9 2 2 28 17 11 6 11 15 4 17 18 18 14 9 15 10 10 10 14 18 2 5 8 4 3 2 12 3 14 4 2 19 18 13 14 12 9 5 15 17 9 12 1 5 15 13 7 9 19 5 3 2 2 13 9 8 0 8 12 16 10 4 7 19 0 5 6 17 13 15 14 6 3 2 18 11 15 9 4 0 3 3 17 5 10 15 6 15 13 2 16 19 10\n",
"1 12\n2\n"
],
"output": [
"2\n",
"4\n",
"3\n",
"5000000000\n",
"1\n",
"1\n",
"4\n",
"1\n",
"846\n",
"4\n",
"1\n",
"301\n",
"3\n",
"0\n",
"7\n",
"10\n",
"1\n",
"671\n",
"0\n",
"1\n",
"596\n",
"722\n",
"1\n",
"4\n",
"2\n",
"2\n",
"1\n",
"2\n",
"7\n",
"841\n",
"5\n",
"0\n",
"8\n",
"672\n",
"596\n",
"721\n",
"6\n",
"5010000000\n",
"10\n",
"840\n",
"673\n",
"600\n",
"720\n",
"9\n",
"4010000000\n",
"835\n",
"676\n",
"598\n",
"4010001000\n",
"828\n",
"679\n",
"716\n",
"4010101000\n",
"3\n",
"829\n",
"595\n",
"4110101000\n",
"4\n",
"678\n",
"593\n",
"722\n",
"4110201000\n",
"826\n",
"589\n",
"726\n",
"4110201010\n",
"586\n",
"728\n",
"4110201011\n",
"834\n",
"677\n",
"583\n",
"732\n",
"4110301011\n",
"669\n",
"588\n",
"733\n",
"4110301111\n",
"1\n",
"1\n",
"2\n",
"2\n",
"5\n",
"1\n",
"1\n",
"1\n",
"6\n",
"1\n",
"5\n",
"1\n",
"1\n",
"9\n",
"7\n",
"1\n",
"721\n",
"5\n",
"8\n",
"1\n",
"1\n",
"5\n",
"6\n",
"1\n",
"596\n",
"5\n",
"1\n",
"5\n",
"1\n",
"679\n",
"721\n",
"2\n",
"829\n",
"1\n",
"7\n",
"1\n",
"679\n",
"828\n",
"2\n",
"676\n",
"1\n",
"835\n",
"1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Enough is enough. Too many times it happened that Vasya forgot to dispose of garbage and his apartment stank afterwards. Now he wants to create a garbage disposal plan and stick to it.
For each of next n days Vasya knows a_i — number of units of garbage he will produce on the i-th day. Each unit of garbage must be disposed of either on the day it was produced or on the next day. Vasya disposes of garbage by putting it inside a bag and dropping the bag into a garbage container. Each bag can contain up to k units of garbage. It is allowed to compose and drop multiple bags into a garbage container in a single day.
Being economical, Vasya wants to use as few bags as possible. You are to compute the minimum number of bags Vasya needs to dispose of all of his garbage for the given n days. No garbage should be left after the n-th day.
Input
The first line of the input contains two integers n and k (1 ≤ n ≤ 2⋅10^5, 1 ≤ k ≤ 10^9) — number of days to consider and bag's capacity. The second line contains n space separated integers a_i (0 ≤ a_i ≤ 10^9) — the number of units of garbage produced on the i-th day.
Output
Output a single integer — the minimum number of bags Vasya needs to dispose of all garbage. Each unit of garbage should be disposed on the day it was produced or on the next day. No garbage can be left after the n-th day. In a day it is allowed to compose and drop multiple bags.
Examples
Input
3 2
3 2 1
Output
3
Input
5 1
1000000000 1000000000 1000000000 1000000000 1000000000
Output
5000000000
Input
3 2
1 0 1
Output
2
Input
4 4
2 8 4 1
Output
4
### Input:
3 2
1 0 1
### Output:
2
### Input:
4 4
2 8 4 1
### Output:
4
### Code:
import sys
n, k = tuple(int(i) for i in sys.stdin.readline().split())
a = tuple(int(i) for i in sys.stdin.readline().split())
assert len(a) == n
bags = 0
r = 0
for ai in a:
leftovers = (r > 0)
q, r = divmod(ai + r, k)
if q == 0:
if leftovers:
bags += 1
r = 0
else:
bags += q
if r > 0:
bags += 1
print(bags)
|
1140_C. Playlist_3028 | You have a playlist consisting of n songs. The i-th song is characterized by two numbers t_i and b_i — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied by the minimum beauty among them. For example, the pleasure of listening to a set of 3 songs having lengths [5, 7, 4] and beauty values [11, 14, 6] is equal to (5 + 7 + 4) ⋅ 6 = 96.
You need to choose at most k songs from your playlist, so the pleasure of listening to the set of these songs them is maximum possible.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5) – the number of songs in the playlist and the maximum number of songs you can choose, respectively.
Each of the next n lines contains two integers t_i and b_i (1 ≤ t_i, b_i ≤ 10^6) — the length and beauty of i-th song.
Output
Print one integer — the maximum pleasure you can get.
Examples
Input
4 3
4 7
15 1
3 6
6 8
Output
78
Input
5 3
12 31
112 4
100 100
13 55
55 50
Output
10000
Note
In the first test case we can choose songs {1, 3, 4}, so the total pleasure is (4 + 3 + 6) ⋅ 6 = 78.
In the second test case we can choose song 3. The total pleasure will be equal to 100 ⋅ 100 = 10000. | import heapq
n,k=map(int,input().split())
b_l=[]
for _ in range(n):
t,b=map(int,input().split())
b_l.append([b,t])
b_l.sort(reverse=True)
ans=0
sum_fg=0
h=[]
heapq.heapify(h)
for i in range(n):
sum_fg+=b_l[i][1]
heapq.heappush(h,b_l[i][1])
while(len(h)>k):
g=heapq.heappop(h)
sum_fg-=g
beauty=b_l[i][0]
ans=max(ans,sum_fg*beauty)
print(ans) | {
"input": [
"5 3\n12 31\n112 4\n100 100\n13 55\n55 50\n",
"4 3\n4 7\n15 1\n3 6\n6 8\n",
"5 1\n11 3\n10 2\n7 4\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 23862\n39951 40870\n56520 69058\n15454 9033\n",
"2 1\n1 2\n2 1\n",
"2 2\n100 100\n100 100\n",
"10 1\n74069 59157\n2735 28902\n43406 39542\n24166 93361\n18565 14980\n69958 53925\n23473 81878\n89682 3949\n18757 31637\n31665 45873\n",
"5 1\n11 3\n10 2\n6 4\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 23862\n39951 40870\n11886 69058\n15454 9033\n",
"2 2\n1 2\n2 1\n",
"2 2\n100 100\n000 100\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 93361\n18565 14980\n69958 53925\n23473 81878\n89682 3949\n18757 31637\n31665 45873\n",
"4 3\n4 7\n15 0\n3 6\n6 8\n",
"5 1\n11 3\n10 2\n6 6\n6 1\n9 1\n",
"4 3\n4 9\n15 0\n3 6\n6 8\n",
"5 1\n11 3\n10 2\n7 6\n6 1\n9 1\n",
"5 1\n11 3\n5 2\n7 9\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 25133\n39410 27719\n63633 27863\n39951 40870\n23184 69058\n22790 9033\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 86000\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n18757 31637\n35580 86000\n",
"10 2\n135600 2970\n4100 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n147177 3949\n8283 60648\n35580 86000\n",
"5 1\n11 1\n10 2\n7 4\n6 1\n9 1\n",
"2 1\n1 2\n0 1\n",
"2 2\n101 100\n100 100\n",
"10 1\n74069 59157\n2735 28902\n43406 39542\n24166 93361\n9939 14980\n69958 53925\n23473 81878\n89682 3949\n18757 31637\n31665 45873\n",
"5 3\n12 31\n112 4\n100 000\n13 55\n55 50\n",
"5 1\n11 0\n10 2\n6 4\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n74448 90641\n39410 27719\n63633 23862\n39951 40870\n11886 69058\n15454 9033\n",
"2 1\n2 2\n2 1\n",
"5 3\n21 31\n197 4\n000 100\n0 55\n55 50\n",
"8 1\n769 58454\n48687 121878\n51730 25133\n39410 27719\n63633 27863\n39951 40870\n43681 69058\n22790 9033\n",
"2 1\n15 3\n5 2\n7 9\n6 1\n9 2\n",
"8 1\n769 58454\n48687 108165\n51730 18857\n39410 27719\n63633 27863\n39951 40870\n43681 69058\n22790 9033\n",
"10 1\n135600 50902\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 86000\n",
"2 1\n11 4\n4 2\n7 9\n6 1\n9 3\n",
"5 1\n135600 2970\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n18757 60648\n35580 86000\n",
"5 3\n12 31\n197 4\n100 100\n13 55\n55 50\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 23862\n39951 40870\n23184 69058\n15454 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 93361\n18565 14980\n69958 53925\n23473 81878\n89682 3949\n18757 31637\n35580 45873\n",
"5 3\n21 31\n197 4\n100 100\n13 55\n55 50\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 27863\n39951 40870\n23184 69058\n15454 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 93361\n18565 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"5 3\n21 31\n197 4\n100 100\n0 55\n55 50\n",
"5 1\n11 3\n5 2\n7 6\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 27863\n39951 40870\n23184 69058\n22790 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 102329\n18565 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 102329\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"2 1\n11 3\n5 2\n7 9\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 25133\n39410 27719\n63633 27863\n39951 40870\n43681 69058\n22790 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"2 1\n11 3\n5 2\n7 9\n6 1\n9 2\n",
"8 1\n769 58454\n48687 67740\n51730 18857\n39410 27719\n63633 27863\n39951 40870\n43681 69058\n22790 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"2 1\n11 3\n4 2\n7 9\n6 1\n9 2\n",
"10 1\n135600 59157\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 86000\n",
"2 1\n11 3\n4 2\n7 9\n6 1\n9 3\n",
"2 1\n11 3\n4 2\n7 9\n4 1\n9 3\n",
"4 1\n11 3\n4 2\n7 9\n4 1\n9 3\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n18757 60648\n35580 86000\n",
"4 1\n11 0\n4 2\n7 9\n4 1\n9 3\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 68098\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n18757 60648\n35580 86000\n",
"4 1\n11 0\n4 2\n7 9\n4 2\n9 3\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 68098\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n8283 60648\n35580 86000\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n89682 3949\n8283 60648\n35580 86000\n",
"10 1\n135600 2970\n4100 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n89682 3949\n8283 60648\n35580 86000\n",
"10 1\n135600 2970\n4100 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n147177 3949\n8283 60648\n35580 86000\n",
"10 2\n135600 2894\n4100 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n147177 3949\n8283 60648\n35580 86000\n",
"10 2\n135600 2894\n4100 28902\n43406 59273\n24166 68098\n24384 8516\n69958 69998\n4871 81878\n75483 3949\n8283 60648\n35580 86000\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 27719\n63633 23862\n39951 30782\n56520 69058\n15454 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 93361\n18565 14980\n69958 53925\n23473 75328\n89682 3949\n18757 31637\n31665 45873\n",
"5 4\n12 31\n197 4\n100 100\n13 55\n55 50\n",
"5 1\n11 3\n10 2\n6 6\n0 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 90641\n39410 47185\n63633 23862\n39951 40870\n23184 69058\n15454 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 178402\n18565 14980\n69958 53925\n23473 81878\n89682 3949\n18757 31637\n35580 45873\n",
"5 3\n21 31\n197 0\n100 100\n13 55\n55 50\n",
"5 1\n11 3\n10 2\n7 6\n6 1\n13 1\n",
"8 1\n1481 58454\n48687 67740\n51730 90641\n39410 27719\n63633 27863\n39951 40870\n23184 69058\n15454 9033\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 26380\n18565 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"5 1\n11 3\n5 2\n7 6\n6 1\n8 1\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 102329\n18565 14980\n69958 53925\n4871 44413\n89682 3949\n18757 31637\n35580 45873\n",
"5 1\n21 3\n5 2\n7 9\n6 1\n9 1\n",
"8 1\n769 58454\n48687 67740\n51730 25133\n39410 27719\n63633 27863\n39951 40870\n23184 69058\n22790 8578\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 102329\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n9366 31637\n35580 45873\n",
"2 1\n11 3\n10 2\n7 9\n6 1\n9 1\n",
"10 1\n135600 59157\n2735 28902\n43406 39542\n24166 97738\n24384 14980\n133003 53925\n4871 81878\n89682 3949\n18757 31637\n35580 45873\n",
"10 1\n135600 59157\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n1333 81878\n89682 3949\n18757 31637\n35580 45873\n",
"2 1\n11 3\n4 2\n7 9\n6 0\n9 2\n",
"10 1\n135600 2970\n2735 28902\n43406 59273\n24166 97738\n24384 14980\n69958 53925\n4871 81878\n89682 3949\n18757 31637\n25303 86000\n",
"2 1\n11 3\n4 2\n13 9\n4 1\n9 3\n",
"10 1\n135600 2970\n2735 28902\n43406 87168\n24166 97738\n24384 14980\n69958 69998\n4871 81878\n89682 3949\n18757 31637\n35580 86000\n",
"4 1\n11 3\n4 2\n7 9\n4 1\n7 3\n",
"4 1\n11 0\n4 2\n7 9\n4 1\n9 4\n"
],
"output": [
"10000",
"78",
"33",
"4688858930",
"2",
"20000",
"4381699833",
"33\n",
"4688858930\n",
"3\n",
"10000\n",
"8021689200\n",
"78\n",
"36\n",
"80\n",
"42\n",
"63\n",
"3298057380\n",
"3772485150\n",
"4896920084\n",
"7387448924\n",
"28\n",
"2\n",
"20100\n",
"4381699833\n",
"3400\n",
"24\n",
"6748041168\n",
"4\n",
"2750\n",
"5933874186\n",
"45\n",
"5266229355\n",
"6902311200\n",
"44\n",
"2572803838\n",
"10000\n",
"4688858930\n",
"8021689200\n",
"10000\n",
"4688858930\n",
"8021689200\n",
"10000\n",
"42\n",
"4688858930\n",
"8021689200\n",
"8021689200\n",
"33\n",
"3298057380\n",
"8021689200\n",
"33\n",
"3298057380\n",
"8021689200\n",
"33\n",
"8021689200\n",
"33\n",
"33\n",
"63\n",
"4896920084\n",
"63\n",
"4896920084\n",
"63\n",
"4896920084\n",
"4896920084\n",
"4896920084\n",
"4896920084\n",
"7387448924\n",
"7387448924\n",
"4688858930\n",
"8021689200\n",
"10000\n",
"36\n",
"4688858930\n",
"8021689200\n",
"10000\n",
"42\n",
"4688858930\n",
"8021689200\n",
"42\n",
"8021689200\n",
"63\n",
"3298057380\n",
"8021689200\n",
"33\n",
"8021689200\n",
"8021689200\n",
"33\n",
"3772485150\n",
"33\n",
"4896920084\n",
"63\n",
"63\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have a playlist consisting of n songs. The i-th song is characterized by two numbers t_i and b_i — its length and beauty respectively. The pleasure of listening to set of songs is equal to the total length of the songs in the set multiplied by the minimum beauty among them. For example, the pleasure of listening to a set of 3 songs having lengths [5, 7, 4] and beauty values [11, 14, 6] is equal to (5 + 7 + 4) ⋅ 6 = 96.
You need to choose at most k songs from your playlist, so the pleasure of listening to the set of these songs them is maximum possible.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5) – the number of songs in the playlist and the maximum number of songs you can choose, respectively.
Each of the next n lines contains two integers t_i and b_i (1 ≤ t_i, b_i ≤ 10^6) — the length and beauty of i-th song.
Output
Print one integer — the maximum pleasure you can get.
Examples
Input
4 3
4 7
15 1
3 6
6 8
Output
78
Input
5 3
12 31
112 4
100 100
13 55
55 50
Output
10000
Note
In the first test case we can choose songs {1, 3, 4}, so the total pleasure is (4 + 3 + 6) ⋅ 6 = 78.
In the second test case we can choose song 3. The total pleasure will be equal to 100 ⋅ 100 = 10000.
### Input:
5 3
12 31
112 4
100 100
13 55
55 50
### Output:
10000
### Input:
4 3
4 7
15 1
3 6
6 8
### Output:
78
### Code:
import heapq
n,k=map(int,input().split())
b_l=[]
for _ in range(n):
t,b=map(int,input().split())
b_l.append([b,t])
b_l.sort(reverse=True)
ans=0
sum_fg=0
h=[]
heapq.heapify(h)
for i in range(n):
sum_fg+=b_l[i][1]
heapq.heappush(h,b_l[i][1])
while(len(h)>k):
g=heapq.heappop(h)
sum_fg-=g
beauty=b_l[i][0]
ans=max(ans,sum_fg*beauty)
print(ans) |
1159_A. A pile of stones_3032 | Vasya has a pile, that consists of some number of stones. n times he either took one stone from the pile or added one stone to the pile. The pile was non-empty before each operation of taking one stone from the pile.
You are given n operations which Vasya has made. Find the minimal possible number of stones that can be in the pile after making these operations.
Input
The first line contains one positive integer n — the number of operations, that have been made by Vasya (1 ≤ n ≤ 100).
The next line contains the string s, consisting of n symbols, equal to "-" (without quotes) or "+" (without quotes). If Vasya took the stone on i-th operation, s_i is equal to "-" (without quotes), if added, s_i is equal to "+" (without quotes).
Output
Print one integer — the minimal possible number of stones that can be in the pile after these n operations.
Examples
Input
3
---
Output
0
Input
4
++++
Output
4
Input
2
-+
Output
1
Input
5
++-++
Output
3
Note
In the first test, if Vasya had 3 stones in the pile at the beginning, after making operations the number of stones will be equal to 0. It is impossible to have less number of piles, so the answer is 0. Please notice, that the number of stones at the beginning can't be less, than 3, because in this case, Vasya won't be able to take a stone on some operation (the pile will be empty).
In the second test, if Vasya had 0 stones in the pile at the beginning, after making operations the number of stones will be equal to 4. It is impossible to have less number of piles because after making 4 operations the number of stones in the pile increases on 4 stones. So, the answer is 4.
In the third test, if Vasya had 1 stone in the pile at the beginning, after making operations the number of stones will be equal to 1. It can be proved, that it is impossible to have less number of stones after making the operations.
In the fourth test, if Vasya had 0 stones in the pile at the beginning, after making operations the number of stones will be equal to 3. | '''
t= input()
lng= len(t)
li1=[]; li2=[]
for i in range(lng):
if t[i]!='a':
li1.append(t[i])
elif t[i]=='a':
li2.append(i)
aa= ''.join(li1)
if len(aa)==0:
print(t); exit(0)
if len(aa)%2==1:
print(':('); exit(0)
if len(aa)%2==0:
#print(123)
l= int(len(aa)/2); lp= l#; print(l)
ll= aa[l:]; lll=aa[0:l] #; print(ll)
if ll!=lll:
print(':('); exit(0)
if ll not in t:
print(':('); exit(0)
tp= t[::-1]; tc= ll[::-1]#; print(tp,tc)
if tp.find(tc)!=0:
print(':('); exit(0)
if tp.find(tc)==0:
ul= len(tc)
lu= tp[ul:][::-1]
print(lu); exit(0)
'''
n= int(input()); s= input(); ln= len(s); sv=0
for i in s:
if i=='+':
sv+=1
if i=='-' and sv>0:
sv-=1
print(sv)
| {
"input": [
"2\n-+\n",
"3\n---\n",
"5\n++-++\n",
"4\n++++\n",
"4\n-+--\n",
"2\n++\n",
"98\n----+-+--+-+-++-++++---+-++++-+--++-++++++-+++--+++-+-----+-+--+-----+++++--+-++-+++-+-+++-+---++-\n",
"3\n+-+\n",
"100\n---+-----------+-++---+----------++++++++++++++++++++++++++++++++++++++++++++-----------------------\n",
"100\n----------------------------------------------------------------------++++++++++++++++-++-++++++++++\n",
"1\n-\n",
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"100\n++--+-+-+-++++++++++++++--+-+++++++++-++++++++++++++++++++++-+-++++-+++++++++-+-+-+++-+++++++++-+++-\n",
"2\n+-\n",
"100\n--------------------------------------------------------------------------------------------------++\n",
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"5\n--+--\n",
"100\n----------------------------------------------------------------------------------------------------\n",
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"100\n--------------------------------------------------++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"78\n+++++++++-----------------------------------------------+++++++++++++---++++++\n",
"3\n-+-\n",
"4\n-++-\n",
"100\n-+-+-+-+-+-+-+-+-+-+-+-+-+-+++++++++++++++-++++++++++++++++++++++++++++++++++-++++++++++++++++++++++\n",
"2\n--\n",
"1\n+\n",
"100\n-++-+-++----+++--+++++-+--++--++----+---+-++++++--+---+-+--+--+--+++++++++++++++++++++++++++++++++++\n",
"100\n+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-\n",
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"100\n+-++++--+-----++--+-++--++-+++-++-+-+++--+--++-----++---+-+-++++++++++++-++-+++-+++-+-+++++-+--+++++\n",
"100\n+-------+-+++-+++-++-+-----+----+----+-+----+-++--+++-+---++-++-+-+++-+----+++-+-----+--+-++----++++\n",
"3\n+--\n",
"100\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"100\n+-++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"100\n-+-+---+-+-+-++-+--+-+++-+---+-++-+-+--++-+--+-+-+-+-+-++--+-+-++--+++++-+-++++++++++-++++++++++++++\n",
"100\n--++---+---------+-++--+--++---------------+---------+---+----+-----+--------------+++++--++++-++-+-\n",
"100\n---------------------------------------------------------------------------------------------------+\n",
"3\n-++\n",
"100\n-----++--+-++-------+-+---++-+++-++++++++++++++-++-++-+-+++++++-+---++-+-+++++-++++++++++++++-+-++++\n",
"100\n--+++--+---+-++--++-+--++++++--+-------+-+----+-++-+--+-+-+++---+++--+--+-+-+-+-++--++-++---++--+-++\n",
"100\n+-+-+-+-+-++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"100\n-++------+---++++-+---++---+--+-++--+-+-++--+-+-++++-+++-+-----++-+--++-+++++---+-----+++---+-+-+-+-\n",
"100\n+-++--+-+-++--++-+++-++++----+--+---+-+-+-+-++--+-+-+-+-+-+-++--+-+-+-+-+-+-+-+++---+++-+-+-+---++--\n",
"3\n--+\n",
"99\n-+-+-+++--+--+-+-++--+-++--+++-+++-++-+++++-+-+-++----------+--++--++--++--+-++--+-+-+-++--+-+-++-+\n",
"4\n--++\n",
"100\n-+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"99\n-++-+-+++--++--+-+--++-+-++-+-----+---+++-+++++--+-+-+-+--+++-+++++---+-+--+----+---------+-+-+-++-\n",
"100\n+-+++--++++-+-++--+--+-++-------+---+-+---+++++++---+----+++-+-++--+-+--+-+-+--+-+-++-+---++-+-+++++\n",
"100\n++-+++-+---+-++-+-++------+++-----++-++++-+-+-+----+++-++++------++++--+-+-+++--+---------++-+-+-+--\n",
"99\n--+++++++++++++++++++++++++++++++++++++++++++++++++------------------------------------------------\n",
"51\n-++---+++++-+-++------+---+-++-+-+-+-++++-++++++-+-\n",
"100\n+--+-+-+-+-+++--++---+-+-+-+-+-+-+-+-++--+-+-+-+-+-+-+-+-+-++--+-+-+-+-++--+-++-+-+-+-+-+-+-+-+-+-+-\n",
"100\n--++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n",
"17\n-++++--+-+----++-\n",
"100\n++++----------------++++-+---+++-++++++++++++++++++++++-++--+++++++-+-++++++++++++++++++++++++++++++\n",
"100\n++--+-+-+-++--+-+-+-+-+-+-+-+-+-+-+-+-+-+-++-+--+-++--+-+-+-++--++--++--+-++--+-+-+-++--+-++--+-+-++\n",
"100\n-----+-+-++--++++-+++---+-++--++-----+-+-+-+-++--+-+++-+--+-+++--+---+-+-++--+-+-+-++-++--+-+-+--+++\n",
"100\n------+---+--------+++--+--------------++--+----------+-+---+------+-+-----++---+------+-+---++-+---\n",
"100\n++++++++++++++++++++------------------------------++++++++++++++++++++++++++++++++++++++++++++++----\n",
"3\n+++\n",
"100\n+---+++--+++--+--++--+--+---+-----+++-+++-+-+--+--+-+--++-+--+-+--+++--++---+-+-++-++-+-+++++++-+--+\n",
"100\n+++++--+-+++-+-++---+-++-+---++-------++-+--+-++-+--+-+--+-+-+----++-+-----++----++++-+-+---+--+--+-\n",
"100\n++++++++++-++-++++++++++++++++----------------------------------------------------------------------\n",
"100\n+-++-+++--+--+--+-+----------+-+---+-+-+-++-+---+--++-++++--+-++--++-+-++-++----++-++-+++-++++---+--\n",
"99\n+----------+---+--------+-+---------+--+-++-------++----------------------------++--++--------++-+-\n",
"100\n++--+-+-+-+++++++++-++++--+-+++++++++-++++++++++++++++++++++-++++++-+++++++++-+-+-+++-+++++++++-+++-\n",
"100\n+++-+-++++++++++++++++++++++++++-+++--++++++-++++-++++++++++++++++++++++++-++++++++++-+++++++-++++++\n",
"99\n-++++--++++++--++++--+--------+-+--++--+--++-++++-+-+++++++-+-++++--+---+-+++---+--+---+++-+-+-+--+\n",
"100\n++++++++++++++++++++++-++++++++++++++++++++++++++++++++++-+++++++++++++++-+-+-+-+-+-+-+-+-+-+-+-+-+-\n",
"100\n+++++++++++++++++++++++++++++++++++--+--+--+-+---+--++++++-+---+----++--++--+-+++++--+++----++-+-++-\n",
"100\n--+---++--++-+++--++----+++++-++++++-----+-+-+-+-+++--+-+-+---+-+++--+-+-+-+++++++++--++-+++++-+++-+\n",
"100\n+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---\n",
"100\n++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++-+\n",
"99\n+-++-+-+--++-+-+-+--++-+--++--++--++--+----------++-+-+-+++++-++-+++-+++--++-+--++-+-+--+--+++-+-+-\n",
"100\n+-+++--++++-+-++--+--+-++-------+---+-+---+++++++---+----+++-+-++--+-+-++-+----+-+-++-+---++-+-+++++\n",
"100\n--+--+-+-++--++++-+++---+-++--++-----+-+-+-+-++--+-+++-+--+-+++--+---+-+-++--+-+-+-++-+---+-+-+--+++\n",
"100\n+---+++--+++--+--++-++------+-----+++-+++-+-+--+--+-+--++-+--+-+--+++--++---+-+-++-++-+-+++++++-+--+\n",
"100\n+-++-+++--+--+--+-+----------+-+-+-+-+-+-++-+---+--++-++++--+-++--++-+-++-++----++-++-++--++++---+--\n",
"100\n+--+-+++++++-+-++-++-+-+---++--+++--+-+--+-++--+-+--+--+-+-+++-+++-----+------++-++--+--+++--+++---+\n",
"100\n-----------------------++++++++++++++++++++++++++++++++++++++++++++----------+---++-+-----------+---\n",
"100\n+-++-++-+---+--+-+++++-+--+-+-+--+-++-+++++++--++++--+---++-++--++++-++++++--+---+-+-++-++--++-+-+-+\n",
"100\n+---------+++++++++++++++++++++++++++++++++++++++++-++++++++++++++++++++++++++++++++++++++++++++++++\n",
"78\n+++++++++-----------------------------+-----------------+++++++++++++---++++-+\n",
"100\n-++-+-++----+++--+++++-+--++--++----+-----++++++--+---+-+--+--+-++++++++++++++++++++++++++++++++++++\n",
"100\n++++++++++++++-++++++++++-+-+++++--++-+-+--++-+-+-+-+-+--+-++--+-+-++-+---+-+++-+--+-++-+-+-+---+-+-\n",
"100\n++++++++++++++++++++++++++++++-+-+++++++--++-++++++++++++++++++++++-+++---+-++++----------------++++\n",
"100\n-+++-+++++++++-+++-+-+-+++++++++-++++++-++++++++++++++++++++++-+++++++++-+--++++-+++++++++-+-+-+--++\n",
"99\n+--+-+-+-+++---+--+---+++-+---+--++++-+-+++++++-+-++++-++--+--++--+-+--------+--++++--++++++--++++-\n",
"100\n+-+++-+++++-++--+++++++++-+-+-+--+++-+---+-+-+--+++-+-+---++----++++++-+++++----++--+++-++--++---+--\n",
"100\n--+---++++--++-++-++----++-++-+-++--++-+--++++-++--+---+-++-+-+-+-+-+-+----------+-+--+--+--+++-++-+\n",
"100\n+++++--+-+++++-+-+++-+++-++-++++++++++++-+-+---++-----++--+--+++-+-++-+++-++--++-+--++-----+--++++-+\n",
"100\n-----++--+-++-----+---+---++-+++-++++++++++++++-++-++-+-+++++++-+---++-+-+++++-++++++++++++++-+-++++\n",
"100\n-+--+-++-+-+-+-+-+-+-+--+-++--++--++---+--+++--+++-+----++++---++--+--++-+++-+--+-++----++++-+-----+\n",
"100\n++--+++-++-+-+--++-++-------+-++--++----+--++-+-------++--+++-+-+-+--+++---+----+--+++++-++----+---+\n",
"73\n+++-+-++-+++--+-----+++---+-+-++++-+++--++--++--++----+--+--+---+-++-+-+-\n",
"100\n+-+-+-+--++-+-+-+-+-+-+-+-+-+-+-+--++-+-+---+++-+-+--++--++--++-+--++-+---+++-++--------------------\n",
"78\n++++++---+++++++++++++-----------------------------------------------+++++++++\n",
"100\n+---------------------------------------------------------------------------------------------------\n",
"100\n++++-+-++++++++++++++-+++++-+-++---+-+++++++-+-++-++-++++++++++++++-+++-++---+-+-------++-+--++-----\n",
"4\n++--\n",
"100\n-+--+--+---+-+-++++----++-----+-++----+-+-+--+-+--+-++-+--+-++-------++---+-++-+---++-+-+++-+--+++++\n",
"100\n+---+----++-+++++--+----+---+++--+-+-+-+++--++-------+-++--+----++--++-+-------++-++--+-+-++-+++--++\n",
"99\n-++++--++++++--++++--+--------+-+--++--+--++-++++-+-+++++++-+-++-+--+---+-+++---+--+---+++-+-+-+-++\n",
"100\n+++++-+-++---+-++-+-+----+-++-+-+--++-+-+++----+---+++++++---+-+---+-------++-+--+--++-+-++++--+++-+\n",
"100\n+---+++--+++--+--++-+++-----+------++-+++-+-+--+--+-+--++-+--+-+--+++--++---+-+-++-++-+-+++++++-+--+\n",
"100\n+++----+-----+-+-++-++-+---+-++-++-+++-+-+--+--+-++++----+++++-----+-++---++++++-+++++--+-+---+-+-++\n",
"100\n-++-+--+--+++-+-+---+---++-++-+-+-++---+--+-+-+-+++-+++-----+--+++-+-++--+-+++-++---+-++--+--++--+--\n",
"100\n++-+++-+-+++-++++--+++----+-+-+-------+-+-++--++----+++++---+-++---++-+-++---+--+-+-++-++-+---++-+--\n",
"100\n+---+----++-+++++--+----+---+++--+-+-+-+++--++------++-++--+----++--++-+-------++-++--+-+-++-+++--+-\n",
"100\n-------+-------+-+-------------------++-----+----+-----+----++----+--+-----+-------------++-+-------\n",
"4\n+-+-\n",
"100\n+++++-+-++---+-++-+-+--+-+-+--+-+--++-+-+++----+---+++++++---+-+---+-------++-+--+--++-+-++++--+++-+\n",
"100\n+--+-+-+-+-+++--++---+-+-+-+-+-+-+-+-++--+-+-+-+-+-+-+-+-+--+--+-+++-+-++--+-++-+-+-+-+-+-+-+-+-+-+-\n",
"100\n++-+-+--++-+--++-+-+-+--++-+--++--++--++-+-+-+--++-+--+-++-+-+-+-+-+-+-+-+-+-+-+-+-+-+--++-+-+-+--++\n",
"100\n-----+++-++--++++-+++---+-++--++-----+---+-+-++--+-+++-+--+-+++--+---+-+-++--+-+-+-++-++--+-+-+--+++\n",
"100\n---+-++---+-+------+---++-----+-+------+---+-+----------+--++--------------+--+++--------+---+------\n",
"100\n-+--+--+---+-+-++++----++-----+-++----+-+-+--+-+--+-+-++--+-++-------++---+-++-+---++-+-+++-+--+++++\n",
"73\n-+-+-++-+---+--+--+----++--++--++--+++-++++-+-+---+++-----+--+++-++-+-+++\n",
"100\n-+--+--+-----+-++++----++-----+-++----+-+-+-++-+--+-++-+--+-++-------++---+-++-+---++-+-+++-+--+++++\n",
"100\n+-++-++-+---+--+-+++++-+--+-+-+--+-++-+++++++--++++--+---++-++--++++-++++++--+---+-+-++--+--++++-+-+\n",
"78\n+++++++++----------------------+------+-----------------+++++++++-+++---++++-+\n",
"100\n++++++++++++++++++++++++++++++++++++-+--+--+-+---+--++++++-----+----++--++--+-+++++--+++----++-+-++-\n",
"100\n+-+++--++++-+-++--+--+-++-------+---+-+---+++++++---+----+++-+-++--+-+--+-+-+--+++-++-+----+-+-+++++\n",
"100\n+--+-+-+-+-+++--++---+-+-+-+-+-+-+-+-+---+-+-+-+-+-+-+-+-+--+--+-+++-+-++--+-++-+-+-+-+-+++-+-+-+-+-\n",
"100\n-+++-+++++++++-+++-+-+-++++++++++++++++-++++++++++++++++++++++-++-++++++-+--++++-+++++++++-+-+-+--++\n",
"100\n--+---++++--++-++-++----++-++-+-++--++-+--++++-++--+---+-++-+-+-+-+-+-+----------+-++-+--+--+++--+-+\n",
"78\n+-++++---+++-+++++++++-----------------+------+----------------------+++++++++\n",
"100\n-+-+-+-+-+++-+-+-+-+-++-+--++-+-+++-+--+--+-+-+-+-+-+-+-+-+---+-+-+-+-+-+-+-+-+---++--+++-+-+-+-+--+\n",
"100\n++--+-+-+-+++++++++-++++--+-++++++-++-++++++++++++++++++++++-++++++++++++++++-+-+-+++-+++++++++-+++-\n",
"4\n--+-\n",
"99\n-+-++--------++--++----------------------------++-------++-+--++--------+-+--------+--------------+\n",
"100\n--+-++---+-++-++-+-+--+---++-+-++---++-+---+++++-+--++--++-+-+-------+-+-+----+++--++++-+++-+-+-+-++\n",
"73\n+++-+-++-+++--+-----++++--+-+-++++-+++--+-+-++--++----+--+--+---+--+-+-+-\n",
"99\n+--+-+-+++++---+--+---+++-+---+--++++-+-+++++++-+-++++-++--+--++--+-+--------+--++++--++++++--++-+-\n",
"78\n+++-++---+++++++++++++---------------------+-------------------------+++++++++\n",
"100\n-+-++-++++--+++++--------------+-----+----+---+---------+---------------++--+--++-+---------+---++--\n",
"100\n++-+--++---++-++--++-+-+-+-+--+--+++---+++-+-+--+-++-+----+-+-------+--++++++--+-++--++-+---+--+++--\n",
"100\n-+-+-+-+---+++-----+---+++++-++--+-++-----+-+++-++++-+-+--++-+-+--++-+--+---++---+-++++---+------++-\n",
"100\n--++---+-+-+-+++---+++-+-+-+-+-+-+-+--++-+-+-+-+-+-+--++-+-+-+-+---+--+----++++-+++-++--++-+-+--++-+\n",
"100\n+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++-\n",
"99\n-++-+-+++--++--+-+---+-+-++-+-----+---+++-+++++--+-+-+-+--+++-+++++---+-+--+----+---------+-+-++++-\n",
"100\n--+-+-+-++---------+--+++-+-+--++++------++++-+++----+-+-+-++++-++-----+++------++-+-++-+---+-+++-++\n",
"51\n-+-++++++-++++-+-+-+-++-+---+------++-+-+++++---++-\n",
"100\n----++++++++++++++++++++++++++++++++++++++++++++++------------------------------++++++++++++++++++++\n",
"100\n+--+-+++++++-+-++-++-+-+---++--+++--+-+--+-++--+-+--+--+-+-+++-+++-----+---+--+--++--+--+++--+++---+\n",
"100\n+++++--+-+++-+-++---+-++-+---++-------++-+--+-++-+--+-+--+-+-+----++-+----+++----++++---+---+--+--+-\n",
"100\n+-++-+++--+--+--+-+--+-------+-+---+-+-+-++-+---+--++-++++--+-++--++-+-++-++----++-++-+++-+++----+--\n",
"100\n-+--+-++-+---+-+-+++-+--+-++--++--++---+--+++--+++-+----++++---++--+--++-+++-+--+-++----++++-+-----+\n",
"100\n++++++++++++++++++++++++++++++++++---+--+--+-+---+--++++++-+---+----++--++--+++++++--+++----++-+-++-\n",
"100\n--+---++--++-+++--++----+++++-++++++-+---+-+-+-+-+++--+-+-+---+-+++--+-+-+-+++++++++--++-+++++--++-+\n",
"99\n++-+-+-+-+++---+--+---+++-+---+--+-++-+-+++++++-+-++++-++--+--++--+-+--------+--++++--++++++--++++-\n",
"100\n+++++-+-++---+-++-+-+----+-++---+--++-+-+++----+---+++++++---+-+---+-------++-+-++--++-+-++++--+++-+\n",
"100\n-++-+--+--+++-+-+---+---++-++-+-+-++---+--+-+-+-+++-+++-----+--+++-+-++--+-++--++---+-++-++--++--+--\n",
"100\n--+-++---+-++-++-+-+--+---++-+-++---++-+---+++++----++--++-+-+-------+-+-+----+++--++++-+++-+-+++-++\n"
],
"output": [
"1\n",
"0\n",
"3\n",
"4\n",
"0\n",
"2\n",
"11\n",
"1\n",
"21\n",
"26\n",
"0\n",
"4\n",
"1\n",
"9\n",
"6\n",
"64\n",
"0\n",
"2\n",
"1\n",
"0\n",
"17\n",
"0\n",
"13\n",
"0\n",
"1\n",
"80\n",
"1\n",
"0\n",
"0\n",
"0\n",
"90\n",
"2\n",
"2\n",
"11\n",
"50\n",
"16\n",
"0\n",
"1\n",
"69\n",
"0\n",
"1\n",
"35\n",
"0\n",
"1\n",
"16\n",
"97\n",
"0\n",
"24\n",
"4\n",
"0\n",
"100\n",
"98\n",
"27\n",
"7\n",
"1\n",
"2\n",
"44\n",
"2\n",
"90\n",
"0\n",
"0\n",
"1\n",
"2\n",
"2\n",
"99\n",
"1\n",
"6\n",
"0\n",
"1\n",
"9\n",
"1\n",
"98\n",
"1\n",
"60\n",
"2\n",
"3\n",
"0\n",
"42\n",
"3\n",
"8\n",
"0\n",
"0\n",
"7\n",
"1\n",
"64\n",
"80\n",
"9\n",
"68\n",
"32\n",
"20\n",
"94\n",
"98\n",
"10\n",
"6\n",
"3\n",
"8\n",
"5\n",
"2\n",
"21\n",
"17\n",
"88\n",
"14\n",
"36\n",
"24\n",
"48\n",
"65\n",
"12\n",
"16\n",
"4\n",
"22\n",
"44\n",
"1\n",
"1\n",
"1\n",
"0\n",
"9\n",
"0\n",
"32\n",
"0\n",
"7\n",
"5\n",
"9\n",
"6\n",
"8\n",
"9\n",
"1\n",
"0\n",
"3\n",
"0\n",
"0\n",
"6\n",
"3\n",
"2\n",
"3\n",
"0\n",
"7\n",
"6\n",
"7\n",
"17\n",
"12\n",
"32\n",
"6\n",
"5\n",
"65\n",
"2\n",
"9\n",
"2\n",
"64\n",
"0\n",
"1\n",
"8\n",
"0\n",
"10\n",
"9\n",
"0\n",
"3\n",
"1\n",
"7\n",
"98\n",
"3\n",
"4\n",
"6\n",
"36\n",
"2\n",
"0\n",
"5\n",
"1\n",
"32\n",
"20\n",
"10\n",
"7\n",
"1\n",
"10\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vasya has a pile, that consists of some number of stones. n times he either took one stone from the pile or added one stone to the pile. The pile was non-empty before each operation of taking one stone from the pile.
You are given n operations which Vasya has made. Find the minimal possible number of stones that can be in the pile after making these operations.
Input
The first line contains one positive integer n — the number of operations, that have been made by Vasya (1 ≤ n ≤ 100).
The next line contains the string s, consisting of n symbols, equal to "-" (without quotes) or "+" (without quotes). If Vasya took the stone on i-th operation, s_i is equal to "-" (without quotes), if added, s_i is equal to "+" (without quotes).
Output
Print one integer — the minimal possible number of stones that can be in the pile after these n operations.
Examples
Input
3
---
Output
0
Input
4
++++
Output
4
Input
2
-+
Output
1
Input
5
++-++
Output
3
Note
In the first test, if Vasya had 3 stones in the pile at the beginning, after making operations the number of stones will be equal to 0. It is impossible to have less number of piles, so the answer is 0. Please notice, that the number of stones at the beginning can't be less, than 3, because in this case, Vasya won't be able to take a stone on some operation (the pile will be empty).
In the second test, if Vasya had 0 stones in the pile at the beginning, after making operations the number of stones will be equal to 4. It is impossible to have less number of piles because after making 4 operations the number of stones in the pile increases on 4 stones. So, the answer is 4.
In the third test, if Vasya had 1 stone in the pile at the beginning, after making operations the number of stones will be equal to 1. It can be proved, that it is impossible to have less number of stones after making the operations.
In the fourth test, if Vasya had 0 stones in the pile at the beginning, after making operations the number of stones will be equal to 3.
### Input:
2
-+
### Output:
1
### Input:
3
---
### Output:
0
### Code:
'''
t= input()
lng= len(t)
li1=[]; li2=[]
for i in range(lng):
if t[i]!='a':
li1.append(t[i])
elif t[i]=='a':
li2.append(i)
aa= ''.join(li1)
if len(aa)==0:
print(t); exit(0)
if len(aa)%2==1:
print(':('); exit(0)
if len(aa)%2==0:
#print(123)
l= int(len(aa)/2); lp= l#; print(l)
ll= aa[l:]; lll=aa[0:l] #; print(ll)
if ll!=lll:
print(':('); exit(0)
if ll not in t:
print(':('); exit(0)
tp= t[::-1]; tc= ll[::-1]#; print(tp,tc)
if tp.find(tc)!=0:
print(':('); exit(0)
if tp.find(tc)==0:
ul= len(tc)
lu= tp[ul:][::-1]
print(lu); exit(0)
'''
n= int(input()); s= input(); ln= len(s); sv=0
for i in s:
if i=='+':
sv+=1
if i=='-' and sv>0:
sv-=1
print(sv)
|
1181_A. Chunga-Changa_3036 | Soon after the Chunga-Changa island was discovered, it started to acquire some forms of civilization and even market economy. A new currency arose, colloquially called "chizhik". One has to pay in chizhiks to buy a coconut now.
Sasha and Masha are about to buy some coconuts which are sold at price z chizhiks per coconut. Sasha has x chizhiks, Masha has y chizhiks. Each girl will buy as many coconuts as she can using only her money. This way each girl will buy an integer non-negative number of coconuts.
The girls discussed their plans and found that the total number of coconuts they buy can increase (or decrease) if one of them gives several chizhiks to the other girl. The chizhiks can't be split in parts, so the girls can only exchange with integer number of chizhiks.
Consider the following example. Suppose Sasha has 5 chizhiks, Masha has 4 chizhiks, and the price for one coconut be 3 chizhiks. If the girls don't exchange with chizhiks, they will buy 1 + 1 = 2 coconuts. However, if, for example, Masha gives Sasha one chizhik, then Sasha will have 6 chizhiks, Masha will have 3 chizhiks, and the girls will buy 2 + 1 = 3 coconuts.
It is not that easy to live on the island now, so Sasha and Mash want to exchange with chizhiks in such a way that they will buy the maximum possible number of coconuts. Nobody wants to have a debt, so among all possible ways to buy the maximum possible number of coconuts find such a way that minimizes the number of chizhiks one girl gives to the other (it is not important who will be the person giving the chizhiks).
Input
The first line contains three integers x, y and z (0 ≤ x, y ≤ 10^{18}, 1 ≤ z ≤ 10^{18}) — the number of chizhics Sasha has, the number of chizhics Masha has and the price of a coconut.
Output
Print two integers: the maximum possible number of coconuts the girls can buy and the minimum number of chizhiks one girl has to give to the other.
Examples
Input
5 4 3
Output
3 1
Input
6 8 2
Output
7 0
Note
The first example is described in the statement. In the second example the optimal solution is to dot exchange any chizhiks. The girls will buy 3 + 4 = 7 coconuts. | x,y,z=map(int,input().split())
sum=(x+y)//z
i1=x//z
i2=y//z
x=x%z
y=y%z
current=i1+i2
nu=0
if current==sum:
print(sum,end=' ')
print(nu)
else:
if x>y:
h=x
else:
h=y
current=sum-current
current=current*z
nu=current-h
print(sum, end=' ')
print(nu) | {
"input": [
"6 8 2\n",
"5 4 3\n",
"5000000000000 6000000000000 10000000000000\n",
"2778787205 1763925790 48326734\n",
"582426543750017 789023129080207 4395672028302\n",
"0 0 1\n",
"1000000000000000000 999999999999999999 3\n",
"7 14 5\n",
"1 0 1\n",
"132940 345844 5\n",
"20021126 20031111 20031208\n",
"15 15 10\n",
"36 23 8\n",
"500000000000000000 500000000000000000 1000000000000000000\n",
"108342 203845 62321\n",
"10 8 11\n",
"35 85 24\n",
"134029398338212 91233423429341 31803121312\n",
"7 9 10\n",
"13240 34544 3\n",
"5673 9835 437\n",
"1000000000000000000 1000000000000000000 1\n",
"44649078746 130022042506 981298434\n",
"37 83 24\n",
"9 7 5\n",
"999999999999999999 999999999999999999 1000000000000000000\n",
"0 1 1\n",
"536 537 39\n",
"100000000000 100000000000 100000000002\n",
"400000000000000000 500000000000000000 1000000000000000000\n",
"13 18 10\n",
"24 66 13\n",
"621 396 113\n",
"99 99 98\n",
"4 4 8\n",
"1000000000000000000 1000000000000000000 2\n",
"36 84 24\n",
"36 53 17\n",
"999999999999999997 999999999999999998 5\n",
"979012465057 6000000000000 10000000000000\n",
"2778787205 1763925790 38110529\n",
"692111989558215 789023129080207 4395672028302\n",
"1000001000000000000 999999999999999999 3\n",
"132940 231014 5\n",
"20021126 20031111 20838322\n",
"25 15 10\n",
"36 29 8\n",
"108342 407675 62321\n",
"5 8 11\n",
"35 56 24\n",
"99371208170826 91233423429341 31803121312\n",
"9 9 10\n",
"7573 34544 3\n",
"2426 9835 437\n",
"1000001000000000000 1000000000000000000 1\n",
"44649078746 116306650415 981298434\n",
"37 21 24\n",
"9 14 5\n",
"999999999999999999 1040156311909887838 1000000000000000000\n",
"536 537 41\n",
"100000000000 100000000000 34528086983\n",
"19 18 10\n",
"24 66 2\n",
"621 396 106\n",
"30 99 98\n",
"1000000000000000000 1000000000000000001 2\n",
"36 53 16\n",
"999999999999999997 1423171663784059281 5\n",
"6 8 1\n",
"2778787205 88766853 38110529\n",
"953515020431913 789023129080207 4395672028302\n",
"1000001000000000000 1673787723046511310 3\n",
"132940 231014 6\n",
"20021126 20031111 39258289\n",
"25 15 2\n",
"11 29 8\n",
"108342 407675 110916\n",
"106284406721328 91233423429341 31803121312\n",
"9 9 8\n",
"3873 9835 437\n",
"1000001000000100000 1000000000000000000 1\n",
"44649078746 116306650415 538723013\n",
"37 21 11\n",
"10 14 5\n",
"536 886 41\n",
"100000100000 100000000000 34528086983\n",
"24 32 2\n",
"1037 396 106\n",
"1000000000000000010 1000000000000000001 2\n",
"36 156 32\n",
"36 99 16\n",
"411180571968784223 1423171663784059281 5\n",
"6 5 1\n",
"1444555415333840 789023129080207 4395672028302\n",
"1000001000000000000 2124617344027391495 3\n",
"5 15 2\n",
"350919308160677995 916982339945800203 1000000000000001000\n",
"108342 407675 206402\n",
"106284406721328 91233423429341 23815570193\n",
"3333 9835 437\n",
"1000001000000100000 1000010000000000000 1\n",
"44649078746 67550885588 538723013\n",
"10 14 2\n",
"380 886 41\n",
"100100000000 100000000000 34528086983\n",
"4 32 2\n",
"1037 426 106\n",
"1000000000000000010 1000000000000000001 4\n",
"5 156 32\n",
"47 99 16\n",
"411180571968784223 1890066056840128151 5\n",
"12 5 1\n",
"0 0 2\n",
"500000000000000000 500000000000000000 1000000000000001000\n",
"-1 1 1\n",
"400000000000000000 76043072352581561 1000000000000000000\n",
"1 4 8\n",
"36 84 32\n",
"5 0 3\n",
"279027845016 6000000000000 10000000000000\n",
"350919308160677995 500000000000000000 1000000000000001000\n",
"5 8 21\n",
"32 56 24\n",
"999999999999999999 1191412650596233425 1000000000000000000\n",
"750107908480166173 76043072352581561 1000000000000000000\n",
"19 13 10\n",
"41 99 98\n",
"0 4 8\n",
"5 0 4\n",
"33851492843 6000000000000 10000000000000\n",
"2778787205 90449696 38110529\n",
"20021126 1766767 39258289\n",
"11 28 8\n",
"5 8 17\n",
"32 56 30\n",
"9 7 8\n",
"37 21 14\n",
"999999999999999999 1153386251228189490 1000000000000000000\n",
"750107908480166173 6696178478312602 1000000000000000000\n"
],
"output": [
"7 0\n",
"3 1\n",
"1 4000000000000\n",
"93 0\n",
"312 2197836014149\n",
"0 0\n",
"666666666666666666 0\n",
"4 1\n",
"1 0\n",
"95756 0\n",
"1 97\n",
"3 5\n",
"7 1\n",
"1 500000000000000000\n",
"5 16300\n",
"1 1\n",
"5 11\n",
"7083 9731614787\n",
"1 1\n",
"15928 1\n",
"35 8\n",
"2000000000000000000 0\n",
"178 490649216\n",
"5 11\n",
"3 1\n",
"1 1\n",
"1 0\n",
"27 9\n",
"1 2\n",
"0 0\n",
"3 2\n",
"6 0\n",
"9 56\n",
"2 0\n",
"1 4\n",
"1000000000000000000 0\n",
"5 12\n",
"5 0\n",
"399999999999999999 2\n",
"0 0\n",
"119 3281412\n",
"336 0\n",
"666666999999999999 0\n",
"72790 0\n",
"1 807211\n",
"4 5\n",
"8 3\n",
"8 16300\n",
"1 3\n",
"3 0\n",
"5993 9731614787\n",
"1 1\n",
"14039 1\n",
"28 196\n",
"2000001000000000000 0\n",
"164 467863231\n",
"2 3\n",
"4 1\n",
"2 1\n",
"26 0\n",
"5 3584260949\n",
"3 1\n",
"45 0\n",
"9 15\n",
"1 0\n",
"1000000000000000000 0\n",
"5 0\n",
"484634332756811855 0\n",
"14 0\n",
"75 3281412\n",
"396 345809709621\n",
"891262907682170436 0\n",
"60659 2\n",
"1 19227178\n",
"20 1\n",
"5 3\n",
"4 2574\n",
"6210 1624703376\n",
"2 0\n",
"31 60\n",
"2000001000000100000 0\n",
"298 57520393\n",
"5 1\n",
"4 0\n",
"34 0\n",
"5 3584160949\n",
"28 0\n",
"13 23\n",
"1000000000000000005 0\n",
"6 4\n",
"8 0\n",
"366870447150568700 0\n",
"11 0\n",
"508 1620681977518\n",
"1041539448009130498 1\n",
"10 1\n",
"1 83017660054200797\n",
"2 5129\n",
"8293 4025980042\n",
"30 163\n",
"2000011000000100000 0\n",
"208 64931333\n",
"12 0\n",
"30 0\n",
"5 3484260949\n",
"18 0\n",
"13 0\n",
"500000000000000002 0\n",
"5 4\n",
"9 1\n",
"460249325761782474 0\n",
"17 0\n",
"0 0\n",
"0 0\n",
"0 0\n",
"0 0\n",
"0 0\n",
"3 0\n",
"1 0\n",
"0 0\n",
"0 0\n",
"0 0\n",
"3 0\n",
"2 1\n",
"0 0\n",
"3 1\n",
"1 0\n",
"0 0\n",
"1 0\n",
"0 0\n",
"75 3281412\n",
"0 0\n",
"4 0\n",
"0 0\n",
"2 0\n",
"2 1\n",
"4 5\n",
"2 1\n",
"0 0\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Soon after the Chunga-Changa island was discovered, it started to acquire some forms of civilization and even market economy. A new currency arose, colloquially called "chizhik". One has to pay in chizhiks to buy a coconut now.
Sasha and Masha are about to buy some coconuts which are sold at price z chizhiks per coconut. Sasha has x chizhiks, Masha has y chizhiks. Each girl will buy as many coconuts as she can using only her money. This way each girl will buy an integer non-negative number of coconuts.
The girls discussed their plans and found that the total number of coconuts they buy can increase (or decrease) if one of them gives several chizhiks to the other girl. The chizhiks can't be split in parts, so the girls can only exchange with integer number of chizhiks.
Consider the following example. Suppose Sasha has 5 chizhiks, Masha has 4 chizhiks, and the price for one coconut be 3 chizhiks. If the girls don't exchange with chizhiks, they will buy 1 + 1 = 2 coconuts. However, if, for example, Masha gives Sasha one chizhik, then Sasha will have 6 chizhiks, Masha will have 3 chizhiks, and the girls will buy 2 + 1 = 3 coconuts.
It is not that easy to live on the island now, so Sasha and Mash want to exchange with chizhiks in such a way that they will buy the maximum possible number of coconuts. Nobody wants to have a debt, so among all possible ways to buy the maximum possible number of coconuts find such a way that minimizes the number of chizhiks one girl gives to the other (it is not important who will be the person giving the chizhiks).
Input
The first line contains three integers x, y and z (0 ≤ x, y ≤ 10^{18}, 1 ≤ z ≤ 10^{18}) — the number of chizhics Sasha has, the number of chizhics Masha has and the price of a coconut.
Output
Print two integers: the maximum possible number of coconuts the girls can buy and the minimum number of chizhiks one girl has to give to the other.
Examples
Input
5 4 3
Output
3 1
Input
6 8 2
Output
7 0
Note
The first example is described in the statement. In the second example the optimal solution is to dot exchange any chizhiks. The girls will buy 3 + 4 = 7 coconuts.
### Input:
6 8 2
### Output:
7 0
### Input:
5 4 3
### Output:
3 1
### Code:
x,y,z=map(int,input().split())
sum=(x+y)//z
i1=x//z
i2=y//z
x=x%z
y=y%z
current=i1+i2
nu=0
if current==sum:
print(sum,end=' ')
print(nu)
else:
if x>y:
h=x
else:
h=y
current=sum-current
current=current*z
nu=current-h
print(sum, end=' ')
print(nu) |
1216_E1. Numerical Sequence (easy version)_3042 | The only difference between the easy and the hard versions is the maximum value of k.
You are given an infinite sequence of form "112123123412345..." which consist of blocks of all consecutive positive integers written one after another. The first block consists of all numbers from 1 to 1, the second one — from 1 to 2, the third one — from 1 to 3, ..., the i-th block consists of all numbers from 1 to i.
So the first 56 elements of the sequence are "11212312341234512345612345671234567812345678912345678910". Elements of the sequence are numbered from one. For example, the 1-st element of the sequence is 1, the 3-rd element of the sequence is 2, the 20-th element of the sequence is 5, the 38-th element is 2, the 56-th element of the sequence is 0.
Your task is to answer q independent queries. In the i-th query you are given one integer k_i. Calculate the digit at the position k_i of the sequence.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries.
The i-th of the following q lines contains one integer k_i (1 ≤ k_i ≤ 10^9) — the description of the corresponding query.
Output
Print q lines. In the i-th line print one digit x_i (0 ≤ x_i ≤ 9) — the answer to the query i, i.e. x_i should be equal to the element at the position k_i of the sequence.
Examples
Input
5
1
3
20
38
56
Output
1
2
5
2
0
Input
4
2132
506
999999999
1000000000
Output
8
2
9
8
Note
Answers on queries from the first example are described in the problem statement. | def isqrt(x):
if x < 0:
raise ValueError('square root not defined for negative numbers')
n = int(x)
if n == 0:
return 0
a, b = divmod(n.bit_length(), 2)
x = 2**(a+b)
while True:
y = (x + n//x)//2
if y >= x:
return x
x = y
p = [0, 45, 9045, 1395495, 189414495, 23939649495, 2893942449495, 339393974949495, 38939394344949495, 1000000000000000001];
nx = [0, 9, 189, 2889, 38889, 488889, 5888889, 68888889, 788888889, 8888888889]
q = int(input())
for ut in range(q):
lk = int(input())
k = lk
idx = 0;
for i in range(len(p)-1):
if (p[i] <= k) and (p[i + 1] > k):
idx = i;
idx = idx;
k-=1
k -= p[idx];
a = idx + 1
b = 2 * nx[idx] + idx + 1;
k = -2 * k;
d = isqrt(b*b-4 * a*k);
x1 = (-b + d) / (2. * a);
x2 = (-b - d) / (2. * a);
a1 = int(x1);
z = lk - p[idx] - nx[idx] * a1 - (a1 * (a1 + 1) // 2) * (idx + 1);
cnt = 0
ww = 1
pow = 0;
pow = 1;
while ((cnt + pow * ww) * 9 < z) :
cnt += pow * ww;
ww+=1
pow *= 10;
sym_cnt = (z - (cnt * 9)) - 1;
ok = (pow)+sym_cnt / ww;
s = str(ok);
if (z < 10):
print(z)
else:
print(s[sym_cnt % ww]) | {
"input": [
"4\n2132\n506\n999999999\n1000000000\n",
"5\n1\n3\n20\n38\n56\n",
"1\n755045\n",
"19\n1\n10\n100\n1000\n10000\n100000\n1000000\n10000000\n100000000\n1000000000\n10000000000\n100000000000\n1000000000000\n10000000000000\n100000000000000\n1000000000000000\n10000000000000000\n100000000000000000\n1000000000000000000\n",
"1\n388645\n",
"1\n9124\n",
"1\n123151223\n",
"2\n555221491191831672\n1395496\n",
"2\n555831672\n1395496\n",
"1\n306200613881388645\n",
"1\n555493\n",
"1\n838469\n",
"1\n310331825476838469\n",
"1\n307853100237555493\n",
"1\n921893\n",
"1\n307026857059472069\n",
"1\n671621\n",
"1\n1231513123\n",
"4\n2132\n506\n999999999999999999\n1000000000000000000\n",
"1\n311158068654921893\n",
"1\n308679339120671621\n",
"1\n309505582298755045\n",
"10\n1\n10\n100\n1000\n10000\n100000\n1000000\n10000000\n100000000\n1000000000\n",
"1\n472069\n",
"1\n1384384\n",
"19\n1\n10\n100\n1000\n10000\n100000\n1000000\n10000000\n100000000\n1000000000\n10000000000\n100000010000\n1000000000000\n10000000000000\n100000000000000\n1000000000000000\n10000000000000000\n100000000000000000\n1000000000000000000\n",
"1\n562859\n",
"1\n192381159\n",
"2\n185272016789432415\n1395496\n",
"2\n760519448\n1395496\n",
"1\n565468207604333237\n",
"1\n580639030704291062\n",
"1\n1173110\n",
"1\n710604811\n",
"4\n4225\n506\n999999999999999999\n1000000000000000000\n",
"1\n468934261213230684\n",
"10\n1\n10\n100\n1000\n10000\n101000\n1000000\n10000000\n100000000\n1000000000\n",
"4\n2132\n506\n712951009\n1000000000\n",
"5\n1\n3\n20\n38\n74\n",
"1\n2295225\n",
"2\n185272016789432415\n741198\n",
"2\n1083995377\n1395496\n",
"4\n2647\n506\n999999999999999999\n1000000000000000000\n",
"10\n1\n10\n101\n1000\n10000\n101000\n1000000\n10000000\n100000000\n1000000000\n",
"5\n1\n3\n10\n38\n74\n",
"2\n276944178593673352\n741198\n",
"2\n1083995377\n646975\n",
"10\n1\n10\n101\n1000\n10000\n101001\n1000000\n10000000\n100000000\n1000000000\n",
"2\n109901670234575601\n741198\n",
"2\n1083995377\n688347\n",
"1\n3513798\n",
"1\n16966\n",
"1\n931813\n",
"1\n1600315\n",
"1\n108658516222278096\n",
"1\n182970454676094390\n",
"1\n1140161\n",
"1\n409744691923775279\n",
"1\n277620016344322585\n",
"1\n681373\n",
"19\n1\n10\n100\n1000\n10000\n100000\n1000000\n10000000\n100000000\n1000000000\n10000000000\n100000110000\n1000000000000\n10000000000000\n100000000000000\n1000000000000000\n10000000000000000\n100000000000000000\n1000000000000000000\n",
"1\n52232\n",
"1\n13891\n",
"1\n224122045\n",
"1\n977336791416487790\n",
"1\n1096563\n",
"1\n1758688\n",
"1\n207932039790763529\n",
"1\n775782282539374883\n",
"1\n1137146\n",
"1\n240440186859734624\n",
"1\n72551\n",
"1\n982846275\n",
"1\n795098499981805957\n",
"1\n752421370688441489\n",
"1\n68931746846803205\n",
"1\n662773\n",
"1\n2850226\n",
"1\n74714\n",
"1\n25335\n",
"1\n370877516\n",
"1\n1846068\n",
"1\n2263101\n",
"1\n402363577523320421\n",
"1\n1757500\n",
"1\n179028464008734729\n",
"1\n79691\n",
"1\n260927618\n",
"1\n857982261986776405\n",
"1\n75804805891657877\n",
"1\n271850\n",
"5\n1\n3\n14\n38\n74\n",
"1\n360450\n",
"1\n126155\n",
"1\n9602\n",
"1\n102617139\n",
"1\n24681\n",
"1\n1828064\n",
"1\n799956254854574834\n",
"1\n179480912340506587\n"
],
"output": [
"8\n2\n9\n8\n",
"1\n2\n5\n2\n0\n",
"4\n",
"1\n4\n1\n4\n9\n2\n6\n2\n6\n8\n1\n1\n9\n8\n3\n7\n6\n1\n1\n",
"3\n",
"4\n",
"7\n",
"7\n1\n",
"5\n1\n",
"1\n",
"2\n",
"4\n",
"5\n",
"1\n",
"8\n",
"5\n",
"3\n",
"6\n",
"8\n2\n4\n1\n",
"4\n",
"4\n",
"1\n",
"1\n4\n1\n4\n9\n2\n6\n2\n6\n8\n",
"4\n",
"1\n",
"1\n4\n1\n4\n9\n2\n6\n2\n6\n8\n1\n1\n9\n8\n3\n7\n6\n1\n1\n",
"0\n",
"2\n",
"5\n1\n",
"3\n1\n",
"3\n",
"8\n",
"7\n",
"5\n",
"9\n2\n4\n1\n",
"4\n",
"1\n4\n1\n4\n9\n6\n6\n2\n6\n8\n",
"8\n2\n9\n8\n",
"1\n2\n5\n2\n5\n",
"9\n",
"5\n2\n",
"1\n1\n",
"1\n2\n4\n1\n",
"1\n4\n3\n4\n9\n6\n6\n2\n6\n8\n",
"1\n2\n4\n2\n5\n",
"1\n2\n",
"1\n5\n",
"1\n4\n3\n4\n9\n4\n6\n2\n6\n8\n",
"9\n2\n",
"1\n6\n",
"6\n",
"1\n",
"3\n",
"1\n",
"2\n",
"1\n",
"0\n",
"7\n",
"8\n",
"7\n",
"1\n4\n1\n4\n9\n2\n6\n2\n6\n8\n1\n1\n9\n8\n3\n7\n6\n1\n1\n",
"5\n",
"9\n",
"2\n",
"8\n",
"7\n",
"3\n",
"8\n",
"7\n",
"5\n",
"7\n",
"1\n",
"1\n",
"8\n",
"7\n",
"2\n",
"5\n",
"2\n",
"5\n",
"1\n",
"2\n",
"7\n",
"3\n",
"5\n",
"1\n",
"2\n",
"7\n",
"5\n",
"3\n",
"4\n",
"0\n",
"1\n2\n4\n2\n5\n",
"9\n",
"2\n",
"9\n",
"9\n",
"4\n",
"8\n",
"1\n",
"5\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The only difference between the easy and the hard versions is the maximum value of k.
You are given an infinite sequence of form "112123123412345..." which consist of blocks of all consecutive positive integers written one after another. The first block consists of all numbers from 1 to 1, the second one — from 1 to 2, the third one — from 1 to 3, ..., the i-th block consists of all numbers from 1 to i.
So the first 56 elements of the sequence are "11212312341234512345612345671234567812345678912345678910". Elements of the sequence are numbered from one. For example, the 1-st element of the sequence is 1, the 3-rd element of the sequence is 2, the 20-th element of the sequence is 5, the 38-th element is 2, the 56-th element of the sequence is 0.
Your task is to answer q independent queries. In the i-th query you are given one integer k_i. Calculate the digit at the position k_i of the sequence.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries.
The i-th of the following q lines contains one integer k_i (1 ≤ k_i ≤ 10^9) — the description of the corresponding query.
Output
Print q lines. In the i-th line print one digit x_i (0 ≤ x_i ≤ 9) — the answer to the query i, i.e. x_i should be equal to the element at the position k_i of the sequence.
Examples
Input
5
1
3
20
38
56
Output
1
2
5
2
0
Input
4
2132
506
999999999
1000000000
Output
8
2
9
8
Note
Answers on queries from the first example are described in the problem statement.
### Input:
4
2132
506
999999999
1000000000
### Output:
8
2
9
8
### Input:
5
1
3
20
38
56
### Output:
1
2
5
2
0
### Code:
def isqrt(x):
if x < 0:
raise ValueError('square root not defined for negative numbers')
n = int(x)
if n == 0:
return 0
a, b = divmod(n.bit_length(), 2)
x = 2**(a+b)
while True:
y = (x + n//x)//2
if y >= x:
return x
x = y
p = [0, 45, 9045, 1395495, 189414495, 23939649495, 2893942449495, 339393974949495, 38939394344949495, 1000000000000000001];
nx = [0, 9, 189, 2889, 38889, 488889, 5888889, 68888889, 788888889, 8888888889]
q = int(input())
for ut in range(q):
lk = int(input())
k = lk
idx = 0;
for i in range(len(p)-1):
if (p[i] <= k) and (p[i + 1] > k):
idx = i;
idx = idx;
k-=1
k -= p[idx];
a = idx + 1
b = 2 * nx[idx] + idx + 1;
k = -2 * k;
d = isqrt(b*b-4 * a*k);
x1 = (-b + d) / (2. * a);
x2 = (-b - d) / (2. * a);
a1 = int(x1);
z = lk - p[idx] - nx[idx] * a1 - (a1 * (a1 + 1) // 2) * (idx + 1);
cnt = 0
ww = 1
pow = 0;
pow = 1;
while ((cnt + pow * ww) * 9 < z) :
cnt += pow * ww;
ww+=1
pow *= 10;
sym_cnt = (z - (cnt * 9)) - 1;
ok = (pow)+sym_cnt / ww;
s = str(ok);
if (z < 10):
print(z)
else:
print(s[sym_cnt % ww]) |
125_A. Measuring Lengths in Baden_3047 | Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches.
You are given a length equal to n centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches.
Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch.
Input
The only line contains an integer n (1 ≤ n ≤ 10000).
Output
Print two non-negative space-separated integers a and b, where a is the numbers of feet and b is the number of inches.
Examples
Input
42
Output
1 2
Input
5
Output
0 2 | n=int(input())
e=(n+1)//36
n-=36*e
print(e,(n+1)//3) | {
"input": [
"42\n",
"5\n",
"4\n",
"71\n",
"9999\n",
"35\n",
"199\n",
"10000\n",
"10\n",
"2\n",
"9876\n",
"8\n",
"120\n",
"3\n",
"1233\n",
"501\n",
"24\n",
"12\n",
"13\n",
"1000\n",
"1\n",
"100\n",
"7\n",
"94\n",
"18864\n",
"11\n",
"51\n",
"00000\n",
"14\n",
"172\n",
"25\n",
"27\n",
"9\n",
"21\n",
"33\n",
"01000\n",
"294\n",
"29\n",
"40\n",
"17\n",
"79\n",
"216\n",
"37\n",
"45\n",
"63\n",
"49\n",
"139\n",
"2784\n",
"390\n",
"00100\n",
"13473\n",
"97\n",
"81\n",
"43\n",
"123\n",
"111\n",
"60\n",
"462\n",
"55\n",
"67\n",
"90\n",
"114\n",
"76\n",
"270\n",
"25368\n",
"132\n",
"69\n",
"88\n",
"117\n",
"6\n",
"0\n",
"0000\n",
"000\n",
"23\n",
"22\n",
"18\n",
"20\n",
"39\n",
"28\n",
"16\n",
"26\n",
"15\n",
"19\n",
"30\n",
"001\n",
"31\n",
"00010\n",
"52\n",
"0100\n",
"36\n",
"32\n",
"010\n",
"75\n",
"64\n",
"48\n",
"011\n",
"46\n",
"87\n"
],
"output": [
"1 2\n",
"0 2\n",
"0 1\n",
"2 0\n",
"277 9\n",
"1 0\n",
"5 6\n",
"277 9\n",
"0 3\n",
"0 1\n",
"274 4\n",
"0 3\n",
"3 4\n",
"0 1\n",
"34 3\n",
"13 11\n",
"0 8\n",
"0 4\n",
"0 4\n",
"27 9\n",
"0 0\n",
"2 9\n",
"0 2\n",
"2 7\n",
"524 0\n",
"0 4\n",
"1 5\n",
"0 0\n",
"0 5\n",
"4 9\n",
"0 8\n",
"0 9\n",
"0 3\n",
"0 7\n",
"0 11\n",
"27 9\n",
"8 2\n",
"0 10\n",
"1 1\n",
"0 6\n",
"2 2\n",
"6 0\n",
"1 0\n",
"1 3\n",
"1 9\n",
"1 4\n",
"3 10\n",
"77 4\n",
"10 10\n",
"2 9\n",
"374 3\n",
"2 8\n",
"2 3\n",
"1 2\n",
"3 5\n",
"3 1\n",
"1 8\n",
"12 10\n",
"1 6\n",
"1 10\n",
"2 6\n",
"3 2\n",
"2 1\n",
"7 6\n",
"704 8\n",
"3 8\n",
"1 11\n",
"2 5\n",
"3 3\n",
"0 2\n",
"0 0\n",
"0 0\n",
"0 0\n",
"0 8\n",
"0 7\n",
"0 6\n",
"0 7\n",
"1 1\n",
"0 9\n",
"0 5\n",
"0 9\n",
"0 5\n",
"0 6\n",
"0 10\n",
"0 0\n",
"0 10\n",
"0 3\n",
"1 5\n",
"2 9\n",
"1 0\n",
"0 11\n",
"0 3\n",
"2 1\n",
"1 9\n",
"1 4\n",
"0 4\n",
"1 3\n",
"2 5\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches.
You are given a length equal to n centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches.
Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch.
Input
The only line contains an integer n (1 ≤ n ≤ 10000).
Output
Print two non-negative space-separated integers a and b, where a is the numbers of feet and b is the number of inches.
Examples
Input
42
Output
1 2
Input
5
Output
0 2
### Input:
42
### Output:
1 2
### Input:
5
### Output:
0 2
### Code:
n=int(input())
e=(n+1)//36
n-=36*e
print(e,(n+1)//3) |
1281_C. Cut and Paste_3051 | We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i.
There is one cursor. The cursor's location ℓ is denoted by an integer in \{0, …, |s|\}, with the following meaning:
* If ℓ = 0, then the cursor is located before the first character of s.
* If ℓ = |s|, then the cursor is located right after the last character of s.
* If 0 < ℓ < |s|, then the cursor is located between s_ℓ and s_{ℓ+1}.
We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor.
We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions:
* The Move action. Move the cursor one step to the right. This increments ℓ once.
* The Cut action. Set c ← s_right, then set s ← s_left.
* The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c.
The cursor initially starts at ℓ = 0. Then, we perform the following procedure:
1. Perform the Move action once.
2. Perform the Cut action once.
3. Perform the Paste action s_ℓ times.
4. If ℓ = x, stop. Otherwise, return to step 1.
You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7.
It is guaranteed that ℓ ≤ |s| at any time.
Input
The first line of input contains a single integer t (1 ≤ t ≤ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases.
The first line of each test case contains a single integer x (1 ≤ x ≤ 10^6). The second line of each test case consists of the initial string s (1 ≤ |s| ≤ 500). It is guaranteed, that s consists of the characters "1", "2", "3".
It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that ℓ ≤ |s| at any time.
Output
For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7.
Example
Input
4
5
231
7
2323
6
333
24
133321333
Output
25
1438
1101
686531475
Note
Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, ℓ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above:
* Step 1, Move once: we get ℓ = 1.
* Step 2, Cut once: we get s = 2 and c = 31.
* Step 3, Paste s_ℓ = 2 times: we get s = 23131.
* Step 4: ℓ = 1 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 2.
* Step 2, Cut once: we get s = 23 and c = 131.
* Step 3, Paste s_ℓ = 3 times: we get s = 23131131131.
* Step 4: ℓ = 2 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 3.
* Step 2, Cut once: we get s = 231 and c = 31131131.
* Step 3, Paste s_ℓ = 1 time: we get s = 23131131131.
* Step 4: ℓ = 3 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 4.
* Step 2, Cut once: we get s = 2313 and c = 1131131.
* Step 3, Paste s_ℓ = 3 times: we get s = 2313113113111311311131131.
* Step 4: ℓ = 4 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 5.
* Step 2, Cut once: we get s = 23131 and c = 13113111311311131131.
* Step 3, Paste s_ℓ = 1 times: we get s = 2313113113111311311131131.
* Step 4: ℓ = 5 = x, so we stop.
At the end of the procedure, s has length 25. | import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
MAX=10**9+7
def solve():
x = int(input())
s = [int(i) for i in input()]
ans=len(s)
c = ""
l = 0
while l < x:
l += 1
k=len(s)
if k < x:
#s += s[l:]*(s[l - 1]-1)
for i in range(s[l-1] - 1):
for j in range(l, k):
s.append(s[j])
ans+= (s[l - 1]-1) *(ans - l)
ans%=MAX
print(ans)
t=int(input())
for _ in range(t):
solve()
#
# mod = 10 ** 9 + 7
#
#
# def solve():
# x = int(input())
# s = [int(i) for i in input()]
# ans = len(s)
# cur = -1
# while cur != x - 1:
# cur += 1
# if len(s) < x:
# k = len(s)
# for _ in range(s[cur] - 1):
# for j in range(cur + 1, k):
# s.append(s[j])
# ans += (s[cur] - 1) * (ans - (cur + 1))
# ans %= mod
# print(ans)
#
#
# t = int(input())
# for i in range(t):
# solve()
| {
"input": [
"4\n5\n231\n7\n2323\n6\n333\n24\n133321333\n",
"9\n1500\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"1\n1000000\n22\n",
"1\n941759\n1223231111\n",
"1\n1000000\n2211\n",
"1\n1000000\n221\n",
"1\n1000000\n1212\n",
"1\n1000000\n1221\n",
"1\n1000000\n2121\n",
"1\n1000000\n2112\n",
"1\n1000000\n223\n",
"4\n5\n231\n7\n2323\n6\n333\n1\n133321333\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"4\n5\n231\n8\n2323\n6\n333\n24\n133321333\n",
"1\n0010000\n223\n",
"4\n5\n231\n5\n2323\n6\n333\n1\n133321333\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n170\n111111122\n1500\n11111121111121111111\n",
"9\n1500\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"4\n5\n231\n7\n2323\n6\n333\n2\n133321333\n",
"4\n5\n231\n8\n2323\n2\n333\n24\n133321333\n",
"4\n5\n231\n8\n2323\n2\n333\n20\n133321333\n",
"4\n5\n231\n14\n2323\n2\n333\n20\n133321333\n",
"4\n5\n231\n14\n2323\n2\n333\n36\n133321333\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n829\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"9\n1676\n1212\n1500\n1221\n549\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n671\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2103\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"4\n3\n231\n7\n2323\n6\n333\n2\n133321333\n",
"4\n5\n231\n14\n2323\n3\n333\n36\n133321333\n",
"4\n3\n231\n14\n2323\n2\n333\n36\n133321333\n",
"9\n1676\n1212\n1500\n1221\n556\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n671\n1111111111221111111\n2970\n111111122\n1500\n11111121111121111111\n",
"9\n2103\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n2660\n111111122\n1500\n11111121111121111111\n",
"4\n3\n231\n6\n2323\n6\n333\n2\n133321333\n",
"4\n5\n231\n16\n2323\n3\n333\n36\n133321333\n",
"4\n3\n231\n6\n2323\n9\n333\n2\n133321333\n",
"4\n3\n231\n16\n2323\n3\n333\n36\n133321333\n",
"4\n3\n231\n6\n2323\n15\n333\n2\n133321333\n",
"4\n3\n231\n5\n2323\n15\n333\n2\n133321333\n",
"9\n1500\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n647\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"4\n5\n231\n7\n2323\n6\n333\n1\n246449458\n",
"1\n0000001\n223\n",
"4\n5\n231\n8\n2323\n1\n333\n24\n133321333\n",
"4\n3\n231\n8\n2323\n2\n333\n20\n133321333\n",
"4\n5\n231\n14\n2323\n2\n131\n36\n133321333\n",
"4\n4\n231\n19\n2323\n2\n333\n36\n133321333\n",
"4\n10\n231\n5\n2323\n6\n333\n1\n131324532\n",
"9\n1676\n1212\n1500\n1221\n1019\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2103\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n2010\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n457\n22\n1500\n1111112111111112\n671\n1111111111221111111\n2970\n111111122\n1500\n11111121111121111111\n",
"4\n3\n231\n6\n2323\n6\n333\n2\n120735757\n",
"4\n5\n231\n23\n2323\n3\n333\n36\n133321333\n",
"4\n3\n231\n6\n2323\n12\n333\n2\n133321333\n",
"4\n5\n231\n12\n2323\n2\n131\n36\n133321333\n",
"4\n4\n231\n32\n2323\n2\n333\n36\n133321333\n",
"9\n2723\n1212\n1500\n1221\n1434\n122\n1500\n12121\n457\n22\n1500\n1111112111111112\n671\n1111111111221111111\n2970\n111111122\n1500\n11111121111121111111\n",
"9\n2103\n1212\n1500\n1221\n1950\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n2660\n111111122\n1457\n11111121111121111111\n",
"4\n3\n231\n9\n2323\n6\n333\n2\n120735757\n",
"4\n5\n231\n35\n2323\n3\n333\n36\n133321333\n",
"4\n5\n231\n12\n2323\n2\n125\n36\n133321333\n",
"9\n2723\n1212\n1500\n1221\n1434\n122\n1500\n12121\n457\n22\n1500\n1111112111111112\n671\n1111111111221111111\n2970\n111111122\n575\n11111121111121111111\n",
"4\n3\n231\n9\n2323\n6\n333\n2\n220427174\n",
"9\n2723\n1212\n1500\n1221\n1434\n122\n1500\n12121\n457\n22\n1500\n1111112111111112\n671\n1111111111221111111\n2970\n111111122\n953\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1434\n122\n1500\n12121\n457\n22\n1500\n1111112111111112\n671\n1111111111221111111\n3904\n111111122\n953\n11111121111121111111\n",
"9\n1500\n1212\n1500\n1221\n1500\n122\n532\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"1\n359857\n1223231111\n",
"4\n7\n231\n7\n2323\n6\n333\n1\n133321333\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1500\n111111122\n748\n11111121111121111111\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n1480\n12121\n1500\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n1710\n111111122\n1500\n11111121111121111111\n",
"9\n2723\n1212\n1500\n1221\n1500\n122\n1500\n12121\n2061\n22\n1500\n1111112111111112\n1500\n1111111111221111111\n170\n111111122\n1500\n11111121111121111111\n",
"4\n5\n231\n8\n2323\n2\n333\n3\n133321333\n",
"9\n1676\n1212\n1500\n1221\n1500\n122\n829\n12121\n1500\n22\n1500\n1111112111111112\n2222\n1111111111221111111\n1500\n111111122\n1500\n11111121111121111111\n",
"4\n4\n231\n14\n2323\n2\n333\n36\n133321333\n",
"4\n5\n231\n5\n2323\n6\n333\n1\n131324532\n",
"9\n2103\n1212\n1500\n1221\n1500\n122\n1500\n12121\n1500\n22\n2223\n1111112111111112\n1500\n1111111111221111111\n2660\n111111122\n1457\n11111121111121111111\n",
"4\n6\n231\n8\n2323\n1\n333\n24\n133321333\n"
],
"output": [
"25\n1438\n1101\n686531475\n",
"1504\n1599\n1502\n1598\n1502\n1510\n1657\n1502\n1763\n",
"1000002\n",
"374870\n",
"1002004\n",
"1001822\n",
"1000004\n",
"1001823\n",
"1001821\n",
"1000006\n",
"899114971\n",
"25\n1438\n1101\n9\n",
"1680\n1599\n1502\n1598\n1502\n1510\n1657\n1502\n1763\n",
"25\n2868\n1101\n686531475\n",
"222930323\n",
"25\n245\n1101\n9\n",
"1680\n1599\n1502\n1598\n1502\n1510\n1657\n1712\n1763\n",
"2726\n1599\n1502\n1598\n1502\n1510\n1657\n1712\n1763\n",
"2726\n1599\n1502\n1598\n1502\n1510\n1657\n172\n1763\n",
"1504\n1599\n1502\n1598\n1502\n2239\n1657\n1502\n1763\n",
"25\n1438\n1101\n23\n",
"25\n2868\n17\n686531475\n",
"25\n2868\n17\n82549793\n",
"25\n926159\n17\n82549793\n",
"25\n926159\n17\n331214873\n",
"1680\n1599\n1502\n905\n1502\n1510\n1657\n1502\n1763\n",
"1680\n1599\n551\n1598\n1502\n1510\n1657\n1712\n1763\n",
"2726\n1599\n1502\n1598\n1502\n1510\n874\n1712\n1763\n",
"2106\n1599\n1502\n1598\n1502\n2239\n1657\n1502\n1763\n",
"11\n1438\n1101\n23\n",
"25\n926159\n45\n331214873\n",
"11\n926159\n17\n331214873\n",
"1680\n1599\n558\n1598\n1502\n1510\n1657\n1712\n1763\n",
"2726\n1599\n1502\n1598\n1502\n1510\n874\n2972\n1763\n",
"2106\n1599\n1502\n1598\n1502\n2239\n1657\n2662\n1763\n",
"11\n484\n1101\n23\n",
"25\n5556878\n45\n331214873\n",
"11\n484\n29535\n23\n",
"11\n5556878\n45\n331214873\n",
"11\n484\n21523377\n23\n",
"11\n245\n21523377\n23\n",
"1504\n1599\n1502\n1598\n1502\n664\n1657\n1502\n1763\n",
"25\n1438\n1101\n17\n",
"5\n",
"25\n2868\n7\n686531475\n",
"11\n2868\n17\n82549793\n",
"25\n926159\n5\n331214873\n",
"25\n150035254\n17\n331214873\n",
"163\n245\n1101\n9\n",
"1680\n1599\n1021\n1598\n1502\n1510\n1657\n1712\n1763\n",
"2106\n1599\n1502\n1598\n1502\n2239\n1657\n1502\n2264\n",
"2726\n1599\n1502\n1598\n459\n1510\n874\n2972\n1763\n",
"11\n484\n1101\n16\n",
"25\n401268385\n45\n331214873\n",
"11\n484\n797175\n23\n",
"25\n154371\n5\n331214873\n",
"25\n197061518\n17\n331214873\n",
"2726\n1599\n1436\n1598\n459\n1510\n874\n2972\n1763\n",
"2106\n1599\n1952\n1598\n1502\n2239\n1657\n2662\n1763\n",
"11\n8586\n1101\n16\n",
"25\n364737833\n45\n331214873\n",
"25\n154371\n4\n331214873\n",
"2726\n1599\n1436\n1598\n459\n1510\n874\n2972\n735\n",
"11\n8586\n1101\n32\n",
"2726\n1599\n1436\n1598\n459\n1510\n874\n2972\n1193\n",
"2726\n1599\n1436\n1598\n459\n1510\n874\n3906\n1193\n",
"1504\n1599\n1502\n597\n1502\n1510\n1657\n1502\n1763\n",
"62305463\n",
"61\n1438\n1101\n9\n",
"1680\n1599\n1502\n1598\n1502\n1510\n1657\n1502\n950\n",
"1680\n1599\n1502\n1542\n1502\n1510\n1657\n1712\n1763\n",
"2726\n1599\n1502\n1598\n2063\n1510\n1657\n172\n1763\n",
"25\n2868\n17\n63\n",
"1680\n1599\n1502\n905\n1502\n1510\n2502\n1502\n1763\n",
"25\n926159\n17\n331214873\n",
"25\n245\n1101\n9\n",
"2106\n1599\n1502\n1598\n1502\n2239\n1657\n2662\n1763\n",
"25\n2868\n7\n686531475\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
We start with a string s consisting only of the digits 1, 2, or 3. The length of s is denoted by |s|. For each i from 1 to |s|, the i-th character of s is denoted by s_i.
There is one cursor. The cursor's location ℓ is denoted by an integer in \{0, …, |s|\}, with the following meaning:
* If ℓ = 0, then the cursor is located before the first character of s.
* If ℓ = |s|, then the cursor is located right after the last character of s.
* If 0 < ℓ < |s|, then the cursor is located between s_ℓ and s_{ℓ+1}.
We denote by s_left the string to the left of the cursor and s_right the string to the right of the cursor.
We also have a string c, which we call our clipboard, which starts out as empty. There are three types of actions:
* The Move action. Move the cursor one step to the right. This increments ℓ once.
* The Cut action. Set c ← s_right, then set s ← s_left.
* The Paste action. Append the value of c to the end of the string s. Note that this doesn't modify c.
The cursor initially starts at ℓ = 0. Then, we perform the following procedure:
1. Perform the Move action once.
2. Perform the Cut action once.
3. Perform the Paste action s_ℓ times.
4. If ℓ = x, stop. Otherwise, return to step 1.
You're given the initial string s and the integer x. What is the length of s when the procedure stops? Since this value may be very large, only find it modulo 10^9 + 7.
It is guaranteed that ℓ ≤ |s| at any time.
Input
The first line of input contains a single integer t (1 ≤ t ≤ 1000) denoting the number of test cases. The next lines contain descriptions of the test cases.
The first line of each test case contains a single integer x (1 ≤ x ≤ 10^6). The second line of each test case consists of the initial string s (1 ≤ |s| ≤ 500). It is guaranteed, that s consists of the characters "1", "2", "3".
It is guaranteed that the sum of x in a single file is at most 10^6. It is guaranteed that in each test case before the procedure will stop it will be true that ℓ ≤ |s| at any time.
Output
For each test case, output a single line containing a single integer denoting the answer for that test case modulo 10^9 + 7.
Example
Input
4
5
231
7
2323
6
333
24
133321333
Output
25
1438
1101
686531475
Note
Let's illustrate what happens with the first test case. Initially, we have s = 231. Initially, ℓ = 0 and c = \varepsilon (the empty string). The following things happen if we follow the procedure above:
* Step 1, Move once: we get ℓ = 1.
* Step 2, Cut once: we get s = 2 and c = 31.
* Step 3, Paste s_ℓ = 2 times: we get s = 23131.
* Step 4: ℓ = 1 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 2.
* Step 2, Cut once: we get s = 23 and c = 131.
* Step 3, Paste s_ℓ = 3 times: we get s = 23131131131.
* Step 4: ℓ = 2 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 3.
* Step 2, Cut once: we get s = 231 and c = 31131131.
* Step 3, Paste s_ℓ = 1 time: we get s = 23131131131.
* Step 4: ℓ = 3 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 4.
* Step 2, Cut once: we get s = 2313 and c = 1131131.
* Step 3, Paste s_ℓ = 3 times: we get s = 2313113113111311311131131.
* Step 4: ℓ = 4 not= x = 5, so we return to step 1.
* Step 1, Move once: we get ℓ = 5.
* Step 2, Cut once: we get s = 23131 and c = 13113111311311131131.
* Step 3, Paste s_ℓ = 1 times: we get s = 2313113113111311311131131.
* Step 4: ℓ = 5 = x, so we stop.
At the end of the procedure, s has length 25.
### Input:
4
5
231
7
2323
6
333
24
133321333
### Output:
25
1438
1101
686531475
### Input:
9
1500
1212
1500
1221
1500
122
1500
12121
1500
22
1500
1111112111111112
1500
1111111111221111111
1500
111111122
1500
11111121111121111111
### Output:
1504
1599
1502
1598
1502
1510
1657
1502
1763
### Code:
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
MAX=10**9+7
def solve():
x = int(input())
s = [int(i) for i in input()]
ans=len(s)
c = ""
l = 0
while l < x:
l += 1
k=len(s)
if k < x:
#s += s[l:]*(s[l - 1]-1)
for i in range(s[l-1] - 1):
for j in range(l, k):
s.append(s[j])
ans+= (s[l - 1]-1) *(ans - l)
ans%=MAX
print(ans)
t=int(input())
for _ in range(t):
solve()
#
# mod = 10 ** 9 + 7
#
#
# def solve():
# x = int(input())
# s = [int(i) for i in input()]
# ans = len(s)
# cur = -1
# while cur != x - 1:
# cur += 1
# if len(s) < x:
# k = len(s)
# for _ in range(s[cur] - 1):
# for j in range(cur + 1, k):
# s.append(s[j])
# ans += (s[cur] - 1) * (ans - (cur + 1))
# ans %= mod
# print(ans)
#
#
# t = int(input())
# for i in range(t):
# solve()
|
1301_C. Ayoub's function_3055 | Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1".
More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≤ l ≤ r ≤ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1".
For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5).
Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s).
Mahmoud couldn't solve the problem so he asked you for help. Can you help him?
Input
The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of the test cases follows.
The only line for each test case contains two integers n, m (1 ≤ n ≤ 10^{9}, 0 ≤ m ≤ n) — the length of the string and the number of symbols equal to "1" in it.
Output
For every test case print one integer number — the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1".
Example
Input
5
3 1
3 2
3 3
4 0
5 2
Output
4
5
6
0
12
Note
In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4.
In the second test case, the string s with the maximum value is "101".
In the third test case, the string s with the maximum value is "111".
In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0.
In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement. | '''input
5
3 1
3 2
3 3
4 0
5 2
'''
import sys
read = lambda: list(map(int,sys.stdin.readline().strip().split()))
# try:
sigma = lambda x:x*(x+1)//2
for _ in range(int(input())):
n,m = read()
k = n-m
total = sigma(n)
# if m==0 or m==n:
# print(total)
# continue
if k>m:
e,f = divmod(k,m+1)
total -= (m+1-f)*sigma(e)+f*sigma(e+1)
else:
total -= k
print(total) | {
"input": [
"5\n3 1\n3 2\n3 3\n4 0\n5 2\n",
"5\n3 1\n3 2\n3 3\n0 0\n5 2\n",
"5\n3 1\n3 2\n3 3\n0 0\n10 2\n",
"5\n3 0\n3 2\n3 3\n0 0\n10 2\n",
"5\n3 0\n3 2\n3 3\n4 0\n5 2\n",
"5\n4 1\n3 2\n3 3\n0 0\n5 2\n",
"5\n3 0\n3 2\n3 3\n0 0\n9 2\n",
"5\n3 0\n3 2\n3 3\n4 0\n8 2\n",
"5\n3 1\n3 2\n3 3\n4 0\n8 2\n",
"5\n2 1\n3 2\n3 3\n2 0\n10 2\n",
"5\n2 1\n3 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 2\n3 3\n8 1\n8 2\n",
"5\n2 1\n3 2\n3 3\n2 1\n12 2\n",
"5\n3 1\n3 2\n3 2\n8 1\n8 2\n",
"5\n3 1\n3 2\n3 2\n8 0\n8 2\n",
"5\n6 1\n3 2\n3 2\n8 0\n8 2\n",
"5\n6 1\n3 2\n3 0\n8 0\n8 2\n",
"5\n3 0\n3 3\n3 3\n4 0\n5 2\n",
"5\n4 1\n4 2\n3 3\n0 0\n5 2\n",
"5\n3 1\n3 2\n3 3\n1 0\n10 3\n",
"5\n2 2\n3 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 2\n3 3\n1 1\n8 2\n",
"5\n2 0\n3 2\n3 3\n2 1\n12 2\n",
"5\n3 1\n3 2\n3 2\n8 1\n8 0\n",
"5\n3 1\n3 2\n3 3\n7 0\n5 4\n",
"5\n4 1\n4 2\n3 3\n0 0\n5 0\n",
"5\n3 0\n3 2\n3 3\n1 0\n10 3\n",
"5\n3 0\n3 2\n3 3\n8 0\n6 2\n",
"5\n3 1\n3 2\n3 3\n6 0\n8 3\n",
"5\n3 2\n3 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 3\n3 3\n1 1\n8 2\n",
"5\n2 0\n3 2\n3 1\n2 1\n12 2\n",
"5\n6 1\n3 2\n3 2\n8 1\n8 0\n",
"5\n3 1\n3 2\n5 3\n7 0\n5 4\n",
"5\n4 1\n4 2\n6 3\n0 0\n5 0\n",
"5\n3 1\n3 2\n3 3\n6 0\n8 6\n",
"5\n6 2\n3 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 3\n3 3\n1 1\n13 2\n",
"5\n2 1\n3 2\n3 1\n2 1\n12 2\n",
"5\n6 1\n3 2\n3 2\n8 2\n8 0\n",
"5\n1 1\n3 2\n5 3\n7 0\n5 4\n",
"5\n4 1\n4 3\n6 3\n0 0\n5 0\n",
"5\n5 0\n3 2\n3 3\n1 0\n20 3\n",
"5\n6 4\n3 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 3\n3 3\n2 1\n13 2\n",
"5\n6 2\n3 2\n3 2\n8 2\n8 0\n",
"5\n6 1\n3 0\n5 0\n16 0\n8 2\n",
"5\n4 1\n4 3\n6 6\n0 0\n5 0\n",
"5\n5 0\n3 3\n3 3\n1 0\n20 3\n",
"5\n6 4\n3 2\n3 2\n2 1\n10 2\n",
"5\n3 2\n3 3\n3 3\n2 1\n13 2\n",
"5\n4 2\n3 2\n3 2\n8 2\n8 0\n",
"5\n6 1\n3 0\n5 0\n16 0\n8 1\n",
"5\n4 1\n4 0\n6 6\n0 0\n5 0\n",
"5\n6 4\n5 2\n3 2\n2 1\n10 2\n",
"5\n3 2\n4 3\n3 3\n2 1\n13 2\n",
"5\n6 4\n5 2\n4 2\n2 1\n10 2\n",
"5\n3 3\n4 3\n3 3\n2 1\n13 2\n",
"5\n6 1\n0 0\n5 0\n16 1\n8 1\n",
"5\n6 4\n5 2\n4 2\n2 2\n10 2\n",
"5\n3 3\n4 3\n4 3\n2 1\n13 2\n",
"5\n6 4\n5 2\n4 2\n2 2\n9 2\n",
"5\n6 5\n5 2\n4 2\n2 2\n9 2\n",
"5\n6 5\n5 2\n4 2\n2 2\n9 3\n",
"5\n6 5\n5 2\n4 2\n3 2\n9 3\n",
"5\n3 1\n6 2\n3 3\n0 0\n10 2\n",
"5\n4 1\n3 2\n6 3\n0 0\n5 2\n",
"5\n3 1\n3 3\n3 3\n1 0\n10 2\n",
"5\n3 1\n3 2\n3 3\n0 0\n9 2\n",
"5\n4 0\n6 2\n3 3\n0 0\n5 2\n",
"5\n3 2\n3 2\n3 3\n1 0\n10 2\n",
"5\n3 1\n3 1\n3 3\n4 0\n8 2\n",
"5\n2 1\n3 2\n3 3\n2 0\n7 2\n",
"5\n5 1\n3 2\n3 3\n8 0\n8 2\n",
"5\n2 1\n5 2\n3 3\n2 1\n10 2\n",
"5\n3 1\n3 2\n3 3\n8 1\n15 2\n",
"5\n2 1\n3 2\n3 0\n2 1\n12 2\n",
"5\n3 1\n3 2\n3 0\n8 1\n8 2\n",
"5\n3 2\n3 2\n3 2\n8 0\n8 2\n",
"5\n6 1\n6 2\n3 2\n8 0\n8 2\n",
"5\n6 1\n3 2\n3 0\n8 0\n8 1\n",
"5\n4 1\n4 2\n3 1\n0 0\n5 2\n",
"5\n3 0\n6 2\n3 3\n0 0\n9 2\n",
"5\n3 0\n3 1\n3 3\n8 0\n8 2\n",
"5\n2 2\n3 2\n3 3\n1 1\n10 2\n",
"5\n3 1\n3 2\n5 3\n1 1\n8 2\n",
"5\n2 0\n2 2\n3 3\n2 1\n12 2\n",
"5\n6 1\n3 2\n3 0\n10 1\n8 2\n",
"5\n3 0\n3 2\n3 3\n1 0\n13 3\n",
"5\n3 1\n3 2\n3 3\n8 0\n6 2\n",
"5\n3 1\n3 2\n3 3\n1 0\n10 2\n",
"5\n4 0\n3 2\n3 3\n0 0\n5 2\n",
"5\n3 1\n3 2\n3 3\n2 0\n10 2\n",
"5\n3 1\n3 2\n3 3\n8 0\n8 2\n",
"5\n3 1\n3 2\n3 3\n7 0\n5 2\n",
"5\n3 0\n3 2\n3 3\n1 0\n9 2\n",
"5\n3 0\n3 2\n3 3\n8 0\n8 2\n",
"5\n3 1\n3 2\n3 3\n6 0\n8 2\n",
"5\n6 1\n3 2\n3 0\n10 0\n8 2\n",
"5\n6 1\n3 2\n3 0\n16 0\n8 2\n",
"5\n5 0\n3 2\n3 3\n1 0\n10 3\n"
],
"output": [
"4\n5\n6\n0\n12\n",
"4\n5\n6\n0\n12\n",
"4\n5\n6\n0\n40\n",
"0\n5\n6\n0\n40\n",
"0\n5\n6\n0\n12\n",
"6\n5\n6\n0\n12\n",
"0\n5\n6\n0\n33\n",
"0\n5\n6\n0\n27\n",
"4\n5\n6\n0\n27\n",
"2\n5\n6\n0\n40\n",
"2\n5\n6\n2\n40\n",
"4\n5\n6\n20\n27\n",
"2\n5\n6\n2\n56\n",
"4\n5\n5\n20\n27\n",
"4\n5\n5\n0\n27\n",
"12\n5\n5\n0\n27\n",
"12\n5\n0\n0\n27\n",
"0\n6\n6\n0\n12\n",
"6\n8\n6\n0\n12\n",
"4\n5\n6\n0\n45\n",
"3\n5\n6\n2\n40\n",
"4\n5\n6\n1\n27\n",
"0\n5\n6\n2\n56\n",
"4\n5\n5\n20\n0\n",
"4\n5\n6\n0\n14\n",
"6\n8\n6\n0\n0\n",
"0\n5\n6\n0\n45\n",
"0\n5\n6\n0\n16\n",
"4\n5\n6\n0\n30\n",
"5\n5\n6\n2\n40\n",
"4\n6\n6\n1\n27\n",
"0\n5\n4\n2\n56\n",
"12\n5\n5\n20\n0\n",
"4\n5\n13\n0\n14\n",
"6\n8\n18\n0\n0\n",
"4\n5\n6\n0\n34\n",
"16\n5\n6\n2\n40\n",
"4\n6\n6\n1\n65\n",
"2\n5\n4\n2\n56\n",
"12\n5\n5\n27\n0\n",
"1\n5\n13\n0\n14\n",
"6\n9\n18\n0\n0\n",
"0\n5\n6\n0\n165\n",
"19\n5\n6\n2\n40\n",
"4\n6\n6\n2\n65\n",
"16\n5\n5\n27\n0\n",
"12\n0\n0\n0\n27\n",
"6\n9\n21\n0\n0\n",
"0\n6\n6\n0\n165\n",
"19\n5\n5\n2\n40\n",
"5\n6\n6\n2\n65\n",
"8\n5\n5\n27\n0\n",
"12\n0\n0\n0\n20\n",
"6\n0\n21\n0\n0\n",
"19\n12\n5\n2\n40\n",
"5\n9\n6\n2\n65\n",
"19\n12\n8\n2\n40\n",
"6\n9\n6\n2\n65\n",
"12\n0\n0\n72\n20\n",
"19\n12\n8\n3\n40\n",
"6\n9\n9\n2\n65\n",
"19\n12\n8\n3\n33\n",
"20\n12\n8\n3\n33\n",
"20\n12\n8\n3\n37\n",
"20\n12\n8\n5\n37\n",
"4\n16\n6\n0\n40\n",
"6\n5\n18\n0\n12\n",
"4\n6\n6\n0\n40\n",
"4\n5\n6\n0\n33\n",
"0\n16\n6\n0\n12\n",
"5\n5\n6\n0\n40\n",
"4\n4\n6\n0\n27\n",
"2\n5\n6\n0\n21\n",
"9\n5\n6\n0\n27\n",
"2\n12\n6\n2\n40\n",
"4\n5\n6\n20\n85\n",
"2\n5\n0\n2\n56\n",
"4\n5\n0\n20\n27\n",
"5\n5\n5\n0\n27\n",
"12\n16\n5\n0\n27\n",
"12\n5\n0\n0\n20\n",
"6\n8\n4\n0\n12\n",
"0\n16\n6\n0\n33\n",
"0\n4\n6\n0\n27\n",
"3\n5\n6\n1\n40\n",
"4\n5\n13\n1\n27\n",
"0\n3\n6\n2\n56\n",
"12\n5\n0\n30\n27\n",
"0\n5\n6\n0\n73\n",
"4\n5\n6\n0\n16\n",
"4\n5\n6\n0\n40\n",
"0\n5\n6\n0\n12\n",
"4\n5\n6\n0\n40\n",
"4\n5\n6\n0\n27\n",
"4\n5\n6\n0\n12\n",
"0\n5\n6\n0\n33\n",
"0\n5\n6\n0\n27\n",
"4\n5\n6\n0\n27\n",
"12\n5\n0\n0\n27\n",
"12\n5\n0\n0\n27\n",
"0\n5\n6\n0\n45\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1".
More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≤ l ≤ r ≤ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1".
For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5).
Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s).
Mahmoud couldn't solve the problem so he asked you for help. Can you help him?
Input
The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of the test cases follows.
The only line for each test case contains two integers n, m (1 ≤ n ≤ 10^{9}, 0 ≤ m ≤ n) — the length of the string and the number of symbols equal to "1" in it.
Output
For every test case print one integer number — the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1".
Example
Input
5
3 1
3 2
3 3
4 0
5 2
Output
4
5
6
0
12
Note
In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4.
In the second test case, the string s with the maximum value is "101".
In the third test case, the string s with the maximum value is "111".
In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0.
In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement.
### Input:
5
3 1
3 2
3 3
4 0
5 2
### Output:
4
5
6
0
12
### Input:
5
3 1
3 2
3 3
0 0
5 2
### Output:
4
5
6
0
12
### Code:
'''input
5
3 1
3 2
3 3
4 0
5 2
'''
import sys
read = lambda: list(map(int,sys.stdin.readline().strip().split()))
# try:
sigma = lambda x:x*(x+1)//2
for _ in range(int(input())):
n,m = read()
k = n-m
total = sigma(n)
# if m==0 or m==n:
# print(total)
# continue
if k>m:
e,f = divmod(k,m+1)
total -= (m+1-f)*sigma(e)+f*sigma(e+1)
else:
total -= k
print(total) |
1325_C. Ehab and Path-etic MEXs_3059 | You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:
* Every label is an integer between 0 and n-2 inclusive.
* All the written labels are distinct.
* The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible.
Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.
Input
The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.
Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.
Output
Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).
Examples
Input
3
1 2
1 3
Output
0
1
Input
6
1 2
1 3
2 4
2 5
5 6
Output
0
3
2
4
1
Note
The tree from the second sample:
<image> | n = int(input())
occ = [0 for i in range(n)]
graph = [[0,0] for i in range(n-1)]
for i in range(n-1):
x, y = map(int,input().split())
occ[x-1]+=1
occ[y-1]+=1
graph[i][0] = x-1
graph[i][1] = y-1
fin = [-1 for i in range(n-1)]
for i in range(n):
if occ[i] >= 3 :
var = 0
for j in range(n-1):
if graph[j][0] == i or graph[j][1] == i:
fin[j] = var
var += 1
break
else:
var = 0
for i in range(n):
if var > 1:
break
if occ[i] == 1:
for j in range(n-1):
if graph[j][0] == i or graph[j][1] == i:
fin[j] = var
var += 1
break
for i in fin:
if n == 2:
print(0)
break
if i == -1:
print(var)
var += 1
else:
print(i) | {
"input": [
"6\n1 2\n1 3\n2 4\n2 5\n5 6\n",
"3\n1 2\n1 3\n",
"6\n1 2\n2 3\n3 4\n3 5\n3 6\n",
"7\n6 4\n3 7\n3 5\n1 3\n4 2\n7 4\n",
"7\n3 2\n5 7\n4 2\n7 6\n6 3\n1 6\n",
"2\n1 2\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n7 8\n7 9\n7 10\n",
"4\n2 3\n2 4\n2 1\n",
"5\n1 3\n4 3\n2 5\n3 2\n",
"2\n2 1\n",
"7\n2 1\n4 7\n2 3\n6 4\n7 3\n1 5\n",
"7\n5 6\n2 6\n6 4\n6 1\n6 3\n6 7\n",
"6\n1 2\n1 3\n2 4\n2 5\n5 6\n",
"11\n2 3\n3 4\n4 7\n7 8\n1 3\n3 5\n4 10\n4 11\n6 7\n7 9\n",
"7\n6 4\n3 7\n5 5\n1 3\n4 2\n7 4\n",
"7\n4 2\n5 7\n4 2\n7 6\n6 3\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n7 8\n7 8\n7 10\n",
"4\n2 3\n2 4\n1 1\n",
"5\n1 3\n4 3\n2 5\n4 2\n",
"7\n5 6\n2 6\n6 4\n0 1\n6 3\n6 7\n",
"6\n1 2\n0 3\n2 4\n2 5\n5 6\n",
"3\n1 2\n2 3\n",
"6\n1 3\n0 3\n2 4\n2 5\n5 6\n",
"7\n6 2\n5 7\n4 3\n7 6\n6 3\n0 6\n",
"7\n3 2\n5 7\n4 3\n7 6\n6 3\n0 6\n",
"6\n1 2\n2 3\n3 4\n6 5\n3 6\n",
"2\n1 1\n",
"5\n0 5\n4 3\n3 5\n3 2\n",
"7\n5 6\n2 6\n1 4\n6 1\n6 3\n6 7\n",
"5\n0 3\n4 3\n2 5\n3 2\n",
"6\n1 5\n0 3\n2 4\n2 5\n5 6\n",
"6\n1 3\n0 3\n2 4\n2 3\n5 1\n",
"7\n6 4\n3 7\n5 5\n0 3\n4 2\n7 4\n",
"7\n4 2\n5 7\n4 3\n7 6\n6 3\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n7 8\n7 8\n7 10\n",
"5\n0 3\n4 3\n2 5\n4 2\n",
"7\n4 2\n5 7\n4 3\n7 6\n6 3\n0 6\n",
"7\n6 3\n3 7\n3 5\n1 3\n4 2\n7 4\n",
"7\n3 2\n5 7\n4 2\n7 4\n6 3\n1 6\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n7 8\n7 9\n7 10\n",
"4\n2 3\n2 4\n2 0\n",
"5\n1 3\n0 3\n2 5\n4 2\n",
"2\n2 0\n",
"6\n1 2\n1 3\n2 4\n2 5\n3 6\n",
"3\n1 2\n1 2\n",
"7\n6 4\n3 7\n5 5\n1 6\n4 2\n7 4\n",
"7\n4 3\n5 7\n4 2\n7 6\n6 3\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n13 1\n6 7\n7 8\n7 8\n7 10\n",
"4\n2 3\n2 4\n1 2\n",
"5\n1 3\n4 3\n3 5\n3 2\n",
"3\n1 2\n2 1\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n6 8\n7 8\n7 10\n",
"6\n1 3\n0 3\n2 4\n2 5\n5 1\n",
"7\n6 3\n3 7\n3 5\n1 3\n4 2\n7 5\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n5 8\n7 9\n7 10\n",
"4\n3 3\n2 4\n2 0\n",
"6\n1 2\n1 3\n2 6\n2 5\n3 6\n",
"3\n1 2\n1 0\n",
"7\n4 6\n5 7\n4 2\n7 6\n6 3\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n13 1\n6 7\n11 8\n7 8\n7 10\n",
"4\n2 3\n2 4\n2 2\n",
"5\n0 3\n4 3\n3 5\n3 2\n",
"3\n1 2\n2 0\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n6 3\n7 8\n7 10\n",
"6\n1 3\n0 3\n2 4\n2 4\n5 1\n",
"7\n6 3\n3 7\n3 5\n1 6\n4 2\n7 5\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n5 8\n0 9\n7 10\n",
"6\n1 2\n1 3\n2 6\n2 5\n6 6\n",
"7\n4 6\n5 7\n4 2\n7 6\n6 0\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n11 1\n6 7\n11 8\n7 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n6 3\n7 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 12\n12 13\n13 11\n6 7\n5 8\n0 9\n7 10\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n11 1\n6 7\n11 6\n7 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n9 11\n11 12\n12 13\n13 11\n6 7\n5 8\n0 9\n7 10\n",
"7\n5 2\n5 7\n4 2\n7 6\n6 3\n1 6\n",
"2\n2 2\n",
"7\n2 1\n4 7\n2 3\n6 6\n7 3\n1 5\n",
"6\n1 4\n1 3\n2 4\n2 5\n5 6\n",
"3\n1 2\n0 3\n",
"7\n5 6\n2 6\n6 4\n0 0\n6 3\n6 7\n",
"6\n1 1\n0 3\n2 4\n2 5\n5 6\n",
"7\n4 2\n5 7\n1 3\n7 6\n6 3\n0 6\n",
"6\n1 2\n2 3\n3 4\n6 5\n3 0\n",
"6\n1 0\n1 3\n2 4\n2 5\n3 6\n",
"7\n4 3\n5 1\n4 2\n7 6\n6 3\n1 6\n",
"4\n2 3\n1 4\n1 2\n",
"5\n1 3\n4 3\n3 5\n5 2\n",
"3\n1 2\n0 1\n",
"13\n0 4\n2 4\n3 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n6 8\n7 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 12\n12 13\n13 6\n6 7\n5 8\n7 9\n0 10\n",
"6\n1 2\n1 3\n2 6\n2 5\n3 2\n",
"7\n4 6\n5 7\n4 2\n7 6\n6 3\n0 6\n",
"3\n0 2\n2 0\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 10\n12 13\n13 6\n6 7\n7 3\n7 8\n7 10\n",
"6\n1 3\n0 3\n0 4\n2 4\n5 1\n",
"7\n6 3\n3 7\n3 5\n1 6\n7 2\n7 5\n",
"7\n4 6\n5 7\n4 2\n7 2\n6 0\n1 6\n",
"13\n1 4\n2 4\n3 4\n4 5\n5 11\n11 12\n12 13\n11 1\n6 7\n11 8\n10 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n5 11\n11 10\n12 13\n13 6\n7 7\n6 3\n7 8\n7 10\n",
"13\n1 4\n2 4\n6 4\n4 5\n7 11\n11 12\n12 13\n13 11\n6 7\n5 8\n0 9\n7 10\n"
],
"output": [
"0\n3\n1\n2\n4\n",
"0\n1\n",
"0\n4\n1\n2\n3\n",
"3\n0\n1\n2\n4\n5\n",
"3\n4\n5\n0\n1\n2\n",
"0\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n1\n3\n2\n",
"0\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n5\n",
"0\n3\n1\n2\n4\n",
"0\n1\n3\n4\n2\n5\n6\n7\n8\n9\n",
"0\n3\n4\n5\n1\n2\n",
"3\n4\n5\n0\n1\n2\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n1\n2\n3\n",
"0\n1\n2\n3\n4\n5\n",
"0\n3\n1\n2\n4\n",
"0\n1\n",
"0\n1\n2\n3\n4\n",
"0\n3\n4\n1\n2\n5\n",
"0\n3\n1\n4\n2\n5\n",
"3\n0\n1\n4\n2\n",
"0\n",
"3\n0\n1\n2\n",
"0\n1\n3\n2\n4\n5\n",
"0\n1\n3\n2\n",
"0\n3\n4\n1\n2\n",
"0\n1\n3\n2\n4\n",
"0\n3\n4\n5\n1\n2\n",
"3\n4\n5\n0\n1\n2\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n",
"3\n4\n5\n0\n1\n2\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n1\n2\n3\n",
"0\n",
"0\n3\n1\n2\n4\n",
"0\n1\n",
"0\n3\n4\n5\n1\n2\n",
"3\n4\n5\n0\n1\n2\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n1\n2\n3\n",
"0\n1\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n3\n1\n2\n4\n",
"0\n1\n",
"0\n3\n4\n1\n2\n5\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n",
"0\n1\n2\n3\n",
"0\n1\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n3\n1\n2\n4\n",
"0\n3\n4\n1\n2\n5\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"3\n4\n5\n0\n1\n2\n",
"0\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n",
"0\n1\n",
"0\n1\n2\n3\n4\n5\n",
"0\n1\n2\n3\n4\n",
"3\n4\n5\n0\n1\n2\n",
"3\n0\n1\n4\n2\n",
"0\n1\n2\n3\n4\n",
"3\n4\n5\n0\n1\n2\n",
"0\n1\n2\n",
"0\n1\n2\n3\n",
"0\n1\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n3\n1\n2\n4\n",
"0\n3\n4\n1\n2\n5\n",
"0\n1\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n",
"0\n1\n2\n3\n4\n5\n",
"0\n3\n4\n5\n1\n2\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n",
"0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:
* Every label is an integer between 0 and n-2 inclusive.
* All the written labels are distinct.
* The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible.
Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.
Input
The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.
Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.
Output
Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).
Examples
Input
3
1 2
1 3
Output
0
1
Input
6
1 2
1 3
2 4
2 5
5 6
Output
0
3
2
4
1
Note
The tree from the second sample:
<image>
### Input:
6
1 2
1 3
2 4
2 5
5 6
### Output:
0
3
1
2
4
### Input:
3
1 2
1 3
### Output:
0
1
### Code:
n = int(input())
occ = [0 for i in range(n)]
graph = [[0,0] for i in range(n-1)]
for i in range(n-1):
x, y = map(int,input().split())
occ[x-1]+=1
occ[y-1]+=1
graph[i][0] = x-1
graph[i][1] = y-1
fin = [-1 for i in range(n-1)]
for i in range(n):
if occ[i] >= 3 :
var = 0
for j in range(n-1):
if graph[j][0] == i or graph[j][1] == i:
fin[j] = var
var += 1
break
else:
var = 0
for i in range(n):
if var > 1:
break
if occ[i] == 1:
for j in range(n-1):
if graph[j][0] == i or graph[j][1] == i:
fin[j] = var
var += 1
break
for i in fin:
if n == 2:
print(0)
break
if i == -1:
print(var)
var += 1
else:
print(i) |
1344_B. Monopole Magnets_3063 | A monopole magnet is a magnet that only has one pole, either north or south. They don't actually exist since real magnets have two poles, but this is a programming contest problem, so we don't care.
There is an n× m grid. Initially, you may place some north magnets and some south magnets into the cells. You are allowed to place as many magnets as you like, even multiple in the same cell.
An operation is performed as follows. Choose a north magnet and a south magnet to activate. If they are in the same row or the same column and they occupy different cells, then the north magnet moves one unit closer to the south magnet. Otherwise, if they occupy the same cell or do not share a row or column, then nothing changes. Note that the south magnets are immovable.
Each cell of the grid is colored black or white. Let's consider ways to place magnets in the cells so that the following conditions are met.
1. There is at least one south magnet in every row and every column.
2. If a cell is colored black, then it is possible for a north magnet to occupy this cell after some sequence of operations from the initial placement.
3. If a cell is colored white, then it is impossible for a north magnet to occupy this cell after some sequence of operations from the initial placement.
Determine if it is possible to place magnets such that these conditions are met. If it is possible, find the minimum number of north magnets required (there are no requirements on the number of south magnets).
Input
The first line contains two integers n and m (1≤ n,m≤ 1000) — the number of rows and the number of columns, respectively.
The next n lines describe the coloring. The i-th of these lines contains a string of length m, where the j-th character denotes the color of the cell in row i and column j. The characters "#" and "." represent black and white, respectively. It is guaranteed, that the string will not contain any other characters.
Output
Output a single integer, the minimum possible number of north magnets required.
If there is no placement of magnets that satisfies all conditions, print a single integer -1.
Examples
Input
3 3
.#.
###
##.
Output
1
Input
4 2
##
.#
.#
##
Output
-1
Input
4 5
....#
####.
.###.
.#...
Output
2
Input
2 1
.
#
Output
-1
Input
3 5
.....
.....
.....
Output
0
Note
In the first test, here is an example placement of magnets:
<image>
In the second test, we can show that no required placement of magnets exists. Here are three example placements that fail to meet the requirements. The first example violates rule 3 since we can move the north magnet down onto a white square. The second example violates rule 2 since we cannot move the north magnet to the bottom-left black square by any sequence of operations. The third example violates rule 1 since there is no south magnet in the first column.
<image>
In the third test, here is an example placement of magnets. We can show that there is no required placement of magnets with fewer north magnets.
<image>
In the fourth test, we can show that no required placement of magnets exists. Here are two example placements that fail to meet the requirements. The first example violates rule 1 since there is no south magnet in the first row. The second example violates rules 1 and 3 since there is no south magnet in the second row and we can move the north magnet up one unit onto a white square.
<image>
In the fifth test, we can put the south magnet in each cell and no north magnets. Because there are no black cells, it will be a correct placement. | # -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 2020/6/16
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def check(row):
start, end = 0, len(row) - 1
while start < len(row) and row[start] == 0:
start += 1
if start >= len(row):
return True, True
while end >= start and row[end] == 0:
end -= 1
for i in range(start, end):
if row[i] == 0:
return False, False
return True, False
def solve(N, M, A):
blankrow = []
for r in range(N):
row = A[r]
a, b = check(row)
if not a:
return -1
if b:
blankrow.append(r)
blankcol = []
for c in range(M):
col = [A[r][c] for r in range(N)]
a, b = check(col)
if not a:
return -1
if b:
blankcol.append(c)
if (len(blankcol) > 0 and len(blankrow) == 0) or (len(blankrow) > 0 and len(blankcol) == 0):
return -1
if len(blankcol) * len(blankrow) == N * M:
return 0
for r in blankrow:
for c in blankcol:
A[r][c] = 2
idx = 2
for r in range(N):
for c in range(M):
if A[r][c] == 1:
idx += 1
A[r][c] = idx
q = [(r, c)]
while q:
nq = []
for x, y in q:
for nx, ny in [(x+1, y), (x-1, y), (x, y+1), (x, y-1)]:
if 0 <= nx < N and 0 <= ny < M and A[nx][ny] == 1:
A[nx][ny] = idx
nq.append((nx, ny))
q = nq
# for row in A:
# print(' '.join(map(str, row)))
return idx - 2
if __name__ == '__main__':
N, M = map(int, input().split())
A = []
for i in range(N):
row = [1 if v == '#' else 0 for v in list(input())]
A.append(row)
print(solve(N, M, A))
| {
"input": [
"3 3\n.#.\n###\n##.\n",
"4 5\n....#\n####.\n.###.\n.#...\n",
"4 2\n##\n.#\n.#\n##\n",
"3 5\n.....\n.....\n.....\n",
"2 1\n.\n#\n",
"19 19\n##############.....\n.#############.....\n.###########.......\n.###########.......\n.....#######.......\n.....###...........\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n..................#\n..................#\n................###\n..............#####\n.................##\n",
"19 19\n................###\n...............###.\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n.......##..........\n...########........\n.##########........\n############.......\n..#................\n",
"10 10\n.#..#....#\n#..##...##\n.....##.#.\n.#....#..#\n##.##.###.\n####.##...\n..##.#..##\n..##..#.#.\n..#######.\n####...#.#\n",
"5 5\n####.\n.####\n#.###\n####.\n.###.\n",
"4 4\n..##\n..#.\n##..\n##..\n",
"3 3\n..#\n.#.\n#..\n",
"10 10\n....#..#..\n.#........\n.....#....\n.........#\n........#.\n.#........\n.#........\n..#...#...\n...#....#.\n#.........\n",
"10 10\n......#...\n.........#\n.#........\n........#.\n....#.....\n.....#....\n.......#..\n#.........\n..#.......\n...#......\n",
"5 5\n.#...\n..#..\n....#\n#....\n...#.\n",
"10 10\n........#.\n#########.\n.########.\n.#########\n.#######..\n.#######..\n.#######..\n...#####..\n...###....\n.....#....\n",
"10 10\n..######..\n..######..\n..######..\n..######..\n..######..\n...#####..\n...#####..\n...#######\n...#......\n##........\n",
"10 10\n#.........\n.....#....\n.....###..\n...#####..\n...#####..\n.#######..\n.########.\n....#####.\n.....#####\n.....#....\n",
"1 1\n#\n",
"5 5\n#....\n.#...\n...#.\n..##.\n..###\n",
"18 22\n....................#.\n...................#..\n..........#...........\n..................#...\n..................#...\n..................#...\n......................\n......................\n...........#..........\n..............#.......\n..............#.......\n..............#.......\n..............#.......\n.......#..............\n.......#..............\n...##.................\n..#.......#...........\n.....................#\n",
"3 3\n.#.\n.##\n###\n",
"1 1\n.\n",
"10 10\n.........#\n........##\n#####.....\n####......\n#.........\n#.........\n.....#....\n.....#....\n......##..\n......#...\n",
"19 19\n##############.....\n.#############.....\n.###########.......\n.###########.......\n.....#######.......\n.....###...........\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n..................#\n..................#\n................###\n...........-..#####\n.................##\n",
"3 19\n................###\n...............###.\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n.......##..........\n...########........\n.##########........\n############.......\n..#................\n",
"2 5\n....#\n####.\n.###.\n.#...\n",
"10 10\n.#..#....#\n#..##...##\n.....##.#.\n.#....#..#\n##.##.###.\n####.##...\n..##.#..##\n.#.#..##..\n..#######.\n####...#.#\n",
"5 5\n.####\n.####\n#.###\n####.\n.###.\n",
"4 4\n..##\n..#.\n##..\n..##\n",
"10 10\n....#..#/.\n.#........\n.....#....\n.........#\n........#.\n.#........\n.#........\n..#...#...\n...#....#.\n#.........\n",
"18 22\n....................#.\n...................#..\n..........#...........\n..................#...\n..................#...\n..................#...\n......................\n......................\n...........#..........\n..............#.......\n..............#.......\n..............#.......\n..............#.......\n.......#..............\n.......#..............\n...##.................\n..#.......#...........\n.............-.......#\n",
"19 19\n##############..-..\n.#############.....\n.###########.......\n.###########.......\n.....#######.......\n.....###...........\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n...................\n..................#\n..................#\n................###\n...........-..#####\n.................##\n",
"10 10\n.#..#....#\n#..##...##\n.....##.#.\n.#....#..#\n##.##.###.\n####.##...\n..##.#..##\n.#.#..##..\n..#######.\n####..##..\n",
"4 4\n..##\n..#.\n##..\n.#.#\n",
"10 10\n.../#..#/.\n.#........\n.....#....\n.........#\n........#.\n.#........\n.#........\n..#...#...\n...#....#.\n#.........\n",
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} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A monopole magnet is a magnet that only has one pole, either north or south. They don't actually exist since real magnets have two poles, but this is a programming contest problem, so we don't care.
There is an n× m grid. Initially, you may place some north magnets and some south magnets into the cells. You are allowed to place as many magnets as you like, even multiple in the same cell.
An operation is performed as follows. Choose a north magnet and a south magnet to activate. If they are in the same row or the same column and they occupy different cells, then the north magnet moves one unit closer to the south magnet. Otherwise, if they occupy the same cell or do not share a row or column, then nothing changes. Note that the south magnets are immovable.
Each cell of the grid is colored black or white. Let's consider ways to place magnets in the cells so that the following conditions are met.
1. There is at least one south magnet in every row and every column.
2. If a cell is colored black, then it is possible for a north magnet to occupy this cell after some sequence of operations from the initial placement.
3. If a cell is colored white, then it is impossible for a north magnet to occupy this cell after some sequence of operations from the initial placement.
Determine if it is possible to place magnets such that these conditions are met. If it is possible, find the minimum number of north magnets required (there are no requirements on the number of south magnets).
Input
The first line contains two integers n and m (1≤ n,m≤ 1000) — the number of rows and the number of columns, respectively.
The next n lines describe the coloring. The i-th of these lines contains a string of length m, where the j-th character denotes the color of the cell in row i and column j. The characters "#" and "." represent black and white, respectively. It is guaranteed, that the string will not contain any other characters.
Output
Output a single integer, the minimum possible number of north magnets required.
If there is no placement of magnets that satisfies all conditions, print a single integer -1.
Examples
Input
3 3
.#.
###
##.
Output
1
Input
4 2
##
.#
.#
##
Output
-1
Input
4 5
....#
####.
.###.
.#...
Output
2
Input
2 1
.
#
Output
-1
Input
3 5
.....
.....
.....
Output
0
Note
In the first test, here is an example placement of magnets:
<image>
In the second test, we can show that no required placement of magnets exists. Here are three example placements that fail to meet the requirements. The first example violates rule 3 since we can move the north magnet down onto a white square. The second example violates rule 2 since we cannot move the north magnet to the bottom-left black square by any sequence of operations. The third example violates rule 1 since there is no south magnet in the first column.
<image>
In the third test, here is an example placement of magnets. We can show that there is no required placement of magnets with fewer north magnets.
<image>
In the fourth test, we can show that no required placement of magnets exists. Here are two example placements that fail to meet the requirements. The first example violates rule 1 since there is no south magnet in the first row. The second example violates rules 1 and 3 since there is no south magnet in the second row and we can move the north magnet up one unit onto a white square.
<image>
In the fifth test, we can put the south magnet in each cell and no north magnets. Because there are no black cells, it will be a correct placement.
### Input:
3 3
.#.
###
##.
### Output:
1
### Input:
4 5
....#
####.
.###.
.#...
### Output:
2
### Code:
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 2020/6/16
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def check(row):
start, end = 0, len(row) - 1
while start < len(row) and row[start] == 0:
start += 1
if start >= len(row):
return True, True
while end >= start and row[end] == 0:
end -= 1
for i in range(start, end):
if row[i] == 0:
return False, False
return True, False
def solve(N, M, A):
blankrow = []
for r in range(N):
row = A[r]
a, b = check(row)
if not a:
return -1
if b:
blankrow.append(r)
blankcol = []
for c in range(M):
col = [A[r][c] for r in range(N)]
a, b = check(col)
if not a:
return -1
if b:
blankcol.append(c)
if (len(blankcol) > 0 and len(blankrow) == 0) or (len(blankrow) > 0 and len(blankcol) == 0):
return -1
if len(blankcol) * len(blankrow) == N * M:
return 0
for r in blankrow:
for c in blankcol:
A[r][c] = 2
idx = 2
for r in range(N):
for c in range(M):
if A[r][c] == 1:
idx += 1
A[r][c] = idx
q = [(r, c)]
while q:
nq = []
for x, y in q:
for nx, ny in [(x+1, y), (x-1, y), (x, y+1), (x, y-1)]:
if 0 <= nx < N and 0 <= ny < M and A[nx][ny] == 1:
A[nx][ny] = idx
nq.append((nx, ny))
q = nq
# for row in A:
# print(' '.join(map(str, row)))
return idx - 2
if __name__ == '__main__':
N, M = map(int, input().split())
A = []
for i in range(N):
row = [1 if v == '#' else 0 for v in list(input())]
A.append(row)
print(solve(N, M, A))
|
1366_B. Shuffle_3067 | You are given an array consisting of n integers a_1, a_2, ..., a_n. Initially a_x = 1, all other elements are equal to 0.
You have to perform m operations. During the i-th operation, you choose two indices c and d such that l_i ≤ c, d ≤ r_i, and swap a_c and a_d.
Calculate the number of indices k such that it is possible to choose the operations so that a_k = 1 in the end.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Then the description of t testcases follow.
The first line of each test case contains three integers n, x and m (1 ≤ n ≤ 10^9; 1 ≤ m ≤ 100; 1 ≤ x ≤ n).
Each of next m lines contains the descriptions of the operations; the i-th line contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).
Output
For each test case print one integer — the number of indices k such that it is possible to choose the operations so that a_k = 1 in the end.
Example
Input
3
6 4 3
1 6
2 3
5 5
4 1 2
2 4
1 2
3 3 2
2 3
1 2
Output
6
2
3
Note
In the first test case, it is possible to achieve a_k = 1 for every k. To do so, you may use the following operations:
1. swap a_k and a_4;
2. swap a_2 and a_2;
3. swap a_5 and a_5.
In the second test case, only k = 1 and k = 2 are possible answers. To achieve a_1 = 1, you have to swap a_1 and a_1 during the second operation. To achieve a_2 = 1, you have to swap a_1 and a_2 during the second operation. | from __future__ import division, print_function
# import threading
# threading.stack_size(2**27)
# import sys
# sys.setrecursionlimit(10**7)
# sys.stdin = open('inpy.txt', 'r')
# sys.stdout = open('outpy.txt', 'w')
from sys import stdin, stdout
import bisect #c++ upperbound
import math
import heapq
i_m=9223372036854775807
def inin():
return int(input())
def stin():
return input()
def spin():
return map(int,stin().split())
def lin(): #takes array as input
return list(map(int,stin().split()))
def matrix(n):
#matrix input
return [list(map(int,input().split()))for i in range(n)]
################################################
def count2Dmatrix(i,list):
return sum(c.count(i) for c in list)
def modinv(n,p):
return pow(n,p-2,p)
def GCD(x, y):
x=abs(x)
y=abs(y)
if(min(x,y)==0):
return max(x,y)
while(y):
x, y = y, x % y
return x
def Divisors(n) :
l = []
for i in range(1, int(math.sqrt(n) + 1)) :
if (n % i == 0) :
if (n // i == i) :
l.append(i)
else :
l.append(i)
l.append(n//i)
return l
prime=[]
def SieveOfEratosthenes(n):
global prime
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
f=[]
for p in range(2, n):
if prime[p]:
f.append(p)
return f
q=[]
def dfs(n,d,v,c):
global q
v[n]=1
x=d[n]
q.append(n)
j=c
for i in x:
if i not in v:
f=dfs(i,d,v,c+1)
j=max(j,f)
# print(f)
return j
# d = {}
"""*******************************************************"""
for _ in range(inin()):
n, x, m = spin()
l0, r0 = x, x
for i in range(m):
l, r = spin()
if max(l, l0) <= min(r, r0):
l0 = min(l, l0)
r0 = max(r, r0)
print(r0 - l0 + 1)
# arr = [0] * (n+1)
# arr[x] = 1
# c = 0
# l1 = 10**9; r1 = -10**9
# for i in range(1, m+1, 1):
# l, r = spin()
# # print(arr[l:r+1])
# if arr[l:r+1].count(1)>=1 or (l<=l1 or r>=r1) :
# if arr[l:r+1].count(1)>=1:
# l1 = min(l1, l)
# r1 = max(r1, r)
# elif l1<=l<=r1 or l1<=r<=r1:
# l1 = min(l1, l)
# r1 = max(r1, r)
# # print(l1, r1)
# # for j in range(l,r+1,1):
# # arr[j] = 1
# # print(arr[1:])
# print(abs(l1-r1)+1) | {
"input": [
"3\n6 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 4\n1 2\n3 3 2\n2 3\n1 2\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 2\n2 3\n3 4\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"1\n666 666 1\n228 666\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 4\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"1\n666 666 1\n228 483\n",
"3\n6 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 4\n1 2\n3 3 2\n2 4\n1 2\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"3\n6 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 4\n2 2\n3 3 2\n2 3\n1 2\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 4\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n0 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"1\n666 666 1\n228 803\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 2\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n39 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n3 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n39 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n3 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n3 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"3\n9 4 3\n1 6\n1 3\n5 5\n3 1 2\n2 4\n1 2\n3 3 2\n2 8\n1 2\n",
"1\n210 666 1\n228 483\n",
"3\n9 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 4\n1 2\n3 3 2\n2 4\n1 2\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n3 100\n4 5\n1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 5\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"1\n210 1054 1\n228 483\n",
"3\n9 4 3\n1 6\n1 3\n5 5\n4 1 2\n2 4\n1 2\n3 3 2\n2 4\n1 2\n",
"1\n210 1054 0\n228 483\n",
"1\n210 1054 0\n228 505\n",
"1\n334 1054 0\n228 505\n",
"1\n334 1054 0\n353 505\n",
"1\n334 1054 0\n454 505\n",
"1\n334 1054 0\n454 658\n",
"1\n334 1054 0\n281 658\n",
"1\n334 1054 0\n281 146\n",
"1\n308 1054 0\n281 146\n",
"1\n308 1625 0\n281 146\n",
"1\n308 1625 0\n414 146\n",
"1\n308 771 0\n414 146\n",
"1\n308 771 0\n188 146\n",
"1\n308 771 0\n92 146\n",
"1\n152 771 0\n92 146\n",
"1\n152 771 0\n10 146\n",
"1\n152 771 1\n10 146\n",
"1\n152 771 0\n13 146\n",
"1\n152 771 0\n13 282\n",
"1\n152 771 0\n3 282\n",
"1\n152 1380 0\n3 282\n",
"1\n65 1380 0\n3 282\n",
"1\n13 1380 0\n3 282\n",
"1\n666 666 1\n228 38\n",
"3\n6 4 3\n1 6\n2 3\n5 5\n4 1 2\n3 4\n1 2\n3 3 2\n2 4\n1 2\n",
"1\n210 666 1\n228 388\n",
"3\n9 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 0\n1 2\n3 3 2\n2 4\n1 2\n",
"1\n210 1054 1\n228 209\n",
"3\n9 4 3\n1 6\n1 3\n5 5\n3 1 2\n2 4\n1 2\n3 3 2\n2 4\n1 2\n",
"1\n210 736 0\n228 483\n",
"1\n210 1684 0\n228 505\n",
"1\n334 1054 0\n442 505\n",
"1\n334 362 0\n353 505\n",
"1\n334 894 0\n454 505\n",
"1\n334 1675 0\n454 658\n",
"1\n334 1054 0\n48 146\n",
"1\n308 1054 0\n281 174\n",
"1\n308 526 0\n281 146\n",
"1\n308 433 0\n414 146\n",
"1\n308 771 0\n205 146\n",
"1\n152 277 0\n92 146\n",
"1\n152 771 1\n2 146\n",
"1\n187 771 1\n10 146\n",
"1\n152 771 0\n13 15\n",
"1\n152 771 0\n20 282\n",
"1\n239 771 0\n3 282\n",
"1\n152 1380 0\n4 282\n",
"1\n65 2224 0\n3 282\n",
"1\n13 1380 0\n2 282\n",
"1\n666 666 1\n228 57\n",
"3\n6 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 4\n3 2\n3 3 2\n2 3\n1 2\n",
"1\n516 666 1\n228 803\n",
"3\n6 4 3\n1 6\n2 2\n5 5\n4 1 2\n3 4\n1 2\n3 3 2\n2 4\n1 2\n",
"9\n100 50 6\n1 49\n51 100\n40 60\n30 70\n20 30\n70 80\n100 1 11\n1 1\n1 1\n1 1\n2 2\n2 100\n1 4\n2 3\n3 7\n5 6\n6 100\n4 5\n1 1 5\n1 1\n1 2\n1 1\n1 1\n1 1\n11 6 4\n6 6\n1 4\n7 11\n6 6\n3 3 2\n1 2\n2 3\n1000000000 1 1\n1 1000000000\n1000000000 1 1\n1 999999999\n1000000000 1 1\n2 1000000000\n1000000000 2 1\n1 1000000000\n",
"1\n210 666 1\n344 388\n",
"3\n9 4 3\n1 6\n2 3\n5 5\n4 1 2\n2 -1\n1 2\n3 3 2\n2 4\n1 2\n",
"1\n266 1054 1\n228 209\n",
"1\n210 736 0\n228 340\n",
"1\n210 1684 0\n241 505\n",
"1\n334 517 0\n442 505\n",
"1\n334 718 0\n353 505\n",
"1\n213 1675 0\n454 658\n",
"1\n334 1054 0\n48 105\n",
"1\n150 1054 0\n281 174\n",
"1\n308 526 0\n65 146\n",
"1\n308 433 1\n414 146\n",
"1\n476 771 0\n205 146\n",
"1\n152 277 0\n5 146\n",
"1\n16 771 1\n2 146\n",
"1\n187 771 1\n10 193\n"
],
"output": [
"6\n2\n3\n",
"61\n5\n1\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"439\n",
"61\n5\n1\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"1\n",
"6\n2\n4\n",
"61\n100\n1\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"6\n1\n3\n",
"61\n5\n1\n1\n4\n1000000000\n999999999\n1\n1000000000\n",
"576\n",
"61\n100\n2\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"42\n100\n1\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"42\n100\n1\n1\n1\n1000000000\n999999999\n1\n1000000000\n",
"6\n2\n8\n",
"1\n",
"6\n2\n4\n",
"61\n100\n1\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"1\n",
"6\n2\n4\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"6\n2\n4\n",
"1\n",
"6\n2\n4\n",
"1\n",
"6\n2\n4\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"6\n1\n3\n",
"576\n",
"6\n2\n4\n",
"61\n100\n2\n1\n2\n1000000000\n999999999\n1\n1000000000\n",
"1\n",
"6\n2\n4\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an array consisting of n integers a_1, a_2, ..., a_n. Initially a_x = 1, all other elements are equal to 0.
You have to perform m operations. During the i-th operation, you choose two indices c and d such that l_i ≤ c, d ≤ r_i, and swap a_c and a_d.
Calculate the number of indices k such that it is possible to choose the operations so that a_k = 1 in the end.
Input
The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Then the description of t testcases follow.
The first line of each test case contains three integers n, x and m (1 ≤ n ≤ 10^9; 1 ≤ m ≤ 100; 1 ≤ x ≤ n).
Each of next m lines contains the descriptions of the operations; the i-th line contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).
Output
For each test case print one integer — the number of indices k such that it is possible to choose the operations so that a_k = 1 in the end.
Example
Input
3
6 4 3
1 6
2 3
5 5
4 1 2
2 4
1 2
3 3 2
2 3
1 2
Output
6
2
3
Note
In the first test case, it is possible to achieve a_k = 1 for every k. To do so, you may use the following operations:
1. swap a_k and a_4;
2. swap a_2 and a_2;
3. swap a_5 and a_5.
In the second test case, only k = 1 and k = 2 are possible answers. To achieve a_1 = 1, you have to swap a_1 and a_1 during the second operation. To achieve a_2 = 1, you have to swap a_1 and a_2 during the second operation.
### Input:
3
6 4 3
1 6
2 3
5 5
4 1 2
2 4
1 2
3 3 2
2 3
1 2
### Output:
6
2
3
### Input:
9
100 50 6
1 49
51 100
40 60
30 70
20 30
70 80
100 1 11
1 1
1 1
1 1
2 2
2 100
1 2
2 3
3 4
5 6
6 100
4 5
1 1 5
1 1
1 1
1 1
1 1
1 1
11 6 4
6 6
1 5
7 11
6 6
3 3 2
1 2
2 3
1000000000 1 1
1 1000000000
1000000000 1 1
1 999999999
1000000000 1 1
2 1000000000
1000000000 2 1
1 1000000000
### Output:
61
5
1
1
2
1000000000
999999999
1
1000000000
### Code:
from __future__ import division, print_function
# import threading
# threading.stack_size(2**27)
# import sys
# sys.setrecursionlimit(10**7)
# sys.stdin = open('inpy.txt', 'r')
# sys.stdout = open('outpy.txt', 'w')
from sys import stdin, stdout
import bisect #c++ upperbound
import math
import heapq
i_m=9223372036854775807
def inin():
return int(input())
def stin():
return input()
def spin():
return map(int,stin().split())
def lin(): #takes array as input
return list(map(int,stin().split()))
def matrix(n):
#matrix input
return [list(map(int,input().split()))for i in range(n)]
################################################
def count2Dmatrix(i,list):
return sum(c.count(i) for c in list)
def modinv(n,p):
return pow(n,p-2,p)
def GCD(x, y):
x=abs(x)
y=abs(y)
if(min(x,y)==0):
return max(x,y)
while(y):
x, y = y, x % y
return x
def Divisors(n) :
l = []
for i in range(1, int(math.sqrt(n) + 1)) :
if (n % i == 0) :
if (n // i == i) :
l.append(i)
else :
l.append(i)
l.append(n//i)
return l
prime=[]
def SieveOfEratosthenes(n):
global prime
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
f=[]
for p in range(2, n):
if prime[p]:
f.append(p)
return f
q=[]
def dfs(n,d,v,c):
global q
v[n]=1
x=d[n]
q.append(n)
j=c
for i in x:
if i not in v:
f=dfs(i,d,v,c+1)
j=max(j,f)
# print(f)
return j
# d = {}
"""*******************************************************"""
for _ in range(inin()):
n, x, m = spin()
l0, r0 = x, x
for i in range(m):
l, r = spin()
if max(l, l0) <= min(r, r0):
l0 = min(l, l0)
r0 = max(r, r0)
print(r0 - l0 + 1)
# arr = [0] * (n+1)
# arr[x] = 1
# c = 0
# l1 = 10**9; r1 = -10**9
# for i in range(1, m+1, 1):
# l, r = spin()
# # print(arr[l:r+1])
# if arr[l:r+1].count(1)>=1 or (l<=l1 or r>=r1) :
# if arr[l:r+1].count(1)>=1:
# l1 = min(l1, l)
# r1 = max(r1, r)
# elif l1<=l<=r1 or l1<=r<=r1:
# l1 = min(l1, l)
# r1 = max(r1, r)
# # print(l1, r1)
# # for j in range(l,r+1,1):
# # arr[j] = 1
# # print(arr[1:])
# print(abs(l1-r1)+1) |
1408_B. Arrays Sum_3073 | You are given a non-decreasing array of non-negative integers a_1, a_2, …, a_n. Also you are given a positive integer k.
You want to find m non-decreasing arrays of non-negative integers b_1, b_2, …, b_m, such that:
* The size of b_i is equal to n for all 1 ≤ i ≤ m.
* For all 1 ≤ j ≤ n, a_j = b_{1, j} + b_{2, j} + … + b_{m, j}. In the other word, array a is the sum of arrays b_i.
* The number of different elements in the array b_i is at most k for all 1 ≤ i ≤ m.
Find the minimum possible value of m, or report that there is no possible m.
Input
The first line contains one integer t (1 ≤ t ≤ 100): the number of test cases.
The first line of each test case contains two integers n, k (1 ≤ n ≤ 100, 1 ≤ k ≤ n).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_1 ≤ a_2 ≤ … ≤ a_n ≤ 100, a_n > 0).
Output
For each test case print a single integer: the minimum possible value of m. If there is no such m, print -1.
Example
Input
6
4 1
0 0 0 1
3 1
3 3 3
11 3
0 1 2 2 3 3 3 4 4 4 4
5 3
1 2 3 4 5
9 4
2 2 3 5 7 11 13 13 17
10 7
0 1 1 2 3 3 4 5 5 6
Output
-1
1
2
2
2
1
Note
In the first test case, there is no possible m, because all elements of all arrays should be equal to 0. But in this case, it is impossible to get a_4 = 1 as the sum of zeros.
In the second test case, we can take b_1 = [3, 3, 3]. 1 is the smallest possible value of m.
In the third test case, we can take b_1 = [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2] and b_2 = [0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2]. It's easy to see, that a_i = b_{1, i} + b_{2, i} for all i and the number of different elements in b_1 and in b_2 is equal to 3 (so it is at most 3). It can be proven that 2 is the smallest possible value of m. | import sys as _sys
def main():
t = int(input())
for i_t in range(t):
n, k = _read_ints()
a = tuple(_read_ints())
try:
result = find_min_m(a, k)
except ValueError:
result = -1
print(result)
def _read_line():
result = _sys.stdin.readline()
assert result[-1] == "\n"
return result[:-1]
def _read_ints():
return map(int, _read_line().split(" "))
def find_min_m(a_seq, k):
assert k >= 1
a_seq = tuple(a_seq)
if a_seq.count(0) == len(a_seq):
return 0
steps_n = sum(x1 != x2 for x1, x2 in zip(a_seq, a_seq[1:]))
if k == 1:
if steps_n == 0:
return 1
else:
raise ValueError("can't find min m")
result = 0
steps_per_b_seq = k - 1
if a_seq[0] != 0:
steps_n += 1
if steps_n <= k:
return 1
steps_n -= k
result += 1
result += _ceil_div(steps_n, steps_per_b_seq)
return result
def _ceil_div(x, y):
assert y > 0
result = x // y
if x % y != 0:
result += 1
return result
if __name__ == '__main__':
main()
| {
"input": [
"6\n4 1\n0 0 0 1\n3 1\n3 3 3\n11 3\n0 1 2 2 3 3 3 4 4 4 4\n5 3\n1 2 3 4 5\n9 4\n2 2 3 5 7 11 13 13 17\n10 7\n0 1 1 2 3 3 4 5 5 6\n",
"1\n3 2\n3 3 3\n",
"1\n3 3\n1 1 1\n",
"1\n5 5\n5 5 5 5 5\n",
"1\n5 3\n1 1 1 1 1\n",
"1\n5 2\n5 5 5 5 5\n",
"1\n2 2\n3 3\n",
"1\n4 2\n1 1 1 1\n",
"1\n2 2\n1 1\n",
"1\n3 3\n3 3 3\n",
"1\n3 2\n5 5 5\n",
"1\n2 2\n2 2\n",
"1\n5 2\n1 1 1 1 1\n",
"1\n3 2\n2 2 2\n",
"1\n3 1\n1 2 2\n",
"1\n4 4\n1 1 1 1\n",
"1\n5 5\n1 1 1 1 1\n",
"1\n2 2\n3 5\n",
"1\n3 1\n1 1 2\n",
"1\n4 2\n0 1 1 1\n",
"1\n2 1\n1 1\n",
"1\n3 5\n3 3 3\n",
"1\n2 2\n1 2\n",
"1\n2 2\n1 4\n",
"1\n3 1\n1 1 3\n",
"1\n2 2\n2 4\n",
"1\n3 4\n3 3 3\n",
"1\n3 4\n1 1 1\n",
"1\n5 2\n1 5 5 5 5\n",
"1\n2 2\n2 3\n",
"1\n4 2\n1 1 1 2\n",
"1\n2 2\n0 2\n",
"1\n2 2\n1 5\n",
"1\n2 1\n1 2\n",
"1\n3 1\n1 0 2\n",
"1\n2 4\n2 4\n",
"1\n3 2\n1 1 3\n",
"1\n2 2\n2 6\n",
"1\n2 4\n2 3\n",
"1\n4 2\n1 1 1 4\n",
"1\n2 2\n0 4\n",
"1\n2 2\n1 8\n",
"1\n2 1\n0 2\n",
"1\n2 4\n2 6\n",
"1\n2 2\n1 6\n",
"1\n2 2\n1 3\n",
"1\n2 4\n0 6\n",
"1\n2 2\n3 4\n",
"1\n2 4\n1 6\n",
"1\n2 4\n1 12\n",
"1\n3 2\n1 1 1\n",
"1\n3 3\n1 3 3\n",
"1\n3 2\n5 5 6\n",
"1\n5 2\n0 1 1 1 1\n",
"1\n4 4\n1 1 1 2\n",
"1\n2 4\n1 2\n",
"1\n3 1\n1 1 1\n",
"1\n2 3\n1 4\n",
"1\n2 2\n2 5\n",
"1\n2 3\n0 2\n",
"1\n3 1\n1 2 4\n",
"1\n2 2\n0 8\n",
"1\n2 2\n1 7\n",
"1\n2 1\n2 2\n",
"1\n2 4\n3 6\n",
"1\n2 4\n1 5\n",
"1\n2 7\n0 6\n",
"1\n2 4\n1 14\n",
"1\n4 4\n1 1 1 3\n",
"1\n2 2\n0 1\n",
"1\n2 1\n1 4\n",
"1\n2 2\n0 5\n",
"1\n2 4\n5 6\n",
"1\n2 1\n1 5\n",
"1\n2 4\n1 23\n",
"1\n2 8\n1 23\n",
"1\n2 15\n1 23\n",
"1\n2 7\n1 23\n",
"1\n2 13\n1 23\n",
"1\n2 13\n1 32\n",
"1\n4 4\n1 1 2 2\n",
"1\n2 3\n1 1\n",
"1\n3 1\n5 5 5\n",
"1\n2 3\n2 3\n",
"1\n3 3\n2 2 2\n"
],
"output": [
"-1\n1\n2\n2\n2\n1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a non-decreasing array of non-negative integers a_1, a_2, …, a_n. Also you are given a positive integer k.
You want to find m non-decreasing arrays of non-negative integers b_1, b_2, …, b_m, such that:
* The size of b_i is equal to n for all 1 ≤ i ≤ m.
* For all 1 ≤ j ≤ n, a_j = b_{1, j} + b_{2, j} + … + b_{m, j}. In the other word, array a is the sum of arrays b_i.
* The number of different elements in the array b_i is at most k for all 1 ≤ i ≤ m.
Find the minimum possible value of m, or report that there is no possible m.
Input
The first line contains one integer t (1 ≤ t ≤ 100): the number of test cases.
The first line of each test case contains two integers n, k (1 ≤ n ≤ 100, 1 ≤ k ≤ n).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_1 ≤ a_2 ≤ … ≤ a_n ≤ 100, a_n > 0).
Output
For each test case print a single integer: the minimum possible value of m. If there is no such m, print -1.
Example
Input
6
4 1
0 0 0 1
3 1
3 3 3
11 3
0 1 2 2 3 3 3 4 4 4 4
5 3
1 2 3 4 5
9 4
2 2 3 5 7 11 13 13 17
10 7
0 1 1 2 3 3 4 5 5 6
Output
-1
1
2
2
2
1
Note
In the first test case, there is no possible m, because all elements of all arrays should be equal to 0. But in this case, it is impossible to get a_4 = 1 as the sum of zeros.
In the second test case, we can take b_1 = [3, 3, 3]. 1 is the smallest possible value of m.
In the third test case, we can take b_1 = [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2] and b_2 = [0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2]. It's easy to see, that a_i = b_{1, i} + b_{2, i} for all i and the number of different elements in b_1 and in b_2 is equal to 3 (so it is at most 3). It can be proven that 2 is the smallest possible value of m.
### Input:
6
4 1
0 0 0 1
3 1
3 3 3
11 3
0 1 2 2 3 3 3 4 4 4 4
5 3
1 2 3 4 5
9 4
2 2 3 5 7 11 13 13 17
10 7
0 1 1 2 3 3 4 5 5 6
### Output:
-1
1
2
2
2
1
### Input:
1
3 2
3 3 3
### Output:
1
### Code:
import sys as _sys
def main():
t = int(input())
for i_t in range(t):
n, k = _read_ints()
a = tuple(_read_ints())
try:
result = find_min_m(a, k)
except ValueError:
result = -1
print(result)
def _read_line():
result = _sys.stdin.readline()
assert result[-1] == "\n"
return result[:-1]
def _read_ints():
return map(int, _read_line().split(" "))
def find_min_m(a_seq, k):
assert k >= 1
a_seq = tuple(a_seq)
if a_seq.count(0) == len(a_seq):
return 0
steps_n = sum(x1 != x2 for x1, x2 in zip(a_seq, a_seq[1:]))
if k == 1:
if steps_n == 0:
return 1
else:
raise ValueError("can't find min m")
result = 0
steps_per_b_seq = k - 1
if a_seq[0] != 0:
steps_n += 1
if steps_n <= k:
return 1
steps_n -= k
result += 1
result += _ceil_div(steps_n, steps_per_b_seq)
return result
def _ceil_div(x, y):
assert y > 0
result = x // y
if x % y != 0:
result += 1
return result
if __name__ == '__main__':
main()
|
1428_E. Carrots for Rabbits_3077 | There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought n carrots with lengths a_1, a_2, a_3, …, a_n. However, rabbits are very fertile and multiply very quickly. Zookeeper now has k rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into k pieces. For some reason, all resulting carrot lengths must be positive integers.
Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size x is x^2.
Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.
Input
The first line contains two integers n and k (1 ≤ n ≤ k ≤ 10^5): the initial number of carrots and the number of rabbits.
The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6): lengths of carrots.
It is guaranteed that the sum of a_i is at least k.
Output
Output one integer: the minimum sum of time taken for rabbits to eat carrots.
Examples
Input
3 6
5 3 1
Output
15
Input
1 4
19
Output
91
Note
For the first test, the optimal sizes of carrots are \{1,1,1,2,2,2\}. The time taken is 1^2+1^2+1^2+2^2+2^2+2^2=15
For the second test, the optimal sizes of carrots are \{4,5,5,5\}. The time taken is 4^2+5^2+5^2+5^2=91. | import sys
from heapq import heapify, heappush, heappop
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10
N, K = MAP()
A = LIST()
def calc(a, cnt):
d, m = divmod(a, cnt)
return d**2 * (cnt-m) + (d+1)**2 * m
que = []
for a in A:
if a // 2 == 0:
que.append((0, 1, a))
else:
que.append((calc(a, 2) - calc(a, 1), 1, a))
heapify(que)
for _ in range(K-N):
val, cnt, a = heappop(que)
if a // (cnt+2) == 0:
heappush(que, (0, cnt+1, a))
else:
heappush(que, (calc(a, cnt+2) - calc(a, cnt+1), cnt+1, a))
ans = 0
for _, cnt, a in que:
ans += calc(a, cnt)
print(ans)
| {
"input": [
"1 4\n19\n",
"3 6\n5 3 1\n",
"10 23\n343 984 238 758983 231 74 231 548 893 543\n",
"1 1\n1\n",
"29 99047\n206580 305496 61753 908376 272137 803885 675070 665109 995787 667887 164508 634877 994427 270698 931765 721679 518973 65009 804367 608526 535640 117656 342804 398273 369209 298745 365459 942772 89584\n",
"1 100000\n1000000\n",
"1 100000\n100000\n",
"12 21223\n992192 397069 263753 561788 903539 521894 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 827248 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 285066 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"1 3\n1000000\n",
"20 40\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"10 36\n343 984 238 758983 231 74 231 548 893 543\n",
"29 99047\n206580 305496 61753 908376 272137 803885 675070 665109 995787 667887 164508 634877 994427 270698 931765 721679 518973 65009 804367 608526 535640 117656 342804 398273 369209 298745 365459 87924 89584\n",
"1 100100\n1000000\n",
"12 21223\n992192 397069 35660 561788 903539 521894 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 285066 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"1 5\n1000000\n",
"20 40\n2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
"1 8\n19\n",
"10 36\n343 984 238 758983 231 112 231 548 893 543\n",
"29 99047\n206580 305496 67337 908376 272137 803885 675070 665109 995787 667887 164508 634877 994427 270698 931765 721679 518973 65009 804367 608526 535640 117656 342804 398273 369209 298745 365459 87924 89584\n",
"1 101100\n1000000\n",
"12 855\n992192 397069 35660 561788 903539 521894 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"1 5\n1001000\n",
"20 40\n2 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2\n",
"1 15\n19\n",
"10 36\n343 984 238 758983 231 112 231 548 1192 543\n",
"1 111100\n1000000\n",
"12 855\n992192 397069 35660 561788 903539 521894 818097 223467 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"20 40\n2 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2\n",
"10 36\n343 984 16 758983 231 112 231 548 1192 543\n",
"1 111100\n1000100\n",
"12 51\n992192 397069 35660 561788 903539 521894 818097 223467 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 29 758983 231 112 231 548 1192 543\n",
"1 111101\n1000100\n",
"12 51\n992192 397069 35660 561788 87461 521894 818097 223467 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 29 758983 231 112 231 164 1192 543\n",
"1 110101\n1000100\n",
"12 51\n16072 397069 35660 561788 87461 521894 818097 223467 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 33 758983 231 112 231 164 1192 543\n",
"54 42164\n810471 434523 231187 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"54 42164\n810471 434523 231187 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 148016 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 134703 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 134703 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 42598\n",
"10 23\n343 984 238 758983 231 74 231 15 893 543\n",
"29 99047\n206580 305496 61753 908376 272137 803885 675070 665109 995787 453881 164508 634877 994427 270698 931765 721679 518973 65009 804367 608526 535640 117656 342804 398273 369209 298745 365459 942772 89584\n",
"12 21223\n992192 397069 388480 561788 903539 521894 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 827248 452285 531124 257259 453752 114536 833190 689989 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 285066 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"1 4\n6\n",
"10 35\n343 984 238 758983 231 74 231 548 893 543\n",
"1 100101\n1000000\n",
"12 1558\n992192 397069 35660 561788 903539 521894 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 191201 285066 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"1 5\n1000100\n",
"10 63\n343 984 238 758983 231 112 231 548 893 543\n",
"1 101101\n1000000\n",
"12 855\n992192 397069 35660 561788 903539 623171 818097 223467 511651 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 564982 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 238 758983 231 112 231 548 163 543\n",
"54 42164\n810471 434523 262846 930807 148016 958180 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 16 758983 173 112 231 548 1192 543\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 738264 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 1592 29 758983 231 112 231 548 1192 543\n",
"12 51\n992192 397069 35660 561788 87461 521894 818097 446392 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 341096 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 557070 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 984 29 758983 231 112 231 164 1192 695\n",
"12 51\n16072 397069 35660 561788 87461 521894 743585 223467 943024 737418 975119 528954\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 44740 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 36\n343 939 33 758983 231 112 231 164 1192 543\n",
"54 42164\n810471 434523 231187 930807 148016 633714 247313 369038 142288 30094 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 1010649 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 148016 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 8144 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 251409 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 280340 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 289835\n",
"54 42164\n810471 434523 231187 930807 134703 633714 247313 369038 142288 56869 599543 829013 182512 647950 512266 246841 452285 531124 257259 453752 114536 833190 737596 267349 598567 781294 390500 318098 354290 725051 978831 905185 764187 709518 55532 608148 631077 893214 355245 929381 153672 620004 59929 42159 82460 348896 446782 672690 364747 339938 715721 870099 357424 42598\n",
"10 23\n343 984 238 758983 231 74 231 15 893 664\n",
"12 21223\n992192 397069 388480 561788 903539 521894 818097 223467 511651 737418 975119 45386\n",
"54 42164\n810471 434523 262846 930807 148016 633714 247313 376546 142288 30094 599543 829013 182512 647950 512266 827248 452285 531124 257259 453752 114536 833190 689989 267349 598567 781294 390500 318098 354290 725051 978831 905185 849542 761886 55532 608148 631077 557070 355245 929381 280340 620004 285066 42159 70073 348896 446782 672690 364747 339938 715721 870099 357424 323761\n",
"10 35\n661 984 238 758983 231 74 231 548 893 543\n",
"1 000101\n1000000\n",
"12 1558\n992192 397069 35660 561788 903539 713792 818097 223467 511651 737418 975119 528954\n",
"20 40\n2 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 3 2\n",
"20 40\n2 2 4 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2\n",
"20 40\n2 2 4 2 2 2 2 2 3 2 1 2 2 2 2 2 2 2 2 2\n",
"20 40\n1 2 4 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 3 2\n"
],
"output": [
"91\n",
"15\n",
"41149446942\n",
"1\n",
"2192719703\n",
"10000000\n",
"100000\n",
"2604648091\n",
"17049737221\n",
"333333333334\n",
"40\n",
"21338024922\n",
"1945711263\n",
"9991000\n",
"2447286812\n",
"16319568318\n",
"200000000000\n",
"46\n",
"47\n",
"21338031990\n",
"1947280367\n",
"9901000\n",
"60749287366\n",
"16040638219\n",
"200400200000\n",
"43\n",
"27\n",
"21338655405\n",
"9001000\n",
"68237968203\n",
"15976106247\n",
"40\n",
"21338599017\n",
"9002900\n",
"1167755921077\n",
"15871198492\n",
"21338599602\n",
"9002810\n",
"927205203145\n",
"15861986176\n",
"21338326194\n",
"9092810\n",
"690137288329\n",
"16277013188\n",
"21338326442\n",
"16237698753\n",
"16195615071\n",
"16228822900\n",
"16212303719\n",
"15907140662\n",
"41149146863\n",
"2129505471\n",
"2692769768\n",
"16989247148\n",
"10\n",
"22158616366\n",
"9990910\n",
"33337187714\n",
"15790380513\n",
"200040002000\n",
"10670343210\n",
"9900910\n",
"62467557539\n",
"16273934855\n",
"21337261110\n",
"16378051411\n",
"21338575585\n",
"15818440898\n",
"21340165810\n",
"989832065288\n",
"15547719491\n",
"21338514370\n",
"673059915185\n",
"15536066688\n",
"21338239907\n",
"16235082725\n",
"16164627569\n",
"16357362605\n",
"15751914046\n",
"41149292910\n",
"2359294194\n",
"16973528151\n",
"22158935638\n",
"9900990100\n",
"35136588832\n",
"43\n",
"43\n",
"46\n",
"40\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought n carrots with lengths a_1, a_2, a_3, …, a_n. However, rabbits are very fertile and multiply very quickly. Zookeeper now has k rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into k pieces. For some reason, all resulting carrot lengths must be positive integers.
Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size x is x^2.
Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.
Input
The first line contains two integers n and k (1 ≤ n ≤ k ≤ 10^5): the initial number of carrots and the number of rabbits.
The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6): lengths of carrots.
It is guaranteed that the sum of a_i is at least k.
Output
Output one integer: the minimum sum of time taken for rabbits to eat carrots.
Examples
Input
3 6
5 3 1
Output
15
Input
1 4
19
Output
91
Note
For the first test, the optimal sizes of carrots are \{1,1,1,2,2,2\}. The time taken is 1^2+1^2+1^2+2^2+2^2+2^2=15
For the second test, the optimal sizes of carrots are \{4,5,5,5\}. The time taken is 4^2+5^2+5^2+5^2=91.
### Input:
1 4
19
### Output:
91
### Input:
3 6
5 3 1
### Output:
15
### Code:
import sys
from heapq import heapify, heappush, heappop
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c for j in range(b)] for i in range(a)]
def list3d(a, b, c, d): return [[[d for k in range(c)] for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e for l in range(d)] for k in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10**19
MOD = 10**9 + 7
EPS = 10**-10
N, K = MAP()
A = LIST()
def calc(a, cnt):
d, m = divmod(a, cnt)
return d**2 * (cnt-m) + (d+1)**2 * m
que = []
for a in A:
if a // 2 == 0:
que.append((0, 1, a))
else:
que.append((calc(a, 2) - calc(a, 1), 1, a))
heapify(que)
for _ in range(K-N):
val, cnt, a = heappop(que)
if a // (cnt+2) == 0:
heappush(que, (0, cnt+1, a))
else:
heappush(que, (calc(a, cnt+2) - calc(a, cnt+1), cnt+1, a))
ans = 0
for _, cnt, a in que:
ans += calc(a, cnt)
print(ans)
|
1451_F. Nullify The Matrix_3081 | Jeel and Ashish play a game on an n × m matrix. The rows are numbered 1 to n from top to bottom and the columns are numbered 1 to m from left to right. They play turn by turn. Ashish goes first.
Initially, each cell of the matrix contains a non-negative integer. Each turn, a player must perform all of the following actions in order.
* Choose a starting cell (r_1, c_1) with non-zero value.
* Choose a finishing cell (r_2, c_2) such that r_1 ≤ r_2 and c_1 ≤ c_2.
* Decrease the value of the starting cell by some positive non-zero integer.
* Pick any of the shortest paths between the two cells and either increase, decrease or leave the values of cells on this path unchanged. Note that:
* a shortest path is one that passes through the least number of cells;
* all cells on this path excluding the starting cell, but the finishing cell may be modified;
* the resulting value of each cell must be a non-negative integer;
* the cells are modified independently and not necessarily by the same value.
If the starting and ending cells are the same, then as per the rules, the value of the cell is decreased. No other operations are performed.
The game ends when all the values become zero. The player who is unable to make a move loses. It can be shown that the game will end in a finite number of moves if both players play optimally.
Given the initial matrix, if both players play optimally, can you predict who will win?
Input
The first line contains a single integer t (1 ≤ t ≤ 10) — the number of test cases. The description of each test case is as follows.
The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 100) — the dimensions of the matrix.
The next n lines contain m space separated integers a_{i,j} (0 ≤ a_{i,j} ≤ 10^6) — the values of each cell of the matrix.
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Jeel" (without the quotes).
Example
Input
4
1 1
0
1 3
0 0 5
2 2
0 1
1 0
3 3
1 2 3
4 5 6
7 8 9
Output
Jeel
Ashish
Jeel
Ashish
Note
In the first test case, the only cell of the matrix is 0. There are no moves Ashish can make. Jeel is the winner.
In the second test case, Ashish can choose (r_1, c_1) = (r_2, c_2) = (1,3) and reduce the cell to 0, leaving [0, 0, 0]. Jeel cannot perform any moves. Ashish wins. | def solve_case():
n, m = [int(x) for x in input().split()]
a = [[int(x) for x in input().split()] for x in range(n)]
xr = [0] * (n + m)
for i in range(n):
for j in range(m):
xr[i + j] ^= a[i][j]
return sum(xr) > 0
def main():
for _ in range(int(input())):
print(['Jeel', 'Ashish'][solve_case()])
main() | {
"input": [
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n3 3\n1 2 3\n4 5 6\n7 8 9\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n0 0 0 0\n0 0 2 0\n0 1 0 0\n0 0 0 0\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 1 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 0\n0 0 0 0\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n3 3\n1 2 3\n4 5 6\n12 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 6 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 6 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 52\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n2 0\n3 3\n1 0 3\n4 5 6\n7 8 9\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 1\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n6 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 1 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 46 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n37 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n65 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 191\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n51 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 2 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n1 22 1 24 0\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 12 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 191\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n2 3\n1 2 3\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n3 3\n1 0 3\n4 5 6\n12 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 1 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 22 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 12 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 34\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 6 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"4\n1 1\n0\n1 3\n0 1 5\n2 2\n0 1\n1 0\n2 3\n1 2 3\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 54\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n9 4 7 2\n4 4\n0 0 0 0\n0 1 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 12 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 34\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 16 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n4 0 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 6 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 3\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 16 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 54\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n9 4 11 2\n4 4\n0 0 0 0\n0 1 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 153 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n4 -1 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 6 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 0\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 118 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n1 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 153 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 0\n4 5 6\n7 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 83\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 118 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 0\n4 5 6\n5 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 83\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 152 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 -1\n4 5 6\n5 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n1 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 72\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n1 82 44 96 5\n82 20 9 99 66\n61 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 72\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n48 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n1 82 44 96 5\n82 20 9 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 72\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 15 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n48 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 83 60\n69 54 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 41 0\n5 5\n1 82 44 96 5\n82 20 9 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 83 60\n69 54 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 41 0\n5 5\n1 82 44 96 5\n82 20 10 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 83 60\n69 54 24 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 7 124 41 0\n5 5\n1 82 44 96 5\n82 20 10 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 24 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 131 23 -1\n5 5\n100 112 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 7 124 41 0\n5 5\n1 82 44 96 5\n82 20 10 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 19\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 24 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 131 23 -1\n5 5\n100 75 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 7 124 41 0\n5 5\n1 82 44 96 5\n82 20 10 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 19\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 15 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n24 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 131 23 -1\n5 5\n100 75 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 26 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 7 124 41 0\n5 5\n1 82 44 96 5\n82 20 10 99 66\n61 10 90 63 70\n99 87 1 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 19\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 15 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n24 47 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 131 23 -1\n5 5\n100 75 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n24 47 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n78 10 90 63 70\n99 87 103 0 23\n107 26 131 23 -1\n5 5\n100 75 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n15 30 110 82 25\n119 117 87 99 97\n24 47 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n78 10 90 63 70\n82 87 103 0 23\n107 26 131 23 -1\n5 5\n100 75 41 120 29\n32 20 36 102 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 60\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 63 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 17 90 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 10\n82 20 9 130 66\n56 17 90 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 87 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 10\n82 20 9 130 66\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 108 0\n5 5\n0 82 44 96 10\n82 20 9 130 66\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 108 0\n5 5\n0 82 44 5 10\n82 20 9 130 66\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 108 0\n5 5\n0 82 44 5 10\n82 20 9 130 66\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 66\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 108\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 41 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 31\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 115 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 148 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 160 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 103 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 70\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 30 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 16 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n98 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 266 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 9 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n55 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 10 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n60 72 124 102 0\n5 5\n0 82 44 5 10\n82 20 10 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n60 72 232 102 0\n5 5\n0 82 44 5 10\n82 20 10 130 16\n56 17 157 39 110\n148 87 17 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n60 72 232 102 0\n5 5\n0 82 44 5 10\n82 20 10 130 16\n56 17 157 39 110\n148 87 3 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"5\n5 5\n0 47 30 208 77\n126 98 21 0 45\n124 30 100 115 56\n147 202 63 47 61\n60 72 232 102 0\n5 5\n0 82 44 5 10\n82 20 10 130 16\n56 17 157 39 110\n148 82 3 0 23\n107 26 70 23 0\n5 5\n110 112 53 137 29\n63 20 36 251 50\n100 7 18 0 30\n80 93 1 11 33\n69 54 15 204 48\n5 2\n0 11\n73 33\n113 2\n119 38\n38 0\n1 2\n114 12 10 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 -1 0 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n1 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n0 0 0 0\n0 0 2 0\n0 1 0 0\n0 0 0 0\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n3 3\n1 0 3\n4 5 6\n7 8 9\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n6 8 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 1 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 16 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 1\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 0\n0 0 0 0\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n3 2\n1 2 3\n4 5 6\n12 8 9\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 0 0\n5 5\n0 3 4 5 0\n7 8 9 10 11\n12 13 14 15 5\n17 18 19 20 21\n1 22 1 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 39 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 0 1 2\n0 1 3 0\n0 0 0 0\n4 4\n0 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 53\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 17 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 81 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n216 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 62 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 12 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 13 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n37 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 119 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 191\n",
"4\n1 1\n0\n1 3\n0 0 5\n2 2\n0 1\n1 0\n2 3\n1 2 3\n4 5 6\n7 8 3\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 2 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n147 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n6 4 7 2\n4 4\n0 0 0 0\n0 1 1 2\n0 2 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 62 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 89 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 22 36 160 50\n100 11 18 0 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 62 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n2 0 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 6 9 10 11\n12 6 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 54\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 3 3 6\n4 1 6 7\n9 4 7 2\n4 4\n0 0 0 0\n0 1 1 2\n0 1 3 0\n1 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 42\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 96 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 67\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 12 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 196 41 120 34\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 16 24 102 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n4 0 0 0\n0 0 1 0\n5 5\n1 3 4 5 0\n7 6 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 22 23 24 0\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n1 3\n1 2 3\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 16 29\n32 20 36 160 50\n110 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 73\n73 113\n113 119\n119 38\n38 0\n1 5\n114 6 80 58 54\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 115 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 165 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n4 4\n0 2 3 4\n0 3 3 6\n4 1 7 7\n5 4 7 0\n4 4\n0 2 3 0\n0 3 3 6\n4 1 6 7\n0 4 7 0\n4 4\n5 2 3 1\n0 1 3 6\n4 1 6 7\n9 4 11 2\n4 4\n0 0 0 0\n0 1 1 2\n0 1 3 0\n0 0 0 0\n4 4\n-1 0 0 0\n0 0 2 0\n0 1 0 1\n0 0 0 0\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n28 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 153 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 71 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n151 20 9 99 66\n56 10 90 13 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 15\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"3\n5 5\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n4 4\n0 0 3 0\n0 2 0 0\n4 -1 0 0\n0 0 1 0\n5 5\n0 3 4 5 0\n7 6 9 10 11\n12 13 14 15 16\n17 18 19 20 21\n0 32 23 24 0\n",
"4\n1 1\n0\n1 3\n1 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 0\n4 5 6\n7 8 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 61\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 178\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 118 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n172 16 80 44 123\n",
"5\n5 5\n1 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 5 70\n99 153 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 61\n38 0\n1 5\n114 16 80 40 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 46 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n163 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 2 0\n4 5 6\n12 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 83\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 28 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 68 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 118 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n107 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 54 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 100 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n92 38\n38 0\n1 2\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n2 2 0\n4 5 6\n5 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 83\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 10 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n30 10 90 13 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n113 119\n119 38\n38 0\n1 5\n114 16 80 58 123\n",
"4\n1 1\n0\n1 3\n0 1 3\n2 2\n0 1\n1 0\n2 3\n1 0 -1\n4 5 6\n5 10 9\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 65\n38 0\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 72 21 0 108\n241 30 110 115 31\n39 117 87 99 61\n55 72 124 61 0\n5 5\n1 82 44 96 5\n82 20 9 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 0 30\n80 93 1 42 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n165 119\n119 38\n38 0\n1 5\n172 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 38\n38 -1\n1 5\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n124 30 110 115 31\n98 117 87 99 72\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 99 66\n56 10 90 13 70\n99 120 103 0 23\n193 26 70 23 0\n5 5\n110 112 41 120 29\n32 22 36 47 50\n100 11 18 0 30\n80 93 1 83 60\n69 31 24 102 48\n5 2\n0 87\n73 113\n48 119\n119 38\n38 0\n1 5\n114 28 80 58 123\n",
"5\n5 5\n0 126 30 105 77\n126 98 21 0 108\n201 30 100 115 31\n98 117 87 103 61\n55 72 124 61 0\n5 5\n0 82 44 96 5\n82 20 9 130 66\n56 10 90 30 70\n99 87 103 0 23\n107 26 70 23 0\n5 5\n100 112 41 225 29\n32 20 36 160 50\n100 7 18 0 30\n80 93 1 83 60\n69 31 24 204 48\n5 2\n0 87\n73 113\n113 2\n119 38\n38 0\n1 2\n114 16 80 58 123\n",
"5\n5 5\n0 126 30 105 44\n126 98 21 0 108\n124 30 110 82 31\n119 117 87 99 97\n55 72 124 61 0\n5 5\n0 154 44 96 5\n82 20 16 99 66\n56 10 90 63 70\n99 87 103 0 23\n107 26 70 23 -1\n5 5\n100 112 41 120 29\n32 20 36 160 50\n100 11 92 7 30\n80 93 0 83 60\n69 31 24 102 48\n5 2\n0 100\n73 113\n113 119\n119 1\n38 0\n1 5\n114 16 80 58 123\n"
],
"output": [
"\nJeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nJeel\nAshish\n",
"Ashish\nJeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\nJeel\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Jeel\nJeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nJeel\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Jeel\nAshish\nJeel\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n",
"Ashish\nAshish\nAshish\nAshish\nAshish\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Jeel and Ashish play a game on an n × m matrix. The rows are numbered 1 to n from top to bottom and the columns are numbered 1 to m from left to right. They play turn by turn. Ashish goes first.
Initially, each cell of the matrix contains a non-negative integer. Each turn, a player must perform all of the following actions in order.
* Choose a starting cell (r_1, c_1) with non-zero value.
* Choose a finishing cell (r_2, c_2) such that r_1 ≤ r_2 and c_1 ≤ c_2.
* Decrease the value of the starting cell by some positive non-zero integer.
* Pick any of the shortest paths between the two cells and either increase, decrease or leave the values of cells on this path unchanged. Note that:
* a shortest path is one that passes through the least number of cells;
* all cells on this path excluding the starting cell, but the finishing cell may be modified;
* the resulting value of each cell must be a non-negative integer;
* the cells are modified independently and not necessarily by the same value.
If the starting and ending cells are the same, then as per the rules, the value of the cell is decreased. No other operations are performed.
The game ends when all the values become zero. The player who is unable to make a move loses. It can be shown that the game will end in a finite number of moves if both players play optimally.
Given the initial matrix, if both players play optimally, can you predict who will win?
Input
The first line contains a single integer t (1 ≤ t ≤ 10) — the number of test cases. The description of each test case is as follows.
The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 100) — the dimensions of the matrix.
The next n lines contain m space separated integers a_{i,j} (0 ≤ a_{i,j} ≤ 10^6) — the values of each cell of the matrix.
Output
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Jeel" (without the quotes).
Example
Input
4
1 1
0
1 3
0 0 5
2 2
0 1
1 0
3 3
1 2 3
4 5 6
7 8 9
Output
Jeel
Ashish
Jeel
Ashish
Note
In the first test case, the only cell of the matrix is 0. There are no moves Ashish can make. Jeel is the winner.
In the second test case, Ashish can choose (r_1, c_1) = (r_2, c_2) = (1,3) and reduce the cell to 0, leaving [0, 0, 0]. Jeel cannot perform any moves. Ashish wins.
### Input:
4
1 1
0
1 3
0 0 5
2 2
0 1
1 0
3 3
1 2 3
4 5 6
7 8 9
### Output:
Jeel
Ashish
Jeel
Ashish
### Input:
3
5 5
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
4 4
0 0 3 0
0 2 0 0
2 0 0 0
0 0 0 0
5 5
0 3 4 5 0
7 8 9 10 11
12 13 14 15 16
17 18 19 20 21
0 22 23 24 0
### Output:
Jeel
Ashish
Ashish
### Code:
def solve_case():
n, m = [int(x) for x in input().split()]
a = [[int(x) for x in input().split()] for x in range(n)]
xr = [0] * (n + m)
for i in range(n):
for j in range(m):
xr[i + j] ^= a[i][j]
return sum(xr) > 0
def main():
for _ in range(int(input())):
print(['Jeel', 'Ashish'][solve_case()])
main() |
1475_E. Advertising Agency_3085 | Masha works in an advertising agency. In order to promote the new brand, she wants to conclude contracts with some bloggers. In total, Masha has connections of n different bloggers. Blogger numbered i has a_i followers.
Since Masha has a limited budget, she can only sign a contract with k different bloggers. Of course, Masha wants her ad to be seen by as many people as possible. Therefore, she must hire bloggers with the maximum total number of followers.
Help her, find the number of ways to select k bloggers so that the total number of their followers is maximum possible. Two ways are considered different if there is at least one blogger in the first way, which is not in the second way. Masha believes that all bloggers have different followers (that is, there is no follower who would follow two different bloggers).
For example, if n=4, k=3, a=[1, 3, 1, 2], then Masha has two ways to select 3 bloggers with the maximum total number of followers:
* conclude contracts with bloggers with numbers 1, 2 and 4. In this case, the number of followers will be equal to a_1 + a_2 + a_4 = 6.
* conclude contracts with bloggers with numbers 2, 3 and 4. In this case, the number of followers will be equal to a_2 + a_3 + a_4 = 6.
Since the answer can be quite large, output it modulo 10^9+7.
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.
The first line of each test case contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the number of bloggers and how many of them you can sign a contract with.
The second line of each test case contains n integers a_1, a_2, … a_n (1 ≤ a_i ≤ n) — the number of followers of each blogger.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, on a separate line output one integer — the number of ways to select k bloggers so that the total number of their followers is maximum possible.
Example
Input
3
4 3
1 3 1 2
4 2
1 1 1 1
2 1
1 2
Output
2
6
1
Note
The test case is explained in the statements.
In the second test case, the following ways are valid:
* conclude contracts with bloggers with numbers 1 and 2. In this case, the number of followers will be equal to a_1 + a_2 = 2;
* conclude contracts with bloggers with numbers 1 and 3. In this case, the number of followers will be equal to a_1 + a_3 = 2;
* conclude contracts with bloggers with numbers 1 and 4. In this case, the number of followers will be equal to a_1 + a_4 = 2;
* conclude contracts with bloggers with numbers 2 and 3. In this case, the number of followers will be equal to a_2 + a_3 = 2;
* conclude contracts with bloggers with numbers 2 and 4. In this case, the number of followers will be equal to a_2 + a_4 = 2;
* conclude contracts with bloggers with numbers 3 and 4. In this case, the number of followers will be equal to a_3 + a_4 = 2.
In the third test case, the following ways are valid:
* concludes a contract with a blogger with the number 2. In this case, the number of followers will be equal to a_2 = 2. |
import math
def c (k, n):
return (math.factorial(n) // (math.factorial(k) * math.factorial(n - k))) % (10**9 + 7)
def solve():
n, k = map(int, input().split())
a = []
for i in input().split():
a.append(int(i))
a.sort()
m = dict()
for i in a:
if(m.get(i, 0) == 0): m[i] = 1
else: m[i] += 1
ind = n - k
while ind < n - 1 and a[ind + 1] == a[ind]: ind += 1
print(c(ind - (n - k) + 1, m[a[n - k]]))
t = int(input())
while t > 0:
t -= 1
solve()
| {
"input": [
"3\n4 3\n1 3 1 2\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 2 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 3 1 2\n4 2\n1 1 1 2\n2 1\n1 2\n",
"3\n4 3\n1 3 2 2\n4 1\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 4\n1 1 1 2\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 1\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 2\n4 2\n1 1 1 2\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 1 1\n2 1\n2 1\n",
"3\n4 3\n1 1 1 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 1 1 1\n2 2\n2 2\n",
"3\n4 1\n1 3 1 2\n4 1\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 2\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 1 1 1\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n2 2 2 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 1 2 2\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 2\n2 2 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 2\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 3 2 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n1 2 2 4\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 2 2 4\n4 3\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 1 2\n2 1\n1 2\n",
"3\n4 3\n1 4 2 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 4\n4 2\n1 1 3 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 1 1 2\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 1\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 1\n1 1 1 2\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 2 1\n2 2\n2 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 1 2 2\n4 4\n2 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 1 2 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 4 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 4 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 4\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 1\n1 1 4 1\n2 2\n2 2\n",
"3\n4 1\n1 3 2 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 2 2 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 2 2\n4 4\n2 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 3 1 2\n4 2\n1 1 1 4\n2 1\n1 2\n",
"3\n4 3\n1 3 4 4\n4 4\n1 1 2 1\n2 1\n2 2\n",
"3\n4 2\n1 1 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 3\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 2 2\n4 1\n1 1 4 1\n2 2\n2 2\n",
"3\n4 1\n1 2 2 2\n4 4\n2 1 1 1\n2 1\n2 2\n",
"3\n4 2\n1 1 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 4\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n2 3 2 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 4\n1 3 1 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n2 1 1 2\n4 2\n1 1 1 2\n2 1\n1 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 1 2 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 1\n4 4\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 4\n4 2\n1 1 1 1\n2 1\n2 1\n",
"3\n4 1\n1 3 2 4\n4 1\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 2 2 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n4 3 1 2\n4 2\n1 1 1 4\n2 1\n1 2\n",
"3\n4 4\n1 1 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 3\n1 1 4 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 2 1 1\n2 2\n2 2\n",
"3\n4 4\n1 1 2 3\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n4 2 2 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n4 2 3 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n4 2 3 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 2\n1 3 1 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 2 3\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 4\n1 4 1 1\n2 1\n1 2\n",
"3\n4 3\n1 1 2 2\n4 4\n1 1 1 3\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 4 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 1\n1 1 2 1\n2 2\n2 2\n",
"3\n4 3\n1 4 2 2\n4 4\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 3 4 4\n4 1\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 2\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 4 2\n4 1\n1 1 4 1\n2 2\n2 2\n",
"3\n4 2\n2 1 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 4\n1 3 1 2\n4 4\n1 1 1 1\n2 1\n1 2\n",
"3\n4 2\n1 2 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 1\n4 4\n1 1 3 1\n2 2\n2 2\n",
"3\n4 1\n1 3 2 2\n4 1\n1 1 1 1\n2 2\n2 2\n",
"3\n4 1\n1 3 1 4\n4 2\n1 1 1 1\n2 1\n2 1\n",
"3\n4 2\n1 3 2 4\n4 1\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 3\n1 2 1 1\n2 2\n2 2\n",
"3\n4 4\n1 3 1 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 4\n1 3 1 3\n4 4\n1 1 1 1\n2 1\n1 2\n",
"3\n4 2\n1 2 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 3 2 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 4\n1 3 1 2\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n2 4 2 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 3\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n2 1 4 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 1\n1 3 2 2\n4 1\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 4\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 3\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n4 3 2 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 2\n1 3 1 1\n4 4\n1 1 4 1\n2 2\n2 2\n",
"3\n4 1\n1 3 1 2\n4 2\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 3\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 1\n4 2\n1 1 1 1\n2 1\n2 1\n",
"3\n4 1\n1 3 2 4\n4 1\n1 1 3 1\n2 1\n2 2\n",
"3\n4 3\n1 2 2 2\n4 2\n1 4 1 1\n2 1\n1 2\n",
"3\n4 3\n4 3 2 2\n4 2\n1 1 1 4\n2 1\n1 2\n",
"3\n4 3\n1 1 2 1\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n4 2 3 2\n4 2\n1 4 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 2 3\n4 3\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 4\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 1\n4 1\n1 1 2 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 1\n4 2\n1 1 4 1\n2 2\n2 2\n",
"3\n4 2\n1 2 2 4\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 1\n1 3 2 2\n4 1\n2 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 2 2\n4 1\n1 2 1 1\n2 2\n2 2\n",
"3\n4 4\n1 3 1 4\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 2\n1 4 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n2 3 2 4\n4 2\n1 1 3 1\n2 1\n2 2\n",
"3\n4 3\n2 2 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 2\n4 1\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n4 3 2 4\n4 2\n1 1 2 1\n2 1\n1 2\n",
"3\n4 2\n1 3 1 1\n4 4\n1 1 2 1\n2 2\n2 2\n",
"3\n4 1\n1 3 1 2\n4 2\n1 2 1 1\n2 2\n2 2\n",
"3\n4 3\n1 3 1 1\n4 2\n1 1 1 2\n2 1\n2 1\n",
"3\n4 3\n1 3 2 1\n4 1\n1 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 2 2 4\n4 4\n1 1 1 1\n2 1\n2 1\n",
"3\n4 1\n1 3 1 2\n4 1\n2 1 1 1\n2 2\n2 2\n",
"3\n4 3\n2 2 2 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n2 3 4 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 2\n4 3 2 4\n4 2\n1 1 2 1\n2 1\n1 2\n",
"3\n4 2\n1 3 1 2\n4 4\n1 1 2 1\n2 2\n2 2\n",
"3\n4 4\n1 3 2 1\n4 1\n1 1 1 1\n2 2\n2 2\n",
"3\n4 4\n2 2 2 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n1 3 1 4\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 1 2\n4 3\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 1 2\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 2\n1 1 3 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 3\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 2 2 4\n4 2\n1 1 3 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 4\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n2 1 2 2\n4 3\n1 2 1 1\n2 1\n1 2\n",
"3\n4 1\n1 2 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 1\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 4 2\n4 4\n1 1 1 2\n2 1\n2 2\n",
"3\n4 3\n1 3 1 2\n4 4\n1 1 3 1\n2 2\n2 2\n",
"3\n4 1\n1 3 3 4\n4 2\n1 1 2 1\n2 1\n2 2\n",
"3\n4 2\n1 2 2 2\n4 4\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 2 1\n4 4\n2 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 1\n1 3 1 2\n4 1\n1 1 2 1\n2 2\n2 2\n",
"3\n4 2\n1 3 1 2\n4 2\n1 4 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 2 2\n4 4\n1 1 1 3\n2 1\n2 2\n",
"3\n4 3\n1 1 2 2\n4 1\n1 1 2 1\n2 2\n2 2\n",
"3\n4 2\n1 3 4 4\n4 1\n1 1 2 1\n2 1\n2 2\n",
"3\n4 3\n2 1 1 2\n4 2\n1 1 4 1\n2 2\n2 2\n",
"3\n4 2\n1 2 2 2\n4 4\n1 1 2 1\n2 1\n2 2\n",
"3\n4 1\n1 3 1 4\n4 1\n1 1 1 1\n2 1\n2 1\n",
"3\n4 4\n1 3 1 2\n4 2\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 4\n4 1\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 2 2\n4 3\n2 1 1 1\n2 2\n2 2\n",
"3\n4 4\n1 3 1 1\n4 4\n1 1 4 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 3\n4 2\n2 1 1 1\n2 1\n1 2\n",
"3\n4 3\n4 2 2 2\n4 2\n1 4 1 1\n2 1\n1 2\n",
"3\n4 1\n1 3 2 2\n4 1\n3 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 4 2 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n2 1 2 2\n4 4\n1 1 1 1\n2 2\n2 2\n",
"3\n4 3\n2 3 2 2\n4 2\n1 4 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 4\n4 2\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 1 2\n4 4\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 1 2 3\n4 2\n1 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 2 2 2\n4 1\n1 2 1 1\n2 1\n1 2\n",
"3\n4 2\n1 2 1 2\n4 2\n1 4 1 1\n2 1\n1 2\n",
"3\n4 3\n2 2 1 2\n4 2\n1 1 4 1\n2 2\n2 2\n",
"3\n4 1\n1 3 2 4\n4 1\n1 1 1 1\n2 1\n2 1\n",
"3\n4 4\n1 3 1 2\n4 2\n1 3 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 1 4\n4 1\n1 2 1 1\n2 1\n2 2\n",
"3\n4 3\n1 3 3 2\n4 3\n2 1 1 1\n2 2\n2 2\n",
"3\n4 3\n1 1 1 3\n4 4\n2 1 1 1\n2 1\n1 2\n",
"3\n4 3\n2 2 2 4\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 1\n1 1 2 2\n4 1\n3 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 4 3 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n2 1 2 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 3\n1 1 4 3\n4 2\n1 1 1 1\n2 2\n2 2\n",
"3\n4 2\n1 3 2 2\n4 1\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n4 2 2 4\n4 3\n1 1 1 1\n2 1\n2 2\n",
"3\n4 2\n1 4 3 2\n4 4\n1 1 1 4\n2 2\n2 2\n",
"3\n4 3\n3 1 2 2\n4 4\n1 1 1 2\n2 2\n2 2\n",
"3\n4 2\n1 3 2 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 2 2\n4 2\n1 1 1 1\n2 1\n1 2\n",
"3\n4 3\n1 2 1 2\n4 2\n1 2 1 1\n2 1\n1 2\n",
"3\n4 3\n1 3 2 2\n4 1\n1 1 1 1\n2 1\n2 2\n",
"3\n4 3\n1 4 2 4\n4 2\n1 1 1 1\n2 1\n2 2\n"
],
"output": [
"\n2\n6\n1\n",
"2\n3\n1\n",
"2\n6\n2\n",
"1\n6\n2\n",
"1\n3\n2\n",
"2\n3\n2\n",
"2\n1\n1\n",
"1\n1\n1\n",
"2\n1\n2\n",
"1\n3\n1\n",
"1\n1\n2\n",
"3\n6\n2\n",
"3\n1\n2\n",
"2\n4\n1\n",
"3\n3\n1\n",
"2\n6\n1\n",
"3\n1\n1\n",
"1\n6\n1\n",
"1\n4\n1\n",
"3\n6\n1\n",
"4\n1\n1\n",
"4\n3\n1\n",
"2\n4\n2\n",
"6\n1\n1\n",
"3\n4\n2\n",
"3\n3\n2\n",
"1\n4\n2\n",
"3\n4\n1\n",
"2\n3\n1\n",
"1\n6\n2\n",
"1\n3\n2\n",
"2\n6\n2\n",
"1\n3\n2\n",
"2\n1\n2\n",
"2\n1\n1\n",
"2\n1\n1\n",
"2\n3\n1\n",
"2\n1\n1\n",
"2\n1\n2\n",
"1\n1\n1\n",
"1\n1\n2\n",
"1\n3\n2\n",
"2\n1\n1\n",
"2\n3\n1\n",
"2\n1\n1\n",
"2\n1\n1\n",
"1\n3\n2\n",
"1\n1\n1\n",
"1\n1\n2\n",
"1\n3\n1\n",
"1\n1\n2\n",
"1\n1\n1\n",
"2\n3\n1\n",
"1\n1\n1\n",
"3\n1\n2\n",
"1\n1\n2\n",
"2\n1\n2\n",
"1\n1\n2\n",
"2\n3\n2\n",
"1\n1\n1\n",
"1\n1\n2\n",
"3\n1\n1\n",
"2\n3\n1\n",
"2\n1\n1\n",
"3\n1\n1\n",
"2\n6\n1\n",
"1\n1\n2\n",
"1\n3\n1\n",
"1\n3\n1\n",
"1\n1\n1\n",
"2\n3\n2\n",
"1\n3\n1\n",
"1\n1\n1\n",
"3\n3\n1\n",
"2\n3\n1\n",
"2\n3\n2\n",
"1\n3\n1\n",
"1\n3\n2\n",
"1\n1\n1\n",
"2\n1\n2\n",
"2\n3\n2\n",
"1\n1\n1\n",
"1\n1\n2\n",
"1\n1\n2\n",
"3\n3\n1\n",
"1\n1\n1\n",
"3\n1\n2\n",
"1\n1\n1\n",
"3\n1\n2\n",
"3\n1\n1\n",
"1\n4\n1\n",
"1\n6\n1\n",
"1\n1\n2\n",
"1\n3\n1\n",
"1\n3\n1\n",
"1\n1\n1\n",
"3\n1\n1\n",
"1\n3\n2\n",
"1\n6\n1\n",
"2\n3\n2\n",
"1\n3\n2\n",
"3\n6\n2\n",
"2\n1\n1\n",
"1\n1\n1\n",
"1\n1\n1\n",
"2\n1\n2\n",
"1\n4\n1\n",
"1\n3\n2\n",
"3\n1\n1\n",
"1\n6\n1\n",
"3\n6\n1\n",
"3\n6\n1\n",
"1\n1\n2\n",
"1\n3\n1\n",
"2\n3\n1\n",
"3\n1\n1\n",
"2\n3\n1\n",
"1\n3\n2\n",
"2\n4\n2\n",
"2\n1\n1\n",
"4\n3\n1\n",
"2\n1\n2\n",
"1\n1\n1\n",
"1\n1\n1\n",
"1\n3\n1\n",
"2\n1\n1\n",
"2\n3\n2\n",
"4\n1\n1\n",
"2\n1\n2\n",
"1\n3\n1\n",
"3\n1\n1\n",
"1\n3\n1\n",
"3\n3\n1\n",
"2\n4\n1\n",
"2\n1\n1\n",
"1\n1\n1\n",
"4\n1\n1\n",
"2\n3\n2\n",
"1\n3\n1\n",
"1\n1\n1\n",
"1\n4\n1\n",
"1\n1\n1\n",
"2\n6\n1\n",
"2\n3\n1\n",
"2\n6\n2\n",
"2\n3\n2\n",
"2\n6\n2\n",
"1\n3\n2\n",
"2\n1\n2\n",
"1\n3\n1\n",
"3\n1\n2\n",
"3\n4\n2\n",
"2\n1\n2\n",
"2\n1\n1\n",
"1\n3\n2\n",
"3\n1\n1\n",
"2\n1\n2\n",
"1\n1\n2\n",
"1\n1\n1\n",
"1\n3\n1\n",
"1\n1\n2\n",
"2\n1\n1\n",
"1\n1\n2\n",
"2\n3\n1\n",
"3\n1\n2\n",
"1\n4\n1\n",
"1\n3\n2\n",
"2\n4\n2\n",
"1\n3\n1\n",
"1\n1\n1\n",
"3\n3\n1\n",
"3\n3\n1\n",
"1\n1\n1\n",
"2\n1\n1\n",
"1\n1\n1\n",
"3\n3\n2\n",
"2\n6\n2\n",
"3\n1\n2\n",
"2\n6\n1\n",
"3\n1\n1\n",
"1\n3\n1\n",
"1\n3\n1\n",
"1\n4\n1\n",
"1\n3\n2\n",
"2\n1\n2\n",
"1\n3\n1\n",
"3\n1\n1\n",
"3\n4\n2\n",
"2\n1\n1\n",
"1\n1\n1\n",
"1\n1\n1\n",
"2\n6\n1\n",
"2\n1\n1\n",
"2\n4\n2\n",
"1\n1\n1\n",
"1\n1\n1\n",
"2\n3\n1\n",
"1\n6\n1\n",
"2\n3\n1\n",
"1\n4\n2\n",
"1\n6\n2\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Masha works in an advertising agency. In order to promote the new brand, she wants to conclude contracts with some bloggers. In total, Masha has connections of n different bloggers. Blogger numbered i has a_i followers.
Since Masha has a limited budget, she can only sign a contract with k different bloggers. Of course, Masha wants her ad to be seen by as many people as possible. Therefore, she must hire bloggers with the maximum total number of followers.
Help her, find the number of ways to select k bloggers so that the total number of their followers is maximum possible. Two ways are considered different if there is at least one blogger in the first way, which is not in the second way. Masha believes that all bloggers have different followers (that is, there is no follower who would follow two different bloggers).
For example, if n=4, k=3, a=[1, 3, 1, 2], then Masha has two ways to select 3 bloggers with the maximum total number of followers:
* conclude contracts with bloggers with numbers 1, 2 and 4. In this case, the number of followers will be equal to a_1 + a_2 + a_4 = 6.
* conclude contracts with bloggers with numbers 2, 3 and 4. In this case, the number of followers will be equal to a_2 + a_3 + a_4 = 6.
Since the answer can be quite large, output it modulo 10^9+7.
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.
The first line of each test case contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the number of bloggers and how many of them you can sign a contract with.
The second line of each test case contains n integers a_1, a_2, … a_n (1 ≤ a_i ≤ n) — the number of followers of each blogger.
It is guaranteed that the sum of n over all test cases does not exceed 1000.
Output
For each test case, on a separate line output one integer — the number of ways to select k bloggers so that the total number of their followers is maximum possible.
Example
Input
3
4 3
1 3 1 2
4 2
1 1 1 1
2 1
1 2
Output
2
6
1
Note
The test case is explained in the statements.
In the second test case, the following ways are valid:
* conclude contracts with bloggers with numbers 1 and 2. In this case, the number of followers will be equal to a_1 + a_2 = 2;
* conclude contracts with bloggers with numbers 1 and 3. In this case, the number of followers will be equal to a_1 + a_3 = 2;
* conclude contracts with bloggers with numbers 1 and 4. In this case, the number of followers will be equal to a_1 + a_4 = 2;
* conclude contracts with bloggers with numbers 2 and 3. In this case, the number of followers will be equal to a_2 + a_3 = 2;
* conclude contracts with bloggers with numbers 2 and 4. In this case, the number of followers will be equal to a_2 + a_4 = 2;
* conclude contracts with bloggers with numbers 3 and 4. In this case, the number of followers will be equal to a_3 + a_4 = 2.
In the third test case, the following ways are valid:
* concludes a contract with a blogger with the number 2. In this case, the number of followers will be equal to a_2 = 2.
### Input:
3
4 3
1 3 1 2
4 2
1 1 1 1
2 1
1 2
### Output:
2
6
1
### Input:
3
4 3
1 3 1 2
4 2
1 2 1 1
2 1
1 2
### Output:
2
3
1
### Code:
import math
def c (k, n):
return (math.factorial(n) // (math.factorial(k) * math.factorial(n - k))) % (10**9 + 7)
def solve():
n, k = map(int, input().split())
a = []
for i in input().split():
a.append(int(i))
a.sort()
m = dict()
for i in a:
if(m.get(i, 0) == 0): m[i] = 1
else: m[i] += 1
ind = n - k
while ind < n - 1 and a[ind + 1] == a[ind]: ind += 1
print(c(ind - (n - k) + 1, m[a[n - k]]))
t = int(input())
while t > 0:
t -= 1
solve()
|
1525_E. Assimilation IV_3091 | Monocarp is playing a game "Assimilation IV". In this game he manages a great empire: builds cities and conquers new lands.
Monocarp's empire has n cities. In order to conquer new lands he plans to build one Monument in each city. The game is turn-based and, since Monocarp is still amateur, he builds exactly one Monument per turn.
Monocarp has m points on the map he'd like to control using the constructed Monuments. For each point he knows the distance between it and each city. Monuments work in the following way: when built in some city, a Monument controls all points at distance at most 1 to this city. Next turn, the Monument controls all points at distance at most 2, the turn after — at distance at most 3, and so on. Monocarp will build n Monuments in n turns and his empire will conquer all points that are controlled by at least one Monument.
Monocarp can't figure out any strategy, so during each turn he will choose a city for a Monument randomly among all remaining cities (cities without Monuments). Monocarp wants to know how many points (among m of them) he will conquer at the end of turn number n. Help him to calculate the expected number of conquered points!
Input
The first line contains two integers n and m (1 ≤ n ≤ 20; 1 ≤ m ≤ 5 ⋅ 10^4) — the number of cities and the number of points.
Next n lines contains m integers each: the j-th integer of the i-th line d_{i, j} (1 ≤ d_{i, j} ≤ n + 1) is the distance between the i-th city and the j-th point.
Output
It can be shown that the expected number of points Monocarp conquers at the end of the n-th turn can be represented as an irreducible fraction x/y. Print this fraction modulo 998 244 353, i. e. value x ⋅ y^{-1} mod 998244353 where y^{-1} is such number that y ⋅ y^{-1} mod 998244353 = 1.
Example
Input
3 5
1 4 4 3 4
1 4 1 4 2
1 4 4 4 3
Output
166374062
Note
Let's look at all possible orders of cities Monuments will be build in:
* [1, 2, 3]:
* the first city controls all points at distance at most 3, in other words, points 1 and 4;
* the second city controls all points at distance at most 2, or points 1, 3 and 5;
* the third city controls all points at distance at most 1, or point 1.
In total, 4 points are controlled.
* [1, 3, 2]: the first city controls points 1 and 4; the second city — points 1 and 3; the third city — point 1. In total, 3 points.
* [2, 1, 3]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
* [2, 3, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
* [3, 1, 2]: the first city controls point 1; the second city — points 1 and 3; the third city — points 1 and 5. In total, 3 points.
* [3, 2, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — points 1 and 5. In total, 3 points.
The expected number of controlled points is (4 + 3 + 3 + 3 + 3 + 3)/(6) = 19/6 or 19 ⋅ 6^{-1} ≡ 19 ⋅ 166374059 ≡ 166374062 \pmod{998244353} | ans = 0
n,m = map(int,input().split())
mod = 998244353
a = [list(map(int,input().split())) for i in range(n)]
fac = 1
for i in range(1,n+1): fac *= i
inv = pow(fac,mod-2,mod)
for j in range(m):
na = sorted([a[i][j] for i in range(n)])
now = 1
able = 0
for i in range(n):
while len(na) > 0 and na[-1] > n-i:
del na[-1]
able += 1
now *= able
able -= 1
ans += now * inv
ans %= mod
print ((m-ans) % mod) | {
"input": [
"3 5\n1 4 4 3 4\n1 4 1 4 2\n1 4 4 4 3\n",
"1 1\n1\n",
"1 1\n2\n",
"3 1\n1\n1\n1\n",
"3 1\n1\n1\n2\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 4 4 4 3\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 3 4 4 3\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 3 3 4 4\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 4 4 1\n",
"3 5\n1 4 4 2 4\n1 1 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 4 3 4\n1 4 1 4 4\n2 4 4 4 3\n",
"1 1\n2\n1\n1\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 4 2 2 4\n1 1 2 4 2\n1 2 2 4 4\n",
"3 5\n1 3 4 2 4\n2 1 2 4 2\n1 2 3 4 4\n",
"3 5\n1 4 4 3 4\n1 4 2 4 4\n2 4 4 4 3\n",
"3 5\n1 4 2 2 4\n1 1 2 1 2\n1 2 2 4 4\n",
"3 5\n2 3 2 4 4\n1 4 2 3 2\n1 3 4 2 1\n",
"3 5\n1 3 2 2 2\n1 2 2 1 2\n1 1 2 4 4\n",
"3 5\n1 3 4 3 1\n1 1 1 4 2\n1 2 2 2 4\n",
"3 1\n3\n2\n4\n",
"3 1\n4\n4\n2\n",
"3 5\n1 4 4 3 4\n1 4 1 4 2\n2 4 4 4 3\n",
"3 1\n2\n1\n2\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 4 4 3\n",
"3 1\n2\n1\n3\n",
"3 5\n1 4 4 3 4\n1 2 2 4 2\n1 3 3 4 4\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 4 3 4 3\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 4 3 4\n2 4 1 4 2\n2 4 4 4 3\n",
"3 5\n2 2 4 3 4\n1 4 2 4 2\n1 3 4 4 3\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 2 3 4 4\n",
"3 1\n2\n1\n4\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 4 2 1\n",
"3 5\n2 4 4 2 4\n1 4 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 4 3 4\n2 4 1 4 3\n2 4 4 4 3\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 2 2 4 4\n",
"3 5\n2 4 4 2 1\n1 4 2 4 2\n1 3 4 4 4\n",
"3 5\n2 4 4 2 1\n1 4 2 4 2\n2 3 4 4 4\n",
"1 1\n1\n1\n1\n",
"3 5\n1 4 4 1 4\n1 4 1 4 2\n1 4 4 4 3\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 1 4 4 4\n",
"3 5\n1 4 4 3 4\n1 1 4 4 2\n1 3 3 4 4\n",
"3 1\n2\n1\n1\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 4 4 2\n",
"3 5\n1 4 4 3 4\n2 4 1 4 2\n4 4 4 4 3\n",
"3 5\n2 2 4 3 4\n1 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 3 4 3 4\n1 1 2 4 2\n1 2 3 4 4\n",
"3 1\n3\n1\n4\n",
"3 5\n2 1 4 2 4\n1 4 2 4 2\n1 3 4 4 4\n",
"3 5\n1 4 2 3 4\n1 1 2 4 2\n1 2 2 4 4\n",
"3 5\n1 4 4 1 4\n1 4 1 4 2\n1 4 4 3 3\n",
"3 5\n1 4 4 1 4\n1 4 1 4 4\n2 4 4 4 3\n",
"3 5\n1 3 4 3 4\n2 1 2 4 2\n1 2 3 4 4\n",
"3 5\n1 4 4 3 4\n1 4 1 4 2\n1 4 3 4 3\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 3 4 4 3\n",
"3 1\n4\n1\n2\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 4 4 3 4\n1 1 2 4 1\n1 3 3 4 4\n",
"3 5\n2 4 4 3 1\n1 4 2 4 2\n1 3 4 4 1\n",
"3 5\n1 4 4 3 4\n1 3 2 4 2\n1 3 3 4 4\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n2 4 3 4 3\n",
"3 5\n4 2 4 3 4\n1 4 2 4 2\n1 3 4 4 3\n",
"3 5\n2 3 4 3 4\n1 4 2 4 2\n1 3 4 2 1\n",
"1 1\n1\n1\n2\n",
"3 5\n1 4 4 1 4\n2 4 1 4 2\n1 4 4 4 3\n",
"3 5\n2 2 4 3 2\n1 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 3 4 3 1\n1 1 2 4 2\n1 2 3 4 4\n",
"1 1\n2\n1\n0\n",
"3 5\n1 4 4 1 4\n1 4 2 4 2\n1 4 4 3 3\n",
"3 5\n1 4 4 1 4\n1 3 1 4 4\n2 4 4 4 3\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 2 4 3\n",
"3 5\n1 3 4 3 4\n2 1 2 4 2\n1 2 3 2 4\n",
"3 1\n4\n2\n2\n",
"3 5\n1 4 4 3 4\n1 2 2 4 1\n1 3 3 4 4\n",
"3 5\n2 4 4 3 1\n2 4 2 4 2\n1 3 4 4 1\n",
"3 5\n4 2 4 3 4\n1 4 2 4 1\n1 3 4 4 3\n",
"3 5\n2 3 4 3 4\n1 4 2 3 2\n1 3 4 2 1\n",
"3 5\n1 3 4 3 1\n1 1 1 4 2\n1 2 3 4 4\n",
"3 5\n2 4 4 1 4\n1 4 2 4 2\n1 4 4 3 3\n",
"3 5\n1 3 4 3 4\n2 1 2 4 4\n1 2 3 2 4\n",
"3 5\n1 4 2 2 4\n1 1 2 1 2\n1 1 2 4 4\n",
"3 5\n1 4 4 3 4\n1 2 2 4 1\n1 3 3 4 1\n",
"3 5\n2 3 4 4 4\n1 4 2 3 2\n1 3 4 2 1\n",
"3 5\n2 4 4 1 4\n1 4 2 3 2\n1 4 4 3 3\n",
"3 5\n1 4 4 3 4\n1 4 1 4 2\n1 4 4 1 3\n",
"3 5\n1 3 4 3 4\n1 4 2 4 2\n1 3 4 4 3\n",
"3 5\n1 4 4 3 4\n1 4 2 4 2\n1 3 4 4 2\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 4 4 4 4\n",
"3 5\n1 4 3 3 4\n2 4 1 4 2\n2 4 4 4 3\n",
"3 5\n1 4 4 3 4\n2 4 1 4 3\n2 2 4 4 3\n",
"1 1\n1\n0\n1\n",
"3 5\n1 4 4 1 4\n1 4 2 4 2\n1 4 4 4 3\n",
"3 5\n1 4 4 3 4\n1 1 4 4 4\n1 3 3 4 4\n",
"3 5\n2 4 2 3 4\n1 4 2 4 2\n1 3 4 4 2\n",
"3 5\n1 4 2 3 4\n1 2 2 4 2\n1 2 2 4 4\n",
"1 1\n2\n1\n2\n",
"3 5\n1 4 4 2 4\n1 4 1 4 2\n1 4 4 4 3\n",
"3 5\n1 4 2 2 4\n1 2 2 4 2\n1 2 2 4 4\n",
"3 5\n1 4 4 3 4\n2 4 2 4 2\n1 3 1 4 3\n",
"3 5\n2 4 4 3 2\n1 4 2 4 2\n1 3 4 4 1\n",
"3 5\n4 2 4 3 4\n1 4 2 4 2\n1 3 4 1 3\n",
"3 5\n1 3 4 3 1\n1 1 2 4 1\n1 2 3 4 4\n",
"3 5\n1 4 4 1 4\n1 4 2 4 3\n1 4 4 3 3\n",
"3 5\n1 4 4 1 4\n1 3 1 4 4\n2 2 4 4 3\n",
"3 5\n2 4 4 3 4\n2 4 2 4 2\n1 3 2 4 3\n",
"3 5\n1 4 2 2 4\n1 1 2 2 2\n1 2 2 4 4\n",
"3 5\n1 3 4 3 1\n1 1 1 4 2\n1 2 2 4 4\n",
"3 5\n2 4 4 1 4\n1 4 2 4 2\n1 1 4 3 3\n",
"3 5\n1 3 4 3 4\n2 1 2 4 4\n1 3 3 2 4\n",
"3 5\n1 3 2 2 4\n1 1 2 1 2\n1 1 2 4 4\n",
"3 5\n2 3 2 4 4\n1 4 2 3 1\n1 3 4 2 1\n",
"3 5\n1 4 4 3 4\n1 4 1 4 2\n1 4 4 2 3\n",
"3 5\n1 4 4 3 4\n1 1 4 4 4\n1 3 3 4 3\n",
"3 5\n2 4 2 3 4\n1 3 2 4 2\n1 3 4 4 2\n",
"3 5\n1 4 2 3 4\n1 2 2 4 2\n1 2 3 4 4\n",
"3 5\n1 4 4 2 2\n1 4 1 4 2\n1 4 4 4 3\n",
"3 5\n1 4 4 3 4\n3 4 2 4 2\n1 3 1 4 3\n",
"3 5\n4 2 4 3 4\n1 4 2 4 2\n1 3 2 1 3\n",
"3 5\n1 4 4 1 4\n1 3 1 4 4\n3 2 4 4 3\n",
"3 5\n2 4 4 3 4\n2 4 2 4 2\n1 3 2 4 1\n",
"3 5\n1 4 2 2 4\n1 1 2 2 3\n1 2 2 4 4\n",
"3 5\n2 4 4 1 4\n1 4 2 4 3\n1 1 4 3 3\n",
"3 5\n1 3 2 2 4\n1 2 2 1 2\n1 1 2 4 4\n",
"3 5\n2 3 2 2 4\n1 4 2 3 1\n1 3 4 2 1\n",
"3 5\n1 4 4 3 4\n1 1 1 4 4\n1 3 3 4 3\n",
"3 5\n2 4 2 3 4\n1 3 2 4 2\n1 3 4 4 1\n",
"3 5\n1 3 2 3 4\n1 2 2 4 2\n1 2 3 4 4\n",
"3 5\n1 4 4 1 4\n1 3 1 4 2\n3 2 4 4 3\n",
"3 5\n1 4 2 4 4\n1 1 2 2 3\n1 2 2 4 4\n",
"3 5\n4 3 2 2 4\n1 4 2 3 1\n1 3 4 2 1\n",
"3 5\n1 4 2 4 4\n1 1 4 2 3\n1 2 2 4 4\n",
"3 5\n1 3 2 2 2\n1 2 1 1 2\n1 1 2 4 4\n",
"3 5\n4 3 2 2 4\n1 4 2 3 1\n2 3 4 2 1\n",
"3 5\n1 3 2 2 2\n1 2 1 1 2\n1 1 2 3 4\n",
"3 5\n4 3 2 2 4\n1 4 2 1 1\n2 3 4 2 1\n",
"3 5\n1 4 4 3 4\n1 4 2 4 1\n1 4 4 4 3\n",
"3 5\n2 4 4 3 4\n1 1 2 4 2\n1 3 4 4 4\n",
"3 5\n2 4 4 3 3\n1 4 2 4 2\n1 3 4 4 3\n",
"3 1\n2\n2\n3\n",
"3 5\n2 4 4 3 4\n1 4 4 4 2\n1 3 4 4 4\n",
"3 5\n2 4 4 3 4\n2 4 1 4 2\n2 4 4 4 3\n",
"3 5\n1 4 4 4 4\n1 1 2 4 2\n1 2 3 4 4\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 3 3 2 1\n",
"3 5\n1 4 4 3 4\n1 1 2 4 4\n1 2 2 4 4\n",
"3 5\n2 4 4 2 1\n1 4 2 4 1\n2 3 4 4 4\n",
"3 5\n1 4 4 3 4\n1 1 4 4 2\n1 3 3 4 2\n",
"3 5\n2 1 4 2 4\n1 4 2 3 2\n1 3 4 4 4\n",
"2 1\n2\n1\n0\n",
"3 5\n1 2 4 1 4\n1 4 1 4 2\n1 4 4 3 3\n",
"3 5\n1 3 4 2 4\n2 1 2 2 2\n1 2 3 4 4\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n1 3 4 3 3\n",
"3 5\n1 4 4 3 4\n1 4 2 3 2\n1 3 1 4 3\n",
"1 1\n1\n1\n3\n",
"3 5\n1 4 4 1 1\n2 4 1 4 2\n1 4 4 4 3\n",
"3 5\n1 3 4 3 1\n1 1 2 4 2\n2 2 3 4 4\n",
"3 5\n2 4 4 3 4\n1 4 2 4 2\n1 2 2 4 3\n",
"3 5\n1 3 4 3 4\n2 1 4 4 2\n1 2 3 2 4\n",
"3 5\n1 4 2 2 4\n1 1 4 1 2\n1 2 2 4 4\n",
"3 5\n2 2 4 3 4\n1 4 2 4 1\n1 3 4 4 3\n",
"3 5\n2 4 4 1 1\n1 4 2 4 2\n1 4 4 3 3\n",
"3 5\n1 4 4 3 4\n1 2 4 4 1\n1 3 3 4 1\n",
"3 5\n2 3 2 4 4\n1 4 2 3 2\n1 4 4 2 1\n",
"3 5\n1 4 4 2 4\n1 4 1 4 2\n1 4 4 1 3\n",
"3 5\n1 4 3 3 4\n2 4 1 4 2\n2 2 4 4 3\n",
"3 5\n1 4 3 1 4\n1 4 2 4 2\n1 4 4 3 3\n",
"3 5\n1 4 4 2 4\n1 1 4 4 4\n1 3 3 4 4\n",
"3 5\n1 4 2 3 4\n1 4 2 4 2\n1 3 4 4 2\n",
"3 5\n2 4 2 3 4\n1 2 2 4 2\n1 2 2 4 4\n",
"3 5\n2 4 4 3 4\n2 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 3 4 3 1\n1 1 3 4 1\n1 2 3 4 4\n",
"3 5\n1 4 4 1 4\n1 4 2 4 3\n1 4 4 2 3\n",
"3 5\n2 4 4 2 4\n2 4 2 4 2\n1 3 2 4 3\n",
"3 5\n2 4 4 1 4\n1 1 2 4 2\n1 1 4 3 3\n",
"3 5\n1 3 4 3 4\n4 1 2 4 4\n1 3 3 2 4\n",
"3 5\n2 4 2 3 4\n1 3 4 4 2\n1 3 4 4 2\n",
"3 5\n2 4 4 3 4\n3 4 2 4 2\n1 3 1 4 3\n",
"3 5\n1 4 4 1 4\n1 2 1 4 4\n3 2 4 4 3\n",
"3 5\n2 4 4 3 4\n2 4 2 3 2\n1 3 2 4 1\n",
"3 5\n1 3 2 4 4\n1 2 2 1 2\n1 1 2 4 4\n",
"3 5\n1 4 4 3 4\n1 1 1 3 4\n1 3 3 4 3\n",
"3 5\n3 4 2 3 4\n1 3 2 4 2\n1 3 4 4 1\n",
"3 5\n1 3 2 3 4\n2 2 2 4 2\n1 2 3 4 4\n",
"3 5\n1 4 4 1 4\n1 3 1 4 2\n4 2 4 4 3\n",
"3 5\n1 4 2 4 4\n1 1 2 2 3\n1 2 1 4 4\n",
"3 5\n1 3 2 2 2\n1 2 2 1 2\n1 1 3 4 4\n",
"3 5\n4 3 2 1 4\n1 4 2 3 1\n1 3 4 2 1\n",
"3 5\n2 3 2 2 2\n1 2 1 1 2\n1 1 2 4 4\n",
"3 5\n4 3 1 2 4\n1 4 2 1 1\n2 3 4 2 1\n",
"3 5\n1 4 4 3 4\n1 4 2 2 1\n1 4 4 4 3\n",
"3 1\n2\n3\n3\n",
"3 5\n2 4 4 2 1\n1 4 2 4 1\n3 3 4 4 4\n",
"2 1\n2\n1\n-1\n",
"3 5\n1 4 4 3 4\n1 1 2 4 2\n2 3 4 3 3\n",
"3 5\n1 4 4 3 4\n1 4 2 3 2\n2 3 1 4 3\n",
"1 1\n2\n1\n3\n",
"3 5\n4 4 4 3 4\n1 4 2 4 2\n1 2 2 4 3\n",
"3 5\n2 2 4 3 4\n1 1 2 4 1\n1 3 4 4 3\n",
"3 5\n2 4 4 1 2\n1 4 2 4 2\n1 4 4 3 3\n",
"3 5\n1 4 3 3 4\n2 4 1 4 2\n3 2 4 4 3\n",
"3 5\n1 4 3 1 4\n1 4 2 4 1\n1 4 4 3 3\n",
"3 5\n1 4 4 2 4\n1 1 4 4 4\n1 3 3 3 4\n"
],
"output": [
"\n166374062\n",
"1\n",
"0\n",
"1\n",
"1\n",
"831870297\n",
"166374062\n",
"3\n",
"665496239\n",
"831870298\n",
"332748121\n",
"4\n",
"665496238\n",
"0\n",
"499122180\n",
"332748122\n",
"166374063\n",
"332748120\n",
"665496240\n",
"499122181\n",
"5\n",
"831870299\n",
"831870295\n",
"665496236\n",
"166374062\n",
"1\n",
"166374062\n",
"1\n",
"665496239\n",
"3\n",
"3\n",
"166374062\n",
"665496239\n",
"831870298\n",
"1\n",
"831870298\n",
"332748121\n",
"3\n",
"4\n",
"665496239\n",
"665496239\n",
"1\n",
"831870298\n",
"665496239\n",
"332748121\n",
"1\n",
"332748121\n",
"166374062\n",
"4\n",
"831870298\n",
"1\n",
"4\n",
"4\n",
"831870298\n",
"332748121\n",
"831870298\n",
"166374062\n",
"831870298\n",
"1\n",
"499122180\n",
"166374063\n",
"332748121\n",
"499122180\n",
"3\n",
"665496239\n",
"166374063\n",
"1\n",
"831870298\n",
"166374063\n",
"166374063\n",
"0\n",
"499122180\n",
"665496239\n",
"499122180\n",
"332748122\n",
"1\n",
"4\n",
"332748121\n",
"831870298\n",
"332748122\n",
"332748122\n",
"499122180\n",
"665496239\n",
"665496240\n",
"4\n",
"166374063\n",
"499122180\n",
"831870298\n",
"499122180\n",
"332748121\n",
"665496239\n",
"166374062\n",
"665496239\n",
"1\n",
"499122180\n",
"665496238\n",
"665496239\n",
"4\n",
"0\n",
"499122180\n",
"332748122\n",
"499122180\n",
"332748121\n",
"332748122\n",
"166374063\n",
"332748121\n",
"166374063\n",
"499122180\n",
"665496240\n",
"332748122\n",
"499122181\n",
"665496239\n",
"665496240\n",
"499122181\n",
"665496239\n",
"3\n",
"4\n",
"4\n",
"665496239\n",
"499122180\n",
"665496240\n",
"166374063\n",
"665496239\n",
"332748122\n",
"332748122\n",
"665496240\n",
"665496240\n",
"665496239\n",
"4\n",
"4\n",
"665496240\n",
"4\n",
"665496240\n",
"4\n",
"5\n",
"665496240\n",
"5\n",
"665496240\n",
"3\n",
"665496239\n",
"332748121\n",
"1\n",
"332748120\n",
"166374062\n",
"499122180\n",
"4\n",
"332748121\n",
"665496239\n",
"665496239\n",
"166374063\n",
"1\n",
"499122181\n",
"499122181\n",
"166374063\n",
"831870298\n",
"1\n",
"4\n",
"166374063\n",
"831870298\n",
"831870298\n",
"665496240\n",
"831870298\n",
"665496239\n",
"499122180\n",
"166374063\n",
"831870298\n",
"831870298\n",
"665496239\n",
"3\n",
"665496239\n",
"4\n",
"499122180\n",
"4\n",
"332748121\n",
"831870298\n",
"499122181\n",
"665496239\n",
"665496239\n",
"499122180\n",
"332748122\n",
"4\n",
"665496240\n",
"4\n",
"4\n",
"4\n",
"665496240\n",
"4\n",
"5\n",
"665496240\n",
"5\n",
"665496240\n",
"499122180\n",
"1\n",
"665496239\n",
"1\n",
"166374063\n",
"831870298\n",
"0\n",
"831870298\n",
"4\n",
"665496239\n",
"831870298\n",
"831870298\n",
"166374062\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Monocarp is playing a game "Assimilation IV". In this game he manages a great empire: builds cities and conquers new lands.
Monocarp's empire has n cities. In order to conquer new lands he plans to build one Monument in each city. The game is turn-based and, since Monocarp is still amateur, he builds exactly one Monument per turn.
Monocarp has m points on the map he'd like to control using the constructed Monuments. For each point he knows the distance between it and each city. Monuments work in the following way: when built in some city, a Monument controls all points at distance at most 1 to this city. Next turn, the Monument controls all points at distance at most 2, the turn after — at distance at most 3, and so on. Monocarp will build n Monuments in n turns and his empire will conquer all points that are controlled by at least one Monument.
Monocarp can't figure out any strategy, so during each turn he will choose a city for a Monument randomly among all remaining cities (cities without Monuments). Monocarp wants to know how many points (among m of them) he will conquer at the end of turn number n. Help him to calculate the expected number of conquered points!
Input
The first line contains two integers n and m (1 ≤ n ≤ 20; 1 ≤ m ≤ 5 ⋅ 10^4) — the number of cities and the number of points.
Next n lines contains m integers each: the j-th integer of the i-th line d_{i, j} (1 ≤ d_{i, j} ≤ n + 1) is the distance between the i-th city and the j-th point.
Output
It can be shown that the expected number of points Monocarp conquers at the end of the n-th turn can be represented as an irreducible fraction x/y. Print this fraction modulo 998 244 353, i. e. value x ⋅ y^{-1} mod 998244353 where y^{-1} is such number that y ⋅ y^{-1} mod 998244353 = 1.
Example
Input
3 5
1 4 4 3 4
1 4 1 4 2
1 4 4 4 3
Output
166374062
Note
Let's look at all possible orders of cities Monuments will be build in:
* [1, 2, 3]:
* the first city controls all points at distance at most 3, in other words, points 1 and 4;
* the second city controls all points at distance at most 2, or points 1, 3 and 5;
* the third city controls all points at distance at most 1, or point 1.
In total, 4 points are controlled.
* [1, 3, 2]: the first city controls points 1 and 4; the second city — points 1 and 3; the third city — point 1. In total, 3 points.
* [2, 1, 3]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
* [2, 3, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
* [3, 1, 2]: the first city controls point 1; the second city — points 1 and 3; the third city — points 1 and 5. In total, 3 points.
* [3, 2, 1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — points 1 and 5. In total, 3 points.
The expected number of controlled points is (4 + 3 + 3 + 3 + 3 + 3)/(6) = 19/6 or 19 ⋅ 6^{-1} ≡ 19 ⋅ 166374059 ≡ 166374062 \pmod{998244353}
### Input:
3 5
1 4 4 3 4
1 4 1 4 2
1 4 4 4 3
### Output:
166374062
### Input:
1 1
1
### Output:
1
### Code:
ans = 0
n,m = map(int,input().split())
mod = 998244353
a = [list(map(int,input().split())) for i in range(n)]
fac = 1
for i in range(1,n+1): fac *= i
inv = pow(fac,mod-2,mod)
for j in range(m):
na = sorted([a[i][j] for i in range(n)])
now = 1
able = 0
for i in range(n):
while len(na) > 0 and na[-1] > n-i:
del na[-1]
able += 1
now *= able
able -= 1
ans += now * inv
ans %= mod
print ((m-ans) % mod) |
157_B. Trace_3095 | One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall.
Let us remind you that two circles are called concentric if their centers coincide. Several circles are called concentric if any two of them are concentric.
Input
The first line contains the single integer n (1 ≤ n ≤ 100). The second line contains n space-separated integers ri (1 ≤ ri ≤ 1000) — the circles' radii. It is guaranteed that all circles are different.
Output
Print the single real number — total area of the part of the wall that is painted red. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.
Examples
Input
1
1
Output
3.1415926536
Input
3
1 4 2
Output
40.8407044967
Note
In the first sample the picture is just one circle of radius 1. Inner part of the circle is painted red. The area of the red part equals π × 12 = π.
In the second sample there are three circles of radii 1, 4 and 2. Outside part of the second circle is painted blue. Part between the second and the third circles is painted red. Part between the first and the third is painted blue. And, finally, the inner part of the first circle is painted red. Overall there are two red parts: the ring between the second and the third circles and the inner part of the first circle. Total area of the red parts is equal (π × 42 - π × 22) + π × 12 = π × 12 + π = 13π | n=int(input())
s=0
X=[int(x) for x in input().split(" ")]
X.sort(reverse=True)
for i in range(n):
s=s+(-1)**(i)*X[i]*X[i]
print(3.1415926536*s) | {
"input": [
"1\n1\n",
"3\n1 4 2\n",
"6\n258 877 696 425 663 934\n",
"37\n280 281 169 68 249 389 977 101 360 43 448 447 368 496 125 507 747 392 338 270 916 150 929 428 118 266 589 470 774 852 263 644 187 817 808 58 637\n",
"100\n469 399 735 925 62 153 707 723 819 529 200 624 57 708 245 384 889 11 639 638 260 419 8 142 403 298 204 169 887 388 241 983 885 267 643 943 417 237 452 562 6 839 149 742 832 896 100 831 712 754 679 743 135 222 445 680 210 955 220 63 960 487 514 824 481 584 441 997 795 290 10 45 510 678 844 503 407 945 850 84 858 934 500 320 936 663 736 592 161 670 606 465 864 969 293 863 868 393 899 744\n",
"38\n488 830 887 566 720 267 583 102 65 200 884 220 263 858 510 481 316 804 754 568 412 166 374 869 356 977 145 421 500 58 664 252 745 70 381 927 670 772\n",
"6\n109 683 214 392 678 10\n",
"4\n4 1 3 2\n",
"97\n976 166 649 81 611 927 480 231 998 711 874 91 969 521 531 414 993 790 317 981 9 261 437 332 173 573 904 777 882 990 658 878 965 64 870 896 271 732 431 53 761 943 418 602 708 949 930 130 512 240 363 458 673 319 131 784 224 48 919 126 208 212 911 59 677 535 450 273 479 423 79 807 336 18 72 290 724 28 123 605 287 228 350 897 250 392 885 655 746 417 643 114 813 378 355 635 905\n",
"3\n269 918 721\n",
"4\n100 10 2 1\n",
"100\n901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000\n",
"96\n292 235 391 180 840 172 218 997 166 287 329 20 886 325 400 471 182 356 448 337 417 319 58 106 366 764 393 614 90 831 924 314 667 532 64 874 3 434 350 352 733 795 78 640 967 63 47 879 635 272 145 569 468 792 153 761 770 878 281 467 209 208 298 37 700 18 334 93 5 750 412 779 523 517 360 649 447 328 311 653 57 578 767 460 647 663 50 670 151 13 511 580 625 907 227 89\n",
"1\n1000\n",
"52\n270 658 808 249 293 707 700 78 791 167 92 772 807 502 830 991 945 102 968 376 556 578 326 980 688 368 280 853 646 256 666 638 424 737 321 996 925 405 199 680 953 541 716 481 727 143 577 919 892 355 346 298\n",
"8\n872 704 973 612 183 274 739 253\n",
"8\n885 879 891 428 522 176 135 983\n",
"10\n10 9 8 7 6 5 4 3 2 1\n",
"2\n457 898\n",
"27\n167 464 924 575 775 97 944 390 297 315 668 296 533 829 851 406 702 366 848 512 71 197 321 900 544 529 116\n",
"70\n12 347 748 962 514 686 192 159 990 4 10 788 602 542 946 215 523 727 799 717 955 796 529 465 897 103 181 515 495 153 710 179 747 145 16 585 943 998 923 708 156 399 770 547 775 285 9 68 713 722 570 143 913 416 663 624 925 218 64 237 797 138 942 213 188 818 780 840 480 758\n",
"77\n482 532 200 748 692 697 171 863 586 547 301 149 326 812 147 698 303 691 527 805 681 387 619 947 598 453 167 799 840 508 893 688 643 974 998 341 804 230 538 669 271 404 477 759 943 596 949 235 880 160 151 660 832 82 969 539 708 889 258 81 224 655 790 144 462 582 646 256 445 52 456 920 67 819 631 484 534\n",
"98\n29 211 984 75 333 96 840 21 352 168 332 433 130 944 215 210 620 442 363 877 91 491 513 955 53 82 351 19 998 706 702 738 770 453 344 117 893 590 723 662 757 16 87 546 312 669 568 931 224 374 927 225 751 962 651 587 361 250 256 240 282 600 95 64 384 589 813 783 39 918 412 648 506 283 886 926 443 173 946 241 310 33 622 565 261 360 547 339 943 367 354 25 479 743 385 485 896 741\n",
"76\n986 504 673 158 87 332 124 218 714 235 212 122 878 370 938 81 686 323 386 348 410 468 875 107 50 960 82 834 234 663 651 422 794 633 294 771 945 607 146 913 950 858 297 88 882 725 247 872 645 749 799 987 115 394 380 382 971 429 593 426 652 353 351 233 868 598 889 116 71 376 916 464 414 976 138 903\n",
"93\n957 395 826 67 185 4 455 880 683 654 463 84 258 878 553 592 124 585 9 133 20 609 43 452 725 125 801 537 700 685 771 155 566 376 19 690 383 352 174 208 177 416 304 1000 533 481 87 509 358 233 681 22 507 659 36 859 952 259 138 271 594 779 576 782 119 69 608 758 283 616 640 523 710 751 34 106 774 92 874 568 864 660 998 992 474 679 180 409 15 297 990 689 501\n",
"64\n591 387 732 260 840 397 563 136 571 876 831 953 799 493 579 13 559 872 53 678 256 232 969 993 847 14 837 365 547 997 604 199 834 529 306 443 739 49 19 276 343 835 904 588 900 870 439 576 975 955 518 117 131 347 800 83 432 882 869 709 32 950 314 450\n",
"7\n920 570 681 428 866 935 795\n",
"26\n656 508 45 189 561 366 96 486 547 386 703 570 780 689 264 26 11 74 466 76 421 48 982 886 215 650\n",
"8\n8 1 7 2 6 3 5 4\n",
"100\n1000 999 998 997 996 995 994 993 992 991 990 989 988 987 986 985 984 983 982 981 980 979 978 977 976 975 974 973 972 971 970 969 968 967 966 965 964 963 962 961 960 959 958 957 956 955 954 953 952 951 950 949 948 947 946 945 944 943 942 941 940 939 938 937 936 935 934 933 932 931 930 929 928 927 926 925 924 923 922 921 920 919 918 917 916 915 914 913 912 911 910 909 908 907 906 905 904 903 902 901\n",
"2\n151 400\n",
"9\n635 707 108 234 52 180 910 203 782\n",
"100\n110 868 147 888 291 282 916 542 917 337 235 595 498 621 814 249 261 713 445 666 142 275 319 49 900 543 333 606 487 670 620 769 852 258 230 867 603 491 714 839 879 37 21 74 590 190 397 506 499 967 152 862 200 107 145 23 614 167 857 475 79 598 270 906 626 116 89 59 651 846 723 201 50 699 522 408 634 132 226 414 824 764 513 586 526 238 556 162 667 173 684 415 527 743 10 442 552 274 350 822\n",
"97\n768 569 306 968 437 779 227 561 412 60 44 807 234 645 169 858 580 396 343 145 842 723 416 80 456 247 81 150 297 116 760 964 312 558 101 850 549 650 299 868 121 435 579 705 118 424 302 812 970 397 659 565 916 183 933 459 6 593 518 717 326 305 744 470 75 981 824 221 294 324 194 293 251 446 481 215 338 861 528 829 921 945 540 89 450 178 24 460 990 392 148 219 934 615 932 340 937\n",
"100\n859 113 290 762 701 63 188 431 810 485 671 673 99 658 194 227 511 435 941 212 551 124 89 222 42 321 657 815 898 171 216 482 707 567 724 491 414 942 820 351 48 653 685 312 586 24 20 627 602 498 533 173 463 262 621 466 119 299 580 964 510 987 40 698 521 998 847 651 746 215 808 563 785 837 631 772 404 923 682 244 232 214 390 350 968 771 517 900 70 543 934 554 681 368 642 575 891 728 478 317\n",
"95\n936 736 17 967 229 607 589 291 242 244 29 698 800 566 630 667 90 416 11 94 812 838 668 520 678 111 490 823 199 973 681 676 683 721 262 896 682 713 402 691 874 44 95 704 56 322 822 887 639 433 406 35 988 61 176 496 501 947 440 384 372 959 577 370 754 802 1 945 427 116 746 408 308 391 397 730 493 183 203 871 831 862 461 565 310 344 504 378 785 137 279 123 475 138 415\n",
"94\n145 703 874 425 277 652 239 496 458 658 339 842 564 699 893 352 625 980 432 121 798 872 499 859 850 721 414 825 543 843 304 111 342 45 219 311 50 748 465 902 781 822 504 985 919 656 280 310 917 438 464 527 491 713 906 329 635 777 223 810 501 535 156 252 806 112 971 719 103 443 165 98 579 554 244 996 221 560 301 51 977 422 314 858 528 772 448 626 185 194 536 66 577 677\n",
"74\n652 446 173 457 760 847 670 25 196 775 998 279 656 809 883 148 969 884 792 502 641 800 663 938 362 339 545 608 107 184 834 666 149 458 864 72 199 658 618 987 126 723 806 643 689 958 626 904 944 415 427 498 628 331 636 261 281 276 478 220 513 595 510 384 354 561 469 462 799 449 747 109 903 456\n",
"97\n70 611 20 30 904 636 583 262 255 501 604 660 212 128 199 138 545 576 506 528 12 410 77 888 783 972 431 188 338 485 148 793 907 678 281 922 976 680 252 724 253 920 177 361 721 798 960 572 99 622 712 466 608 49 612 345 266 751 63 594 40 695 532 789 520 930 825 929 48 59 405 135 109 735 508 186 495 772 375 587 201 324 447 610 230 947 855 318 856 956 313 810 931 175 668 183 688\n",
"90\n643 197 42 218 582 27 66 704 195 445 641 675 285 639 503 686 242 327 57 955 848 287 819 992 756 749 363 48 648 736 580 117 752 921 923 372 114 313 202 337 64 497 399 25 883 331 24 871 917 8 517 486 323 529 325 92 891 406 864 402 263 773 931 253 625 31 17 271 140 131 232 586 893 525 846 54 294 562 600 801 214 55 768 683 389 738 314 284 328 804\n",
"100\n941 283 349 457 52 837 299 284 796 305 893 624 101 972 738 204 121 70 17 704 836 791 95 111 162 952 472 724 733 580 878 177 705 804 11 211 463 417 288 409 410 485 896 755 921 267 164 656 505 765 539 439 535 19 991 689 220 474 114 944 884 144 926 849 486 566 117 35 749 499 797 303 362 905 690 890 976 66 590 183 234 683 39 297 769 787 376 541 571 759 495 200 261 352 73 493 831 442 273 339\n",
"2\n517 331\n",
"91\n493 996 842 9 748 178 1 807 841 519 796 998 84 670 778 143 707 208 165 893 154 943 336 150 761 881 434 112 833 55 412 682 552 945 758 189 209 600 354 325 440 844 410 20 136 665 88 791 688 17 539 821 133 236 94 606 483 446 429 60 960 476 915 134 137 852 754 908 276 482 117 252 297 903 981 203 829 811 471 135 188 667 710 393 370 302 874 872 551 457 692\n",
"100\n321 200 758 415 190 710 920 992 873 898 814 259 359 66 971 210 838 545 663 652 684 277 36 756 963 459 335 484 462 982 532 423 131 703 307 229 391 938 253 847 542 975 635 928 220 980 222 567 557 181 366 824 900 180 107 979 112 564 525 413 300 422 876 615 737 343 902 8 654 628 469 913 967 785 893 314 909 215 912 262 20 709 363 915 997 954 986 454 596 124 74 159 660 550 787 418 895 786 293 50\n",
"6\n258 877 696 425 182 934\n",
"37\n280 281 169 68 249 520 977 101 360 43 448 447 368 496 125 507 747 392 338 270 916 150 929 428 118 266 589 470 774 852 263 644 187 817 808 58 637\n",
"100\n469 399 735 925 62 153 707 723 819 529 200 624 57 928 245 384 889 11 639 638 260 419 8 142 403 298 204 169 887 388 241 983 885 267 643 943 417 237 452 562 6 839 149 742 832 896 100 831 712 754 679 743 135 222 445 680 210 955 220 63 960 487 514 824 481 584 441 997 795 290 10 45 510 678 844 503 407 945 850 84 858 934 500 320 936 663 736 592 161 670 606 465 864 969 293 863 868 393 899 744\n",
"38\n488 830 887 566 720 267 583 102 65 200 884 220 263 858 510 481 316 804 754 568 412 166 374 585 356 977 145 421 500 58 664 252 745 70 381 927 670 772\n",
"6\n109 683 214 392 678 8\n",
"4\n4 1 4 2\n",
"97\n976 166 649 81 611 927 480 231 998 711 874 91 969 521 129 414 993 790 317 981 9 261 437 332 173 573 904 777 882 990 658 878 965 64 870 896 271 732 431 53 761 943 418 602 708 949 930 130 512 240 363 458 673 319 131 784 224 48 919 126 208 212 911 59 677 535 450 273 479 423 79 807 336 18 72 290 724 28 123 605 287 228 350 897 250 392 885 655 746 417 643 114 813 378 355 635 905\n",
"3\n269 918 90\n",
"4\n110 10 2 1\n",
"100\n901 902 903 904 905 906 907 908 909 695 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000\n",
"96\n292 235 391 180 840 172 218 997 166 287 329 20 886 325 400 471 182 356 448 337 417 319 58 106 366 764 393 614 90 831 924 314 667 532 64 874 3 434 350 352 733 795 78 640 967 63 47 879 635 272 145 569 468 792 153 761 770 878 281 467 209 208 298 37 700 18 334 93 5 750 412 779 523 517 360 649 447 328 311 653 57 578 767 460 647 663 50 670 151 13 511 580 625 907 197 89\n",
"1\n1010\n",
"52\n270 658 808 249 293 707 700 78 791 167 92 772 807 502 830 991 945 102 968 376 556 578 326 980 688 368 280 853 646 256 666 638 424 737 321 996 925 405 199 680 953 836 716 481 727 143 577 919 892 355 346 298\n",
"8\n872 704 1084 612 183 274 739 253\n",
"8\n885 879 891 428 929 176 135 983\n",
"10\n10 9 8 7 6 5 4 3 3 1\n",
"2\n843 898\n",
"27\n167 464 924 575 775 97 944 390 297 315 668 296 533 1636 851 406 702 366 848 512 71 197 321 900 544 529 116\n",
"70\n12 347 748 962 514 686 192 159 990 4 10 788 602 542 946 215 523 727 799 717 955 796 529 465 897 103 181 515 495 153 710 179 747 145 16 585 943 998 923 708 156 399 770 547 775 285 9 68 713 722 570 143 913 416 663 624 925 218 64 237 797 138 942 213 63 818 780 840 480 758\n",
"77\n482 532 200 748 692 697 171 863 586 547 301 149 326 812 147 698 303 691 527 805 681 387 619 947 598 453 167 1508 840 508 893 688 643 974 998 341 804 230 538 669 271 404 477 759 943 596 949 235 880 160 151 660 832 82 969 539 708 889 258 81 224 655 790 144 462 582 646 256 445 52 456 920 67 819 631 484 534\n",
"98\n29 211 984 75 555 96 840 21 352 168 332 433 130 944 215 210 620 442 363 877 91 491 513 955 53 82 351 19 998 706 702 738 770 453 344 117 893 590 723 662 757 16 87 546 312 669 568 931 224 374 927 225 751 962 651 587 361 250 256 240 282 600 95 64 384 589 813 783 39 918 412 648 506 283 886 926 443 173 946 241 310 33 622 565 261 360 547 339 943 367 354 25 479 743 385 485 896 741\n",
"76\n986 504 673 158 87 332 124 218 714 235 212 122 878 370 938 81 686 323 386 348 410 468 875 107 50 960 82 834 234 663 651 422 794 633 294 771 945 607 146 913 950 858 297 88 882 725 247 872 645 749 799 987 115 394 380 382 971 429 593 426 652 353 351 233 868 598 889 116 71 376 916 464 414 1693 138 903\n",
"93\n957 395 826 67 185 4 455 880 683 654 463 84 258 878 553 592 124 585 9 133 20 609 43 452 725 125 801 537 700 685 771 155 566 376 19 690 383 352 174 208 177 416 304 1000 533 481 87 509 358 233 681 22 507 659 36 744 952 259 138 271 594 779 576 782 119 69 608 758 283 616 640 523 710 751 34 106 774 92 874 568 864 660 998 992 474 679 180 409 15 297 990 689 501\n",
"64\n591 387 732 260 840 397 563 136 571 876 831 953 799 493 579 13 559 872 53 678 256 232 969 993 847 14 837 365 547 997 266 199 834 529 306 443 739 49 19 276 343 835 904 588 900 870 439 576 975 955 518 117 131 347 800 83 432 882 869 709 32 950 314 450\n",
"7\n920 570 681 428 866 935 492\n",
"26\n656 508 45 189 561 366 96 486 547 386 1183 570 780 689 264 26 11 74 466 76 421 48 982 886 215 650\n",
"8\n8 1 7 2 6 3 4 4\n",
"100\n1000 999 998 997 996 995 994 993 992 991 990 989 988 987 986 985 984 983 982 981 980 979 978 977 976 975 974 973 972 971 970 969 968 967 966 965 964 897 962 961 960 959 958 957 956 955 954 953 952 951 950 949 948 947 946 945 944 943 942 941 940 939 938 937 936 935 934 933 932 931 930 929 928 927 926 925 924 923 922 921 920 919 918 917 916 915 914 913 912 911 910 909 908 907 906 905 904 903 902 901\n",
"2\n151 299\n",
"9\n635 707 108 234 7 180 910 203 782\n",
"100\n110 868 147 888 291 282 916 542 917 337 235 595 498 621 814 249 261 713 445 666 142 275 319 49 900 543 333 606 487 670 620 769 852 258 230 867 603 491 1401 839 879 37 21 74 590 190 397 506 499 967 152 862 200 107 145 23 614 167 857 475 79 598 270 906 626 116 89 59 651 846 723 201 50 699 522 408 634 132 226 414 824 764 513 586 526 238 556 162 667 173 684 415 527 743 10 442 552 274 350 822\n",
"97\n768 569 306 968 437 779 227 561 412 60 44 807 234 645 169 858 580 396 343 145 842 723 416 80 456 247 81 150 297 116 760 964 312 558 101 850 549 650 299 868 121 435 579 705 118 424 302 812 970 397 659 565 156 183 933 459 6 593 518 717 326 305 744 470 75 981 824 221 294 324 194 293 251 446 481 215 338 861 528 829 921 945 540 89 450 178 24 460 990 392 148 219 934 615 932 340 937\n",
"100\n859 113 290 762 701 63 188 431 810 485 671 673 99 658 194 227 511 435 941 212 551 124 89 222 42 321 657 815 898 171 216 482 707 567 724 491 414 942 820 351 48 653 685 312 586 24 20 627 602 498 533 173 463 262 621 466 119 299 580 964 510 987 40 698 521 998 1601 651 746 215 808 563 785 837 631 772 404 923 682 244 232 214 390 350 968 771 517 900 70 543 934 554 681 368 642 575 891 728 478 317\n",
"95\n936 736 17 967 229 607 589 291 242 244 29 698 800 566 630 667 90 416 11 94 812 838 668 520 678 111 535 823 199 973 681 676 683 721 262 896 682 713 402 691 874 44 95 704 56 322 822 887 639 433 406 35 988 61 176 496 501 947 440 384 372 959 577 370 754 802 1 945 427 116 746 408 308 391 397 730 493 183 203 871 831 862 461 565 310 344 504 378 785 137 279 123 475 138 415\n",
"94\n145 703 874 425 277 652 239 496 458 658 339 842 564 699 893 352 625 980 432 121 798 872 499 859 850 721 414 825 543 843 304 111 342 45 219 311 50 748 465 902 781 822 504 985 919 656 280 310 1468 438 464 527 491 713 906 329 635 777 223 810 501 535 156 252 806 112 971 719 103 443 165 98 579 554 244 996 221 560 301 51 977 422 314 858 528 772 448 626 185 194 536 66 577 677\n",
"74\n652 446 173 457 760 847 670 25 196 775 998 279 656 809 883 148 969 884 792 502 641 800 663 938 362 339 545 608 107 184 834 666 149 458 864 72 199 658 618 987 126 723 806 643 689 958 626 904 944 415 427 498 628 331 636 261 281 517 478 220 513 595 510 384 354 561 469 462 799 449 747 109 903 456\n",
"97\n70 611 20 30 904 636 583 262 255 501 604 660 212 128 199 138 545 576 506 528 12 410 77 888 783 972 431 188 338 485 148 793 907 678 281 922 976 903 252 724 253 920 177 361 721 798 960 572 99 622 712 466 608 49 612 345 266 751 63 594 40 695 532 789 520 930 825 929 48 59 405 135 109 735 508 186 495 772 375 587 201 324 447 610 230 947 855 318 856 956 313 810 931 175 668 183 688\n",
"90\n643 197 42 218 582 27 66 704 195 445 641 675 285 639 503 686 242 327 57 955 848 287 819 992 756 749 363 48 648 736 580 117 209 921 923 372 114 313 202 337 64 497 399 25 883 331 24 871 917 8 517 486 323 529 325 92 891 406 864 402 263 773 931 253 625 31 17 271 140 131 232 586 893 525 846 54 294 562 600 801 214 55 768 683 389 738 314 284 328 804\n",
"100\n941 283 349 457 52 837 299 284 796 305 893 624 101 972 738 204 121 70 17 704 836 791 95 111 162 952 472 724 733 580 878 177 705 804 11 211 463 417 288 409 410 485 896 755 921 267 164 656 505 765 539 439 535 19 991 689 220 474 114 944 884 144 926 849 486 566 117 35 749 499 797 303 362 905 690 890 976 97 590 183 234 683 39 297 769 787 376 541 571 759 495 200 261 352 73 493 831 442 273 339\n",
"2\n104 331\n",
"91\n493 996 842 9 748 178 1 807 841 519 796 998 84 670 778 143 707 208 165 893 154 943 336 150 761 881 434 112 833 55 412 682 552 945 758 189 209 600 354 325 440 844 410 20 136 665 88 791 688 17 539 821 133 236 94 606 483 446 429 60 960 476 915 134 137 852 754 908 276 482 117 252 297 903 981 203 829 811 471 135 188 667 710 393 370 329 874 872 551 457 692\n",
"100\n321 200 758 415 190 710 920 992 873 898 814 259 359 66 971 210 838 545 663 652 684 277 36 756 963 459 335 484 462 982 532 423 131 703 307 229 391 938 253 847 542 975 635 928 220 980 222 567 557 181 366 824 900 180 107 979 112 564 525 413 300 422 876 615 737 343 902 8 654 628 469 913 967 785 893 314 909 215 912 262 20 709 363 915 997 954 986 454 596 124 74 159 660 550 787 418 895 175 293 50\n",
"1\n2\n",
"3\n1 4 1\n",
"6\n258 356 696 425 182 934\n",
"37\n280 281 169 68 249 520 977 101 360 43 448 447 368 496 125 507 747 392 338 270 916 150 929 428 118 266 1002 470 774 852 263 644 187 817 808 58 637\n",
"100\n469 399 735 925 62 153 707 723 819 529 200 624 57 928 245 384 889 11 639 638 145 419 8 142 403 298 204 169 887 388 241 983 885 267 643 943 417 237 452 562 6 839 149 742 832 896 100 831 712 754 679 743 135 222 445 680 210 955 220 63 960 487 514 824 481 584 441 997 795 290 10 45 510 678 844 503 407 945 850 84 858 934 500 320 936 663 736 592 161 670 606 465 864 969 293 863 868 393 899 744\n",
"38\n488 830 887 566 720 267 583 102 65 200 884 220 263 858 510 481 316 804 754 568 412 166 374 585 356 977 145 421 500 102 664 252 745 70 381 927 670 772\n",
"6\n109 683 214 392 678 2\n",
"4\n4 1 0 2\n",
"97\n976 166 649 81 611 927 480 231 998 711 874 91 969 521 129 414 993 790 317 981 9 261 437 332 173 573 904 777 882 990 658 878 965 64 870 896 271 732 431 53 761 943 418 602 708 949 930 130 512 240 363 458 673 319 28 784 224 48 919 126 208 212 911 59 677 535 450 273 479 423 79 807 336 18 72 290 724 28 123 605 287 228 350 897 250 392 885 655 746 417 643 114 813 378 355 635 905\n",
"3\n268 918 90\n",
"4\n110 9 2 1\n",
"100\n901 902 903 904 905 906 907 908 909 695 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 1058 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000\n",
"96\n292 235 391 180 840 172 218 997 166 287 329 20 886 325 400 471 182 356 448 337 417 319 58 106 366 764 376 614 90 831 924 314 667 532 64 874 3 434 350 352 733 795 78 640 967 63 47 879 635 272 145 569 468 792 153 761 770 878 281 467 209 208 298 37 700 18 334 93 5 750 412 779 523 517 360 649 447 328 311 653 57 578 767 460 647 663 50 670 151 13 511 580 625 907 197 89\n",
"1\n1011\n",
"52\n270 658 808 249 293 707 700 78 791 167 92 772 807 502 830 991 945 102 968 376 556 578 326 1749 688 368 280 853 646 256 666 638 424 737 321 996 925 405 199 680 953 836 716 481 727 143 577 919 892 355 346 298\n",
"8\n872 704 681 612 183 274 739 253\n",
"8\n885 879 891 428 929 176 135 1413\n",
"10\n3 9 8 7 6 5 4 3 3 1\n",
"2\n843 1151\n",
"27\n167 464 924 575 775 97 944 390 297 315 668 296 533 1636 851 807 702 366 848 512 71 197 321 900 544 529 116\n",
"70\n12 347 748 962 514 686 192 159 990 4 10 788 602 542 946 215 523 727 799 717 76 796 529 465 897 103 181 515 495 153 710 179 747 145 16 585 943 998 923 708 156 399 770 547 775 285 9 68 713 722 570 143 913 416 663 624 925 218 64 237 797 138 942 213 63 818 780 840 480 758\n",
"77\n482 532 200 748 692 697 171 863 586 547 301 149 326 812 147 698 303 691 527 805 681 404 619 947 598 453 167 1508 840 508 893 688 643 974 998 341 804 230 538 669 271 404 477 759 943 596 949 235 880 160 151 660 832 82 969 539 708 889 258 81 224 655 790 144 462 582 646 256 445 52 456 920 67 819 631 484 534\n",
"98\n29 211 984 75 555 96 840 21 352 168 332 433 130 944 215 210 620 442 363 877 91 491 513 955 53 82 351 19 998 706 702 738 770 453 344 117 893 590 723 662 757 16 87 546 312 669 568 931 224 374 927 225 751 962 651 587 361 250 256 240 282 600 95 64 384 589 813 783 39 918 412 648 506 283 886 926 443 173 946 241 310 33 622 565 261 360 547 339 294 367 354 25 479 743 385 485 896 741\n",
"76\n986 504 673 158 87 332 124 218 714 235 212 122 878 370 938 81 686 323 386 348 410 468 875 107 50 631 82 834 234 663 651 422 794 633 294 771 945 607 146 913 950 858 297 88 882 725 247 872 645 749 799 987 115 394 380 382 971 429 593 426 652 353 351 233 868 598 889 116 71 376 916 464 414 1693 138 903\n",
"93\n957 395 826 67 185 4 455 880 683 654 463 84 258 878 553 592 124 585 9 133 20 609 43 452 725 125 801 537 700 685 771 155 566 376 19 690 702 352 174 208 177 416 304 1000 533 481 87 509 358 233 681 22 507 659 36 744 952 259 138 271 594 779 576 782 119 69 608 758 283 616 640 523 710 751 34 106 774 92 874 568 864 660 998 992 474 679 180 409 15 297 990 689 501\n",
"64\n591 387 732 260 840 397 563 136 416 876 831 953 799 493 579 13 559 872 53 678 256 232 969 993 847 14 837 365 547 997 266 199 834 529 306 443 739 49 19 276 343 835 904 588 900 870 439 576 975 955 518 117 131 347 800 83 432 882 869 709 32 950 314 450\n",
"7\n920 570 473 428 866 935 492\n",
"26\n656 508 45 189 561 121 96 486 547 386 1183 570 780 689 264 26 11 74 466 76 421 48 982 886 215 650\n",
"8\n8 1 7 2 6 4 4 4\n",
"100\n1000 999 998 997 996 995 994 993 992 991 990 989 988 987 986 985 984 983 982 981 980 979 978 977 976 975 974 973 972 971 970 969 968 967 966 965 964 897 962 961 960 959 958 957 956 955 954 953 952 951 950 949 948 947 946 293 944 943 942 941 940 939 938 937 936 935 934 933 932 931 930 929 928 927 926 925 924 923 922 921 920 919 918 917 916 915 914 913 912 911 910 909 908 907 906 905 904 903 902 901\n",
"2\n262 299\n",
"9\n635 1356 108 234 7 180 910 203 782\n",
"100\n110 868 147 888 291 282 916 542 917 337 235 595 498 621 814 249 261 713 445 666 142 275 319 49 900 543 333 606 487 670 620 769 852 258 230 867 603 491 1401 839 879 37 21 74 590 190 397 506 499 967 152 862 200 107 145 23 614 167 857 475 79 598 270 906 626 116 89 59 651 846 723 201 50 699 522 408 143 132 226 414 824 764 513 586 526 238 556 162 667 173 684 415 527 743 10 442 552 274 350 822\n",
"97\n768 569 306 968 437 779 227 561 412 60 44 807 234 645 169 858 580 396 343 145 842 723 416 90 456 247 81 150 297 116 760 964 312 558 101 850 549 650 299 868 121 435 579 705 118 424 302 812 970 397 659 565 156 183 933 459 6 593 518 717 326 305 744 470 75 981 824 221 294 324 194 293 251 446 481 215 338 861 528 829 921 945 540 89 450 178 24 460 990 392 148 219 934 615 932 340 937\n",
"100\n859 113 290 762 701 63 188 431 810 485 671 673 99 658 194 227 511 435 941 212 551 124 89 222 42 321 657 815 898 171 216 482 707 567 724 491 414 942 820 351 48 653 685 312 586 24 20 627 602 498 533 173 463 262 621 466 119 299 580 964 510 987 40 698 521 998 1601 651 746 215 808 563 1134 837 631 772 404 923 682 244 232 214 390 350 968 771 517 900 70 543 934 554 681 368 642 575 891 728 478 317\n",
"95\n936 736 17 967 229 607 589 291 242 244 29 698 800 566 630 667 90 416 11 94 812 838 668 520 678 111 535 823 199 973 681 676 683 721 262 896 682 713 402 691 874 44 95 704 56 322 822 887 639 433 406 35 988 61 176 496 501 947 440 524 372 959 577 370 754 802 1 945 427 116 746 408 308 391 397 730 493 183 203 871 831 862 461 565 310 344 504 378 785 137 279 123 475 138 415\n",
"94\n145 703 874 425 277 652 239 496 458 658 339 842 564 699 893 352 625 980 432 121 798 872 499 859 850 721 414 825 543 843 304 111 342 45 219 311 50 748 465 902 781 822 504 985 919 656 280 310 1468 438 464 527 491 713 906 329 635 777 223 810 501 535 156 252 806 112 971 1412 103 443 165 98 579 554 244 996 221 560 301 51 977 422 314 858 528 772 448 626 185 194 536 66 577 677\n",
"74\n652 446 173 457 760 310 670 25 196 775 998 279 656 809 883 148 969 884 792 502 641 800 663 938 362 339 545 608 107 184 834 666 149 458 864 72 199 658 618 987 126 723 806 643 689 958 626 904 944 415 427 498 628 331 636 261 281 517 478 220 513 595 510 384 354 561 469 462 799 449 747 109 903 456\n",
"97\n70 611 20 30 904 636 583 262 255 501 604 660 212 128 199 138 545 576 506 528 12 410 77 888 783 972 431 188 338 485 148 793 907 678 281 922 976 903 252 724 253 920 177 361 721 798 960 572 99 622 712 466 608 85 612 345 266 751 63 594 40 695 532 789 520 930 825 929 48 59 405 135 109 735 508 186 495 772 375 587 201 324 447 610 230 947 855 318 856 956 313 810 931 175 668 183 688\n",
"90\n643 197 42 218 582 27 66 704 195 445 641 675 285 639 503 686 242 327 57 955 848 288 819 992 756 749 363 48 648 736 580 117 209 921 923 372 114 313 202 337 64 497 399 25 883 331 24 871 917 8 517 486 323 529 325 92 891 406 864 402 263 773 931 253 625 31 17 271 140 131 232 586 893 525 846 54 294 562 600 801 214 55 768 683 389 738 314 284 328 804\n",
"100\n941 283 349 457 52 837 299 284 796 305 893 624 101 972 738 204 121 70 17 704 836 791 95 111 162 952 472 724 733 580 878 177 705 804 11 211 463 417 288 409 410 485 896 755 921 267 164 656 505 765 539 439 535 19 991 689 220 474 114 944 884 144 926 849 486 566 117 14 749 499 797 303 362 905 690 890 976 97 590 183 234 683 39 297 769 787 376 541 571 759 495 200 261 352 73 493 831 442 273 339\n",
"2\n206 331\n",
"91\n493 996 842 9 748 178 1 807 841 519 796 998 84 670 778 143 707 208 165 893 154 943 336 150 761 881 434 112 833 55 412 682 552 945 758 189 209 600 354 325 440 844 410 20 136 665 88 791 688 17 539 821 133 236 94 606 483 446 429 60 960 476 915 134 137 852 754 908 276 482 46 252 297 903 981 203 829 811 471 135 188 667 710 393 370 329 874 872 551 457 692\n",
"100\n321 200 758 415 190 710 920 992 873 898 814 259 359 66 971 210 838 545 663 652 684 277 36 756 963 459 335 484 462 982 532 423 131 703 307 229 391 938 253 847 542 975 1018 928 220 980 222 567 557 181 366 824 900 180 107 979 112 564 525 413 300 422 876 615 737 343 902 8 654 628 469 913 967 785 893 314 909 215 912 262 20 709 363 915 997 954 986 454 596 124 74 159 660 550 787 418 895 175 293 50\n",
"1\n3\n",
"3\n0 4 1\n",
"6\n258 356 696 425 182 1716\n",
"37\n280 281 169 68 249 520 977 101 360 43 448 447 368 496 125 507 747 392 338 270 916 150 1589 428 118 266 1002 470 774 852 263 644 187 817 808 58 637\n",
"100\n469 399 735 925 62 153 707 723 819 529 200 624 57 928 245 384 889 11 639 638 145 419 8 142 2 298 204 169 887 388 241 983 885 267 643 943 417 237 452 562 6 839 149 742 832 896 100 831 712 754 679 743 135 222 445 680 210 955 220 63 960 487 514 824 481 584 441 997 795 290 10 45 510 678 844 503 407 945 850 84 858 934 500 320 936 663 736 592 161 670 606 465 864 969 293 863 868 393 899 744\n",
"38\n488 830 398 566 720 267 583 102 65 200 884 220 263 858 510 481 316 804 754 568 412 166 374 585 356 977 145 421 500 102 664 252 745 70 381 927 670 772\n",
"6\n109 128 214 392 678 2\n",
"97\n976 166 649 81 611 927 480 231 998 711 874 91 969 521 129 414 993 790 317 981 9 261 437 332 173 573 904 777 882 990 658 878 965 64 870 896 271 732 431 53 761 943 418 602 708 949 930 130 512 240 363 458 673 319 28 784 224 48 919 126 208 212 911 59 677 535 450 273 479 423 79 807 336 18 72 290 724 28 123 605 287 228 350 897 250 392 885 655 746 417 643 114 813 378 644 635 905\n",
"3\n467 918 90\n",
"4\n110 9 4 1\n",
"100\n901 902 903 904 905 906 907 908 909 695 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 1058 943 944 945 946 947 948 949 271 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000\n"
],
"output": [
"3.141592653589793\n",
"40.840704496667314\n",
"823521.3902487605\n",
"1495219.032327487\n",
"1556458.0979239128\n",
"1479184.3434235647\n",
"397266.9574170437\n",
"31.41592653589793\n",
"1615601.7212203941\n",
"1241695.6467754443\n",
"31111.19204849972\n",
"298608.3817237098\n",
"1419726.5608617242\n",
"3141592.653589793\n",
"1272941.9273080484\n",
"1780774.0965755312\n",
"895488.9947571954\n",
"172.78759594743863\n",
"1877274.398115849\n",
"1573959.9105970615\n",
"1741821.4892636712\n",
"2045673.1891262224\n",
"2042921.1539616778\n",
"1528494.78171431\n",
"1310703.8710041975\n",
"1258248.6984672088\n",
"1469640.1849419589\n",
"1818821.9252031571\n",
"113.09733552923255\n",
"298608.3817237098\n",
"431023.37047986605\n",
"1100144.9065826489\n",
"1567230.6191330722\n",
"1577239.7333274093\n",
"1447969.4788174964\n",
"1611115.526911068\n",
"1624269.3753516483\n",
"1510006.508947934\n",
"1686117.9099228706\n",
"1569819.2914796302\n",
"1597889.421839455\n",
"495517.1260654109\n",
"1806742.5014501044\n",
"1775109.8050211088\n",
"1383739.61701485\n",
"1436518.37359516\n",
"1587490.75015607\n",
"1937165.72046388\n",
"397380.05475257\n",
"9.42477796\n",
"1638196.05558501\n",
"2445613.64189147\n",
"37708.53662104\n",
"1325799.22370470\n",
"1431903.37398704\n",
"3204738.66592695\n",
"1358069.66344237\n",
"2498084.52239173\n",
"2249732.19834749\n",
"188.49555922\n",
"300823.20454449\n",
"6849356.85202423\n",
"1767717.63750721\n",
"5688321.59662970\n",
"1880701.87570092\n",
"7528079.09527639\n",
"1112051.54273975\n",
"1236942.41709056\n",
"1822249.40278822\n",
"2818608.65446688\n",
"141.37166941\n",
"321397.49483285\n",
"209230.07072908\n",
"1091803.97808737\n",
"4239579.28601943\n",
"1534313.01130876\n",
"6546315.68306631\n",
"1619004.06606423\n",
"4961429.31322006\n",
"1487949.38692708\n",
"1463652.30934422\n",
"1468430.67177033\n",
"1587123.18381560\n",
"310216.56657872\n",
"1843829.00272573\n",
"1644171.36481214\n",
"12.56637061\n",
"50.26548246\n",
"1493101.59887897\n",
"1808749.97915575\n",
"1616987.16358063\n",
"1919290.05826496\n",
"397568.55031179\n",
"40.84070450\n",
"1645311.76294539\n",
"2447300.67714645\n",
"37768.22688146\n",
"1700610.07683388\n",
"1400685.36778832\n",
"3211087.82467985\n",
"7888595.70183174\n",
"1809890.37728900\n",
"5486452.27748799\n",
"147.65485472\n",
"1929415.41138748\n",
"6470999.14078914\n",
"1290921.26206454\n",
"5730566.59304253\n",
"1290324.35946036\n",
"7349620.92458922\n",
"1145562.91157560\n",
"1142609.81448122\n",
"2055858.23250916\n",
"2913525.59330979\n",
"119.38052084\n",
"2556716.06608567\n",
"65210.03871056\n",
"3937254.40018652\n",
"4646946.46381776\n",
"1537517.43581542\n",
"5600925.63059949\n",
"1548676.37292097\n",
"2145704.64080917\n",
"1380981.29866500\n",
"1458028.85849429\n",
"1470237.08754614\n",
"1584342.87431718\n",
"210879.40687221\n",
"1838705.06510773\n",
"1471022.48570954\n",
"28.27433388\n",
"47.12388980\n",
"8003424.05491310\n",
"6718839.38523084\n",
"1743062.41836184\n",
"1131846.71805002\n",
"1091103.40292562\n",
"1510289.25228676\n",
"1987795.62766914\n",
"37805.92599330\n",
"1960089.92205713\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall.
Let us remind you that two circles are called concentric if their centers coincide. Several circles are called concentric if any two of them are concentric.
Input
The first line contains the single integer n (1 ≤ n ≤ 100). The second line contains n space-separated integers ri (1 ≤ ri ≤ 1000) — the circles' radii. It is guaranteed that all circles are different.
Output
Print the single real number — total area of the part of the wall that is painted red. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.
Examples
Input
1
1
Output
3.1415926536
Input
3
1 4 2
Output
40.8407044967
Note
In the first sample the picture is just one circle of radius 1. Inner part of the circle is painted red. The area of the red part equals π × 12 = π.
In the second sample there are three circles of radii 1, 4 and 2. Outside part of the second circle is painted blue. Part between the second and the third circles is painted red. Part between the first and the third is painted blue. And, finally, the inner part of the first circle is painted red. Overall there are two red parts: the ring between the second and the third circles and the inner part of the first circle. Total area of the red parts is equal (π × 42 - π × 22) + π × 12 = π × 12 + π = 13π
### Input:
1
1
### Output:
3.141592653589793
### Input:
3
1 4 2
### Output:
40.840704496667314
### Code:
n=int(input())
s=0
X=[int(x) for x in input().split(" ")]
X.sort(reverse=True)
for i in range(n):
s=s+(-1)**(i)*X[i]*X[i]
print(3.1415926536*s) |
178_A2. Educational Game_3099 | The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 ≤ n ≤ 300
The input limitations for getting 50 points are:
* 1 ≤ n ≤ 2000
The input limitations for getting 100 points are:
* 1 ≤ n ≤ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40 | from math import log
n=int(input())
s=list(map(int,input().split( )))
p=[]
for i in range(0,n-1):
m=(log(n-1-i,2))//1
p.append(i+2**m)
for k in range(1,n):
g=0
f=s[:]
for i in range(0,k):
g+=f[i]
f[int(p[i])]+=f[i]
print(g)
| {
"input": [
"8\n1 2 3 4 5 6 7 8\n",
"4\n1 0 1 2\n",
"9\n13 13 7 11 3 9 3 5 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 18 15 20 10 5 13 5 4 15 9 11 14 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n4 1 4 7 6\n",
"120\n242 524 420 973 816 432 247 666 134 849 145 366 608 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 789 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 490 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 134\n",
"9\n13 13 7 11 3 9 3 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 133 28 100 34 3 24 58 11 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 18 15 20 10 5 13 5 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n2 1 4 7 6\n",
"120\n242 524 420 973 816 432 247 666 134 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 789 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 490 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 134\n",
"8\n0 2 3 4 5 6 7 8\n",
"4\n1 0 0 2\n",
"9\n13 13 7 11 3 9 1 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 133 28 100 34 4 24 58 11 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 18 15 20 10 5 10 5 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n2 2 4 7 6\n",
"120\n242 524 420 973 816 432 247 666 134 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 789 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 134\n",
"9\n13 13 7 11 2 9 1 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 81 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 83 39 100 53 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 18 15 20 10 5 10 10 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n2 2 6 7 6\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 789 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 134\n",
"8\n0 4 3 4 5 6 7 1\n",
"9\n13 13 7 0 2 9 1 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 53 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 0 15 20 10 5 10 10 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n2 2 9 7 6\n",
"8\n0 4 3 4 5 6 6 1\n",
"9\n13 13 0 0 2 9 1 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 90 99 42 85 26 71 47 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 53 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 0 15 20 10 5 19 10 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"5\n2 0 9 7 6\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 4 3 6 6 1\n",
"9\n13 13 0 0 2 9 2 7 5\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 88 13 40 98 57 95 20 36 70 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 7 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 53 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 0 15 20 10 5 19 0 4 15 9 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 4 3 9 6 1\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 88 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 7 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 0 15 20 10 5 19 0 4 15 7 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 4 3 16 6 1\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 82 46 44 22 63 92 71 65 5 7 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 20 15 0 15 15 10 5 19 0 4 15 7 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 4 2 16 6 1\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 19 26 15 10 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 82 46 44 22 63 92 71 65 5 1 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 42 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 6 15 0 15 15 10 5 19 0 4 15 7 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 180 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 2 2 16 6 1\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 27 26 15 10 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 82 46 44 22 63 92 71 65 5 1 45 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 60 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 6 15 0 15 15 2 5 19 0 4 15 7 11 8 18 15 7 16 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 256 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 180 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n0 4 3 2 0 16 6 1\n",
"80\n72 66 82 46 44 22 63 92 71 65 5 30 45 84 29 73 9 90 25 45 26 15 10 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 82 46 44 22 63 92 71 65 5 1 14 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 60 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 6 15 0 15 15 2 5 19 0 4 15 7 11 8 18 15 7 29 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 256 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 180 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 149 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n1 4 3 2 0 16 6 1\n",
"80\n72 66 82 46 53 22 63 92 71 65 5 30 45 84 29 73 9 90 25 45 26 15 10 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 57 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 134 46 44 22 63 92 71 65 5 1 14 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 60 85 26 71 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 6 15 0 15 15 2 5 19 0 4 15 7 0 8 18 15 7 29 18 9 17 7 10 9 5 13 17 16\n",
"120\n242 524 420 973 816 432 247 666 94 849 256 366 1119 930 613 315 863 628 97 127 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 180 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 149 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n1 4 3 2 0 19 6 1\n",
"80\n72 66 82 46 53 22 63 92 71 65 5 30 45 84 29 73 9 90 25 45 26 15 10 29 33 19 85 92 91 66 83 39 100 53 20 99 11 83 26 41 36 51 21 133 28 100 34 4 24 58 17 85 73 18 4 45 88 99 42 85 26 71 47 49 76 32 84 13 40 98 95 95 20 36 88 66 75 12 54 96\n",
"80\n72 114 134 46 44 22 63 92 71 65 5 1 14 84 29 73 9 90 25 19 26 15 12 29 33 19 85 30 91 66 118 39 100 100 33 99 11 81 26 41 36 51 21 72 28 100 34 3 24 58 11 85 73 18 3 45 90 99 60 85 26 102 58 49 76 32 88 13 40 98 57 65 20 36 70 66 75 12 54 96\n",
"30\n8 17 6 15 0 15 15 2 5 19 0 4 15 7 0 8 18 15 7 29 18 9 12 7 10 9 5 13 17 16\n",
"120\n75 524 420 973 816 432 247 666 94 849 256 366 1119 930 613 315 863 628 97 127 65 704 741 314 736 17 872 971 559 410 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 617 893 23 249 116 220 699 863 580 992 861 393 98 253 544 171 336 180 348 496 316 285 286 727 613 616 304 811 592 916 91 554 1289 149 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n",
"8\n1 4 3 3 0 19 6 1\n",
"8\n0 2 3 4 5 6 7 1\n",
"4\n1 0 0 0\n",
"120\n242 524 420 973 816 432 247 666 94 849 145 366 1119 930 613 315 863 628 97 109 65 704 741 314 736 17 872 971 559 648 223 771 171 327 782 837 303 393 292 339 730 834 794 868 540 251 789 893 23 305 116 220 699 863 580 992 861 393 98 253 544 171 336 207 348 496 316 285 286 727 613 616 304 811 592 916 91 554 962 950 475 473 806 510 986 254 290 351 143 710 573 949 256 216 235 246 533 177 12 764 543 689 558 386 849 694 386 693 134 416 293 589 171 76 527 324 782 661 943 195\n"
],
"output": [
"1\n3\n6\n10\n16\n24\n40\n",
"1\n1\n3\n",
"13\n26\n33\n44\n47\n69\n79\n117\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1795\n1894\n1905\n1986\n2012\n2053\n2089\n2140\n2161\n2233\n2261\n2361\n2395\n2398\n2431\n2579\n2615\n2719\n2818\n2851\n2867\n2941\n3064\n3182\n3309\n3486\n3603\n3740\n3881\n3969\n4250\n4549\n4775\n5037\n5231\n5465\n5627\n5929\n6460\n7029\n7478\n8085\n9075\n10211\n12070\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1795\n1894\n1905\n1986\n2012\n2053\n2089\n2140\n2161\n2233\n2261\n2361\n2395\n2398\n2431\n2579\n2615\n2719\n2818\n2851\n2867\n2941\n3064\n3182\n3309\n3486\n3603\n3740\n3881\n3969\n4250\n4549\n4775\n5037\n5231\n5465\n5627\n5929\n6460\n7029\n7478\n8085\n9075\n10211\n12070\n",
"8\n25\n45\n60\n78\n93\n113\n123\n128\n141\n146\n150\n165\n174\n185\n199\n225\n257\n284\n315\n351\n375\n423\n454\n495\n549\n634\n713\n907\n",
"4\n5\n9\n17\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4454\n5303\n5448\n5814\n6422\n7352\n7965\n8280\n9143\n9771\n9868\n9977\n10042\n10746\n11487\n11801\n12537\n12554\n13426\n14397\n14956\n15604\n15827\n16598\n16769\n17096\n17878\n18715\n19018\n19411\n19703\n20042\n20772\n21606\n22400\n23268\n23808\n24059\n24848\n25741\n25764\n26069\n26185\n26405\n27104\n27967\n28547\n29539\n30400\n30793\n30891\n31144\n31688\n31859\n32195\n32402\n32992\n34012\n34748\n36006\n37108\n38267\n39127\n40409\n40847\n42507\n43244\n44526\n45225\n46709\n48284\n49549\n50887\n51988\n52891\n53510\n54561\n55519\n56550\n57215\n58955\n60075\n61618\n63791\n65150\n66185\n66979\n68203\n69497\n71021\n72551\n75410\n77358\n79599\n81241\n83248\n87005\n91313\n94773\n99789\n102521\n105707\n109158\n113129\n119712\n127026\n133562\n142600\n156395\n171618\n199596\n",
"13\n26\n33\n44\n47\n69\n79\n119\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1795\n1894\n1905\n1986\n2012\n2053\n2089\n2140\n2161\n2294\n2322\n2422\n2456\n2459\n2492\n2640\n2676\n2780\n2879\n2912\n2928\n3002\n3125\n3243\n3370\n3547\n3664\n3801\n3942\n4030\n4311\n4610\n4836\n5098\n5292\n5526\n5688\n5990\n6521\n7090\n7539\n8207\n9197\n10333\n12192\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1795\n1894\n1905\n1986\n2012\n2053\n2089\n2140\n2161\n2233\n2261\n2361\n2395\n2398\n2431\n2579\n2615\n2719\n2818\n2851\n2866\n2940\n3063\n3181\n3308\n3485\n3602\n3739\n3880\n3968\n4249\n4548\n4774\n5036\n5230\n5464\n5625\n5927\n6458\n7027\n7476\n8083\n9073\n10209\n12067\n",
"8\n25\n45\n60\n78\n93\n113\n123\n128\n141\n146\n150\n165\n174\n185\n193\n219\n251\n278\n309\n345\n369\n417\n442\n483\n537\n622\n695\n889\n",
"2\n3\n7\n15\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4454\n5303\n5448\n5814\n6933\n7863\n8476\n8791\n9654\n10282\n10379\n10488\n10553\n11257\n11998\n12312\n13048\n13065\n13937\n14908\n15467\n16115\n16338\n17109\n17280\n17607\n18389\n19226\n19529\n19922\n20214\n20553\n21283\n22117\n22911\n23779\n24319\n24570\n25359\n26252\n26275\n26580\n26696\n26916\n27615\n28478\n29058\n30050\n30911\n31304\n31402\n31655\n32199\n32370\n32706\n32913\n33503\n34523\n35259\n36517\n37619\n38778\n39638\n40920\n41358\n43018\n43755\n45037\n46247\n47731\n49306\n50571\n51909\n53010\n53913\n54532\n55583\n56541\n57572\n58237\n59977\n61097\n62640\n64813\n66172\n67207\n68001\n69225\n70519\n72043\n73573\n76432\n78380\n80621\n82263\n84270\n88027\n92335\n95795\n100811\n104054\n107240\n110691\n114662\n121245\n128559\n135095\n144133\n158439\n173662\n202151\n",
"0\n2\n5\n9\n14\n22\n37\n",
"1\n1\n2\n",
"13\n26\n33\n44\n47\n69\n77\n117\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1795\n1894\n1905\n1986\n2012\n2053\n2089\n2140\n2161\n2294\n2322\n2422\n2456\n2460\n2493\n2641\n2677\n2781\n2880\n2913\n2929\n3003\n3126\n3244\n3371\n3548\n3665\n3802\n3943\n4031\n4312\n4611\n4837\n5099\n5293\n5527\n5689\n5991\n6522\n7091\n7540\n8208\n9198\n10334\n12193\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1032\n1058\n1073\n1085\n1114\n1147\n1166\n1251\n1343\n1434\n1500\n1583\n1622\n1722\n1775\n1808\n1907\n1918\n1999\n2025\n2066\n2102\n2153\n2174\n2246\n2274\n2374\n2408\n2411\n2444\n2592\n2628\n2732\n2831\n2864\n2879\n2953\n3076\n3194\n3321\n3498\n3615\n3752\n3893\n3981\n4262\n4561\n4800\n5062\n5256\n5490\n5651\n5953\n6484\n7053\n7515\n8122\n9112\n10248\n12119\n",
"8\n25\n45\n60\n78\n93\n113\n123\n128\n138\n143\n147\n162\n171\n182\n190\n216\n248\n275\n306\n342\n366\n414\n439\n480\n531\n616\n689\n883\n",
"2\n4\n8\n17\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4454\n5303\n5448\n5814\n6933\n7863\n8476\n8791\n9654\n10282\n10379\n10488\n10553\n11257\n11998\n12312\n13048\n13065\n13937\n14908\n15467\n16115\n16338\n17109\n17280\n17607\n18389\n19226\n19529\n19922\n20214\n20553\n21283\n22117\n22911\n23779\n24319\n24570\n25359\n26252\n26275\n26580\n26696\n26916\n27615\n28478\n29058\n30050\n30911\n31304\n31402\n31655\n32199\n32370\n32706\n32913\n33503\n34523\n35259\n36517\n37619\n38778\n39638\n40920\n41358\n43018\n43755\n45037\n46247\n47731\n49306\n50571\n51909\n53010\n53913\n54532\n55583\n56541\n57572\n58237\n59977\n61097\n62640\n64813\n66172\n67207\n68001\n69225\n70519\n72043\n73573\n76432\n78380\n80621\n82331\n84338\n88095\n92403\n95863\n100879\n104122\n107308\n110759\n114730\n121313\n128627\n135163\n144201\n158507\n173730\n202287\n",
"13\n26\n33\n44\n46\n68\n76\n116\n",
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"2\n4\n10\n19\n",
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"0\n4\n7\n11\n16\n26\n41\n",
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"2\n4\n13\n22\n",
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"2\n2\n11\n18\n",
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"0\n4\n7\n11\n14\n27\n39\n",
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"72\n186\n268\n314\n358\n380\n443\n535\n606\n671\n676\n677\n722\n806\n835\n908\n917\n1007\n1032\n1051\n1077\n1092\n1104\n1133\n1166\n1185\n1270\n1300\n1391\n1457\n1575\n1614\n1714\n1814\n1847\n1946\n1957\n2038\n2064\n2105\n2141\n2192\n2213\n2285\n2313\n2413\n2447\n2450\n2483\n2631\n2667\n2771\n2870\n2903\n2918\n2992\n3115\n3233\n3360\n3475\n3592\n3729\n3905\n3993\n4274\n4668\n4907\n5169\n5363\n5597\n5758\n6030\n6561\n7225\n7687\n8203\n9193\n10424\n12330\n",
"8\n25\n31\n46\n46\n61\n76\n86\n91\n110\n110\n114\n129\n136\n147\n155\n181\n213\n226\n257\n275\n299\n342\n367\n408\n468\n529\n602\n754\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4414\n5263\n5408\n5774\n6893\n7823\n8436\n8751\n9614\n10242\n10339\n10448\n10513\n11217\n11958\n12272\n13008\n13025\n13897\n14868\n15427\n15837\n16060\n16831\n17002\n17329\n18111\n18948\n19251\n19644\n19936\n20275\n21005\n21839\n22633\n23501\n24041\n24292\n24909\n25802\n25825\n26074\n26190\n26410\n27109\n27972\n28552\n29544\n30405\n30798\n30896\n31149\n31693\n31864\n32200\n32380\n32970\n33990\n34726\n35984\n37086\n38245\n39105\n40387\n40785\n42445\n43182\n44464\n45674\n47158\n49060\n50325\n51663\n52764\n53667\n54286\n55337\n56295\n57326\n57991\n59731\n60851\n62394\n64567\n65926\n66723\n67517\n68714\n70008\n71532\n73062\n75921\n77869\n80110\n81820\n83827\n87544\n91852\n95312\n100328\n103571\n106519\n110125\n114069\n120612\n127870\n134406\n143444\n157710\n172639\n201311\n",
"0\n4\n7\n9\n11\n31\n42\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1040\n1066\n1081\n1091\n1120\n1153\n1172\n1257\n1349\n1440\n1506\n1589\n1628\n1728\n1781\n1801\n1900\n1911\n1994\n2020\n2061\n2097\n2148\n2169\n2302\n2330\n2430\n2464\n2468\n2501\n2649\n2691\n2803\n2902\n2935\n2949\n3023\n3144\n3262\n3389\n3566\n3683\n3820\n3950\n4038\n4319\n4618\n4846\n5116\n5310\n5546\n5706\n6008\n6537\n7106\n7575\n8251\n9239\n10377\n12241\n",
"72\n186\n268\n314\n358\n380\n443\n535\n606\n671\n676\n677\n722\n806\n835\n908\n917\n1007\n1032\n1051\n1077\n1092\n1104\n1133\n1166\n1185\n1270\n1300\n1391\n1457\n1575\n1614\n1714\n1814\n1847\n1946\n1957\n2038\n2064\n2105\n2141\n2192\n2213\n2285\n2313\n2413\n2447\n2450\n2483\n2631\n2667\n2771\n2870\n2903\n2918\n2992\n3115\n3233\n3378\n3493\n3610\n3747\n3923\n4011\n4292\n4686\n4925\n5187\n5381\n5615\n5776\n6048\n6579\n7243\n7723\n8239\n9229\n10460\n12384\n",
"8\n25\n31\n46\n46\n61\n76\n78\n83\n102\n102\n106\n121\n128\n139\n147\n173\n205\n218\n249\n267\n291\n334\n351\n392\n452\n513\n578\n730\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4414\n5263\n5519\n5885\n7004\n7934\n8547\n8862\n9725\n10353\n10450\n10559\n10624\n11328\n12069\n12383\n13119\n13136\n14008\n14979\n15538\n15948\n16171\n16942\n17113\n17440\n18222\n19059\n19362\n19755\n20047\n20386\n21116\n21950\n22744\n23612\n24152\n24403\n25020\n25913\n25936\n26185\n26301\n26521\n27220\n28083\n28663\n29655\n30516\n30909\n31007\n31260\n31804\n31975\n32311\n32491\n33081\n34101\n34837\n36095\n37197\n38356\n39216\n40498\n40896\n42556\n43404\n44686\n45896\n47380\n49282\n50547\n51885\n52986\n53889\n54508\n55559\n56517\n57548\n58213\n59953\n61073\n62616\n64789\n66148\n66945\n67739\n68936\n70230\n71754\n73284\n76143\n78091\n80332\n82042\n84049\n87766\n92074\n95645\n100661\n103904\n106852\n110458\n114402\n120945\n128203\n134850\n143888\n158154\n173083\n201866\n",
"0\n4\n7\n9\n9\n29\n38\n",
"72\n138\n220\n266\n310\n332\n395\n487\n558\n623\n628\n658\n703\n787\n816\n889\n898\n988\n1013\n1058\n1084\n1099\n1109\n1138\n1171\n1190\n1275\n1367\n1458\n1524\n1607\n1646\n1746\n1799\n1819\n1918\n1929\n2012\n2038\n2079\n2115\n2166\n2187\n2320\n2348\n2448\n2482\n2486\n2519\n2667\n2709\n2839\n2938\n2971\n2985\n3059\n3180\n3298\n3425\n3602\n3719\n3856\n3986\n4074\n4355\n4654\n4882\n5170\n5364\n5600\n5760\n6062\n6591\n7160\n7629\n8323\n9311\n10449\n12313\n",
"72\n186\n268\n314\n358\n380\n443\n535\n606\n671\n676\n677\n691\n775\n804\n877\n886\n976\n1001\n1020\n1046\n1061\n1073\n1102\n1135\n1154\n1239\n1269\n1360\n1426\n1544\n1583\n1683\n1783\n1816\n1915\n1926\n2007\n2033\n2074\n2110\n2161\n2182\n2254\n2282\n2382\n2416\n2419\n2452\n2600\n2636\n2740\n2839\n2872\n2887\n2961\n3084\n3202\n3347\n3462\n3579\n3716\n3892\n3980\n4261\n4655\n4894\n5156\n5350\n5584\n5745\n6017\n6548\n7212\n7692\n8208\n9167\n10398\n12291\n",
"8\n25\n31\n46\n46\n61\n76\n78\n83\n102\n102\n106\n121\n128\n139\n147\n173\n205\n218\n262\n280\n304\n347\n364\n405\n465\n526\n604\n756\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4414\n5263\n5519\n5885\n7004\n7934\n8547\n8862\n9725\n10353\n10450\n10559\n10624\n11328\n12069\n12383\n13119\n13136\n14008\n14979\n15538\n15948\n16171\n16942\n17113\n17440\n18222\n19059\n19362\n19755\n20047\n20386\n21116\n21950\n22744\n23612\n24152\n24403\n25020\n25913\n25936\n26185\n26301\n26521\n27220\n28083\n28663\n29655\n30516\n30909\n31007\n31260\n31804\n31975\n32311\n32491\n33081\n34101\n34837\n36095\n37197\n38356\n39216\n40498\n40896\n42556\n43404\n44686\n45896\n47380\n49282\n49746\n51084\n52185\n53088\n53707\n54758\n55716\n56747\n57412\n59152\n60272\n61815\n63988\n65347\n66144\n66938\n68135\n69429\n70953\n72483\n75342\n77290\n79531\n81241\n83248\n86965\n91273\n94844\n99860\n103103\n106051\n109657\n112800\n119343\n126601\n133248\n142286\n156552\n171481\n200264\n",
"1\n5\n8\n10\n11\n31\n41\n",
"72\n138\n220\n266\n319\n341\n404\n496\n567\n632\n637\n667\n712\n796\n825\n898\n907\n997\n1022\n1067\n1093\n1108\n1118\n1147\n1180\n1199\n1284\n1376\n1467\n1533\n1616\n1655\n1755\n1808\n1828\n1927\n1938\n2021\n2047\n2088\n2124\n2175\n2196\n2329\n2357\n2457\n2491\n2495\n2528\n2676\n2718\n2848\n2947\n2980\n2994\n3068\n3189\n3307\n3434\n3611\n3728\n3865\n3995\n4083\n4364\n4663\n4891\n5179\n5382\n5618\n5778\n6080\n6609\n7178\n7647\n8341\n9338\n10476\n12349\n",
"72\n186\n320\n366\n410\n432\n495\n587\n658\n723\n728\n729\n743\n827\n856\n929\n938\n1028\n1053\n1072\n1098\n1113\n1125\n1154\n1187\n1206\n1291\n1321\n1412\n1478\n1596\n1635\n1735\n1835\n1868\n1967\n1978\n2059\n2085\n2126\n2162\n2213\n2234\n2306\n2334\n2434\n2468\n2471\n2504\n2652\n2688\n2792\n2891\n2924\n2939\n3013\n3136\n3254\n3399\n3514\n3631\n3768\n3944\n4032\n4313\n4707\n4998\n5260\n5454\n5688\n5849\n6121\n6652\n7316\n7848\n8364\n9323\n10554\n12499\n",
"8\n25\n31\n46\n46\n61\n76\n78\n83\n102\n102\n106\n121\n128\n128\n136\n162\n194\n207\n251\n269\n293\n325\n342\n383\n443\n493\n571\n712\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4414\n5263\n5519\n5885\n7004\n7934\n8547\n8862\n9725\n10353\n10450\n10577\n10642\n11346\n12087\n12401\n13137\n13154\n14026\n14997\n15556\n15966\n16189\n16960\n17131\n17458\n18240\n19077\n19380\n19773\n20065\n20404\n21134\n21968\n22762\n23630\n24170\n24421\n25038\n25931\n25954\n26203\n26319\n26539\n27238\n28101\n28681\n29673\n30534\n30927\n31025\n31278\n31822\n31993\n32329\n32509\n33099\n34119\n34855\n36113\n37215\n38374\n39234\n40516\n40914\n42574\n43422\n44704\n45914\n47398\n49300\n49764\n51102\n52203\n53106\n53743\n54794\n55752\n56783\n57448\n59188\n60308\n61851\n64024\n65383\n66180\n66974\n68171\n69465\n70989\n72519\n75378\n77326\n79567\n81277\n83284\n87001\n91309\n94880\n99896\n103139\n106087\n109693\n112836\n119379\n126637\n133284\n142340\n156606\n171535\n200318\n",
"1\n5\n8\n10\n11\n34\n44\n",
"72\n138\n220\n266\n319\n341\n404\n496\n567\n632\n637\n667\n712\n796\n825\n898\n907\n997\n1022\n1067\n1093\n1108\n1118\n1147\n1180\n1199\n1284\n1376\n1467\n1533\n1616\n1655\n1755\n1808\n1828\n1927\n1938\n2021\n2047\n2088\n2124\n2175\n2196\n2329\n2357\n2457\n2491\n2495\n2528\n2676\n2718\n2848\n2947\n2980\n2994\n3068\n3189\n3307\n3434\n3611\n3728\n3865\n3995\n4083\n4364\n4663\n4891\n5179\n5382\n5618\n5816\n6118\n6647\n7216\n7685\n8379\n9376\n10514\n12425\n",
"72\n186\n320\n366\n410\n432\n495\n587\n658\n723\n728\n729\n743\n827\n856\n929\n938\n1028\n1053\n1072\n1098\n1113\n1125\n1154\n1187\n1206\n1291\n1321\n1412\n1478\n1596\n1635\n1735\n1835\n1868\n1967\n1978\n2059\n2085\n2126\n2162\n2213\n2234\n2306\n2334\n2434\n2468\n2471\n2504\n2652\n2688\n2792\n2891\n2924\n2939\n3013\n3136\n3254\n3399\n3514\n3631\n3799\n3975\n4063\n4344\n4738\n5029\n5291\n5485\n5719\n5880\n6152\n6683\n7347\n7879\n8395\n9354\n10616\n12561\n",
"8\n25\n31\n46\n46\n61\n76\n78\n83\n102\n102\n106\n121\n128\n128\n136\n162\n194\n207\n251\n269\n293\n320\n337\n378\n438\n483\n561\n697\n",
"75\n599\n1019\n1992\n2808\n3240\n3487\n4153\n4247\n5096\n5352\n5718\n6837\n7767\n8380\n8695\n9558\n10186\n10283\n10410\n10475\n11179\n11920\n12234\n12970\n12987\n13859\n14830\n15389\n15799\n16022\n16793\n16964\n17291\n18073\n18910\n19213\n19606\n19898\n20237\n20967\n21801\n22595\n23463\n24003\n24254\n24871\n25764\n25787\n26036\n26152\n26372\n27071\n27934\n28514\n29506\n30367\n30760\n30858\n31111\n31655\n31826\n32162\n32342\n32765\n33785\n34521\n35779\n36881\n38040\n38900\n40182\n40580\n42240\n43088\n44370\n45580\n47064\n48966\n49430\n50768\n51869\n52772\n53409\n54460\n55418\n56449\n57114\n58854\n59974\n61517\n63690\n65049\n65846\n66640\n67837\n68964\n70488\n72018\n74877\n76825\n79066\n80776\n82783\n86500\n90808\n94379\n99395\n102638\n105586\n109192\n112335\n118711\n125969\n132616\n141672\n155771\n170700\n199316\n",
"1\n5\n8\n11\n12\n35\n45\n",
"0\n2\n5\n9\n14\n22\n37\n",
"1\n1\n2\n",
"242\n766\n1186\n2159\n2975\n3407\n3654\n4320\n4414\n5263\n5408\n5774\n6893\n7823\n8436\n8751\n9614\n10242\n10339\n10448\n10513\n11217\n11958\n12272\n13008\n13025\n13897\n14868\n15427\n16075\n16298\n17069\n17240\n17567\n18349\n19186\n19489\n19882\n20174\n20513\n21243\n22077\n22871\n23739\n24279\n24530\n25319\n26212\n26235\n26540\n26656\n26876\n27575\n28438\n29018\n30010\n30871\n31264\n31362\n31615\n32159\n32330\n32666\n32873\n33463\n34483\n35219\n36477\n37579\n38738\n39598\n40880\n41278\n42938\n43675\n44957\n46167\n47651\n49226\n50491\n51829\n52930\n53833\n54452\n55503\n56461\n57492\n58157\n59897\n61017\n62560\n64733\n66092\n67127\n67921\n69145\n70439\n71963\n73493\n76352\n78300\n80541\n82251\n84258\n87975\n92283\n95743\n100759\n104002\n107188\n110639\n114610\n121153\n128467\n135003\n144041\n158307\n173530\n202047\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.
The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.
One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).
You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).
Input
The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.
The input limitations for getting 20 points are:
* 1 ≤ n ≤ 300
The input limitations for getting 50 points are:
* 1 ≤ n ≤ 2000
The input limitations for getting 100 points are:
* 1 ≤ n ≤ 105
Output
Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
4
1 0 1 2
Output
1
1
3
Input
8
1 2 3 4 5 6 7 8
Output
1
3
6
10
16
24
40
### Input:
8
1 2 3 4 5 6 7 8
### Output:
1
3
6
10
16
24
40
### Input:
4
1 0 1 2
### Output:
1
1
3
### Code:
from math import log
n=int(input())
s=list(map(int,input().split( )))
p=[]
for i in range(0,n-1):
m=(log(n-1-i,2))//1
p.append(i+2**m)
for k in range(1,n):
g=0
f=s[:]
for i in range(0,k):
g+=f[i]
f[int(p[i])]+=f[i]
print(g)
|
19_C. Deletion of Repeats_3102 | Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat.
You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above.
Input
The first input line contains integer n (1 ≤ n ≤ 105) — length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive — numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times.
Output
In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way.
Examples
Input
6
1 2 3 1 2 3
Output
3
1 2 3
Input
7
4 5 6 5 6 7 7
Output
1
7 | def pow(x, exp, mod):
res = 1
while exp:
if exp & 1:
res = (res * x) % mod
x = (x * x) % mod
exp >>= 1
return res
MOD = 2 ** 121 - 1
M = int(1e9) + 1
n = int(input())
vals = list(map(int, input().split()))
groups = dict()
for i in range(n):
groups.setdefault(vals[i], []).append(i)
powsA = [1]
for i in range(n):
powsA.append((powsA[-1] * M) % MOD)
hashes = [0] * (n + 1)
for i in range(n):
hashes[i + 1] = (hashes[i] * M + vals[i]) % MOD
def get_hash(p, l):
res = hashes[p + l] - (hashes[p] * powsA[l]) % MOD
if res < 0:
res += MOD
elif res > MOD:
res -= MOD
return res
best = 0
i = 0
while i < n:
val = vals[i]
for j in groups[val]:
if j <= i:
continue
l = j - i
if j + l <= n and get_hash(i, l) == get_hash(j, l):
best = max(best, j)
i = j - 1
break
i += 1
res = vals[best:]
print(len(res))
print(" ".join(map(str, res))) | {
"input": [
"6\n1 2 3 1 2 3\n",
"7\n4 5 6 5 6 7 7\n",
"100\n8 43 55 27 70 81 66 10 49 67 24 61 53 0 2 76 96 16 16 1 78 1 69 69 4 59 6 87 98 14 98 20 12 48 20 41 67 90 20 96 44 8 77 94 84 2 61 27 90 42 66 84 5 19 68 13 5 53 13 87 70 41 48 40 19 61 72 31 4 4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"1\n0\n",
"100\n19 17 16 6 4 13 7 12 4 16 2 2 12 15 20 17 3 13 14 2 4 20 14 10 11 17 7 17 12 18 17 14 10 16 20 16 19 12 9 15 2 13 5 6 9 3 14 6 20 3 15 16 0 12 5 11 3 19 5 2 11 18 20 20 11 4 1 10 20 10 19 0 4 10 1 11 4 11 8 19 3 14 6 1 14 2 13 20 8 3 19 19 6 19 19 20 20 8 13 14\n",
"3\n1000000000 1000000000 1000000000\n",
"20\n0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1\n",
"10\n0 1 1 1 0 3 0 1 4 0\n",
"10\n5 7 2 1 8 8 5 10 2 5\n",
"10\n1 2 1 2 1 2 1 2 1 2\n",
"7\n1 2 3 1 2 3 1\n",
"2\n1000000000 1000000000\n",
"30\n17 17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 5 11 25 1 16 6 11 22 19 2 12 16\n",
"30\n0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2\n",
"10\n1 2 3 4 5 1 2 3 4 5\n",
"100\n5 4 8 2 4 7 6 6 9 0 5 9 9 8 2 1 10 7 1 0 0 6 3 5 3 7 8 0 0 10 6 7 10 5 4 10 7 6 7 5 1 5 0 10 3 10 5 7 4 10 0 9 1 2 6 3 3 6 10 6 9 1 6 3 4 6 2 8 8 9 5 2 3 3 10 7 4 1 10 1 8 5 4 3 2 2 0 4 4 1 4 5 7 2 8 7 1 1 2 8\n",
"10\n1 1 1 1 1 1 1 1 1 1\n",
"22\n823078040 389511796 683819000 823078040 389511796 683819000 823078040 389511796 683819000 823078040 389511796 683819000 823078040 389511796 683819000 823078040 389511796 683819000 823078040 389511796 683819000 823078040\n",
"4\n1000000000 1000000000 1000000000 1000000000\n",
"10\n0 1 0 2 0 0 1 1 1 0\n",
"21\n16417014 805849548 385039296 16417014 805849548 385039296 16417014 805849548 385039296 16417014 805849548 385039296 16417014 805849548 385039296 16417014 805849548 385039296 16417014 805849548 385039296\n",
"10\n0 0 0 0 0 0 0 0 0 0\n",
"23\n482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044 835115058 482255418 973174044\n",
"2\n1 2\n",
"100\n8 43 55 27 70 81 66 10 49 67 24 61 53 0 2 76 96 16 16 1 78 1 69 69 4 59 6 87 98 14 98 20 12 48 20 41 67 90 20 96 44 8 77 94 84 2 61 27 90 42 66 84 5 19 68 13 5 53 13 54 70 41 48 40 19 61 72 31 4 4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"100\n19 17 16 6 4 13 7 12 4 16 2 2 12 15 20 17 3 13 14 2 4 20 14 10 11 17 7 17 12 18 17 14 10 16 20 16 19 12 9 15 2 13 5 6 9 4 14 6 20 3 15 16 0 12 5 11 3 19 5 2 11 18 20 20 11 4 1 10 20 10 19 0 4 10 1 11 4 11 8 19 3 14 6 1 14 2 13 20 8 3 19 19 6 19 19 20 20 8 13 14\n",
"20\n0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1\n",
"10\n0 1 2 1 0 3 0 1 4 0\n",
"10\n5 7 2 1 8 8 6 10 2 5\n",
"10\n1 2 1 2 1 2 1 2 1 3\n",
"2\n1000000010 1000000000\n",
"30\n17 17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 5 11 25 1 16 7 11 22 19 2 12 16\n",
"30\n0 0 0 0 -1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2\n",
"4\n1000000000 1000000000 1000000000 1010000000\n",
"10\n1 1 0 2 0 0 1 1 1 0\n",
"10\n0 1 0 0 0 0 0 0 0 0\n",
"7\n4 5 6 5 6 5 7\n",
"10\n0 1 2 1 0 2 0 1 4 0\n",
"2\n1010000010 1000000000\n",
"30\n17 17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 1 11 25 1 16 7 11 22 19 2 12 16\n",
"2\n4 2\n",
"7\n4 5 6 5 9 5 7\n",
"10\n1 2 1 2 1 1 1 3 1 3\n",
"2\n1010000010 1100000000\n",
"30\n17 17 2 4 19 21 17 11 15 0 9 2 23 10 24 21 23 17 1 11 25 1 16 7 11 22 19 2 12 16\n",
"10\n1 1 1 2 1 1 1 1 1 1\n",
"2\n2 2\n",
"100\n8 43 55 27 70 81 66 10 49 67 24 61 53 0 2 76 96 16 16 1 78 1 69 69 4 59 6 87 98 14 98 20 12 48 20 41 67 90 20 96 44 8 77 94 84 2 61 27 90 42 66 84 5 19 68 13 5 53 13 54 70 41 48 40 19 59 72 31 4 4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"100\n19 17 16 6 4 13 7 12 4 16 2 2 12 15 20 17 3 13 14 2 4 20 14 10 11 17 7 17 12 18 17 14 10 16 20 16 19 12 9 3 2 13 5 6 9 4 14 6 20 3 15 16 0 12 5 11 3 19 5 2 11 18 20 20 11 4 1 10 20 10 19 0 4 10 1 11 4 11 8 19 3 14 6 1 14 2 13 20 8 3 19 19 6 19 19 20 20 8 13 14\n",
"10\n5 10 2 1 8 8 6 10 2 5\n",
"10\n1 2 1 2 1 1 1 2 1 3\n",
"30\n0 0 0 0 -2 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2\n",
"10\n1 0 1 2 1 1 1 1 1 1\n",
"10\n2 1 0 2 0 0 1 1 1 0\n",
"10\n0 1 0 0 0 0 -1 0 0 0\n",
"100\n8 43 55 27 70 81 66 10 49 67 24 61 53 0 2 76 96 16 16 1 78 1 69 69 4 59 6 87 98 14 98 20 12 48 20 41 67 90 20 96 44 8 77 94 84 2 61 27 90 42 66 84 5 19 68 13 5 53 13 54 70 41 71 40 19 59 72 31 4 4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"100\n19 17 16 6 4 13 7 12 4 16 2 2 12 15 20 17 3 13 14 2 4 20 14 10 11 17 7 17 12 18 17 14 10 16 20 16 19 12 9 3 2 13 5 6 9 4 14 6 20 3 15 16 0 12 5 11 3 19 5 2 11 18 20 29 11 4 1 10 20 10 19 0 4 10 1 11 4 11 8 19 3 14 6 1 14 2 13 20 8 3 19 19 6 19 19 20 20 8 13 14\n",
"10\n5 11 2 1 8 8 6 10 2 5\n",
"30\n0 0 0 0 -2 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\n",
"10\n0 0 1 2 1 1 1 1 1 1\n"
],
"output": [
"3\n1 2 3 ",
"1\n7 ",
"31\n4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78 ",
"1\n0 ",
"4\n20 8 13 14 ",
"1\n1000000000 ",
"1\n1 ",
"7\n1 0 3 0 1 4 0 ",
"5\n8 5 10 2 5 ",
"2\n1 2 ",
"4\n1 2 3 1 ",
"1\n1000000000 ",
"29\n17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 5 11 25 1 16 6 11 22 19 2 12 16 ",
"1\n2 ",
"5\n1 2 3 4 5 ",
"3\n1 2 8 ",
"1\n1 ",
"4\n823078040 389511796 683819000 823078040 ",
"1\n1000000000 ",
"2\n1 0 ",
"3\n16417014 805849548 385039296 ",
"1\n0 ",
"5\n482255418 973174044 835115058 482255418 973174044 ",
"2\n1 2 ",
"31\n4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"4\n20 8 13 14\n",
"1\n1\n",
"10\n0 1 2 1 0 3 0 1 4 0\n",
"5\n8 6 10 2 5\n",
"4\n1 2 1 3\n",
"2\n1000000010 1000000000\n",
"29\n17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 5 11 25 1 16 7 11 22 19 2 12 16\n",
"1\n2\n",
"2\n1000000000 1010000000\n",
"2\n1 0\n",
"1\n0\n",
"4\n5 6 5 7\n",
"10\n0 1 2 1 0 2 0 1 4 0\n",
"2\n1010000010 1000000000\n",
"29\n17 2 4 13 21 17 11 15 0 9 2 23 10 24 21 23 17 1 11 25 1 16 7 11 22 19 2 12 16\n",
"2\n4 2\n",
"7\n4 5 6 5 9 5 7\n",
"2\n1 3\n",
"2\n1010000010 1100000000\n",
"29\n17 2 4 19 21 17 11 15 0 9 2 23 10 24 21 23 17 1 11 25 1 16 7 11 22 19 2 12 16\n",
"1\n1\n",
"1\n2\n",
"31\n4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"4\n20 8 13 14\n",
"5\n8 6 10 2 5\n",
"4\n1 2 1 3\n",
"1\n2\n",
"1\n1\n",
"2\n1 0\n",
"1\n0\n",
"31\n4 59 100 50 64 84 10 96 16 73 3 63 85 67 91 74 63 22 34 6 96 78 42 61 85 3 95 98 84 66 78\n",
"4\n20 8 13 14\n",
"5\n8 6 10 2 5\n",
"1\n2\n",
"1\n1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Once Bob saw a string. It contained so many different letters, that the letters were marked by numbers, but at the same time each letter could be met in the string at most 10 times. Bob didn't like that string, because it contained repeats: a repeat of length x is such a substring of length 2x, that its first half coincides character by character with its second half. Bob started deleting all the repeats from the string. He does it as follows: while it's possible, Bob takes the shortest repeat, if it is not unique, he takes the leftmost one, and deletes its left half and everything that is to the left of this repeat.
You're given the string seen by Bob. Find out, what it will look like after Bob deletes all the repeats in the way described above.
Input
The first input line contains integer n (1 ≤ n ≤ 105) — length of the string. The following line contains n space-separated integer numbers from 0 to 109 inclusive — numbers that stand for the letters of the string. It's guaranteed that each letter can be met in the string at most 10 times.
Output
In the first line output the length of the string's part, left after Bob's deletions. In the second line output all the letters (separated by a space) of the string, left after Bob deleted all the repeats in the described way.
Examples
Input
6
1 2 3 1 2 3
Output
3
1 2 3
Input
7
4 5 6 5 6 7 7
Output
1
7
### Input:
6
1 2 3 1 2 3
### Output:
3
1 2 3
### Input:
7
4 5 6 5 6 7 7
### Output:
1
7
### Code:
def pow(x, exp, mod):
res = 1
while exp:
if exp & 1:
res = (res * x) % mod
x = (x * x) % mod
exp >>= 1
return res
MOD = 2 ** 121 - 1
M = int(1e9) + 1
n = int(input())
vals = list(map(int, input().split()))
groups = dict()
for i in range(n):
groups.setdefault(vals[i], []).append(i)
powsA = [1]
for i in range(n):
powsA.append((powsA[-1] * M) % MOD)
hashes = [0] * (n + 1)
for i in range(n):
hashes[i + 1] = (hashes[i] * M + vals[i]) % MOD
def get_hash(p, l):
res = hashes[p + l] - (hashes[p] * powsA[l]) % MOD
if res < 0:
res += MOD
elif res > MOD:
res -= MOD
return res
best = 0
i = 0
while i < n:
val = vals[i]
for j in groups[val]:
if j <= i:
continue
l = j - i
if j + l <= n and get_hash(i, l) == get_hash(j, l):
best = max(best, j)
i = j - 1
break
i += 1
res = vals[best:]
print(len(res))
print(" ".join(map(str, res))) |
248_B. Chilly Willy_3108 | Chilly Willy loves playing with numbers. He only knows prime numbers that are digits yet. These numbers are 2, 3, 5 and 7. But Willy grew rather bored of such numbers, so he came up with a few games that were connected with them.
Chilly Willy wants to find the minimum number of length n, such that it is simultaneously divisible by all numbers Willy already knows (2, 3, 5 and 7). Help him with that.
A number's length is the number of digits in its decimal representation without leading zeros.
Input
A single input line contains a single integer n (1 ≤ n ≤ 105).
Output
Print a single integer — the answer to the problem without leading zeroes, or "-1" (without the quotes), if the number that meet the problem condition does not exist.
Examples
Input
1
Output
-1
Input
5
Output
10080 | n = int(input())
if n < 3:
print(-1)
else:
t = 10**(n-1)
print(t+210-t%210)
| {
"input": [
"5\n",
"1\n",
"99996\n",
"99999\n",
"88888\n",
"99987\n",
"7\n",
"99987\n",
"21\n",
"31\n",
"13\n",
"99995\n",
"123\n",
"5000\n",
"20\n",
"10\n",
"45332\n",
"14\n",
"8\n",
"33\n",
"9\n",
"8824\n",
"27324\n",
"18\n",
"99990\n",
"5000\n",
"19\n",
"12398\n",
"10000\n",
"17\n",
"45332\n",
"99988\n",
"99993\n",
"10000\n",
"1000\n",
"99991\n",
"5001\n",
"2\n",
"1000\n",
"5001\n",
"99990\n",
"99993\n",
"8824\n",
"5522\n",
"77777\n",
"99986\n",
"55553\n",
"12398\n",
"55553\n",
"11\n",
"99994\n",
"23\n",
"27324\n",
"66666\n",
"88888\n",
"16\n",
"9003\n",
"99995\n",
"4\n",
"77777\n",
"99999\n",
"5522\n",
"99988\n",
"99997\n",
"66666\n",
"5002\n",
"99989\n",
"9003\n",
"25\n",
"99996\n",
"5002\n",
"2345\n",
"99998\n",
"2345\n",
"99986\n",
"99989\n",
"100000\n",
"34532\n",
"99992\n",
"12\n",
"99998\n",
"24\n",
"22\n",
"34532\n",
"99994\n",
"100000\n",
"15\n",
"65\n",
"122\n",
"6\n",
"99991\n",
"120\n",
"3\n",
"99997\n",
"99992\n",
"121\n",
"44821\n",
"427\n",
"62236\n",
"46\n",
"74452\n",
"100\n",
"5027\n",
"29\n",
"73715\n",
"6050\n",
"15637\n",
"30\n",
"65590\n",
"2361\n",
"7079\n",
"10001\n",
"28\n",
"82349\n",
"76187\n",
"13906\n",
"10100\n",
"1001\n",
"3873\n",
"1010\n",
"9166\n",
"54546\n",
"3917\n",
"257\n",
"61617\n",
"18596\n",
"45677\n",
"15985\n",
"28156\n",
"27\n",
"15794\n",
"39755\n",
"45\n",
"15746\n",
"667\n",
"10567\n",
"3830\n",
"11620\n",
"21090\n",
"9599\n",
"1632\n",
"9241\n",
"1337\n",
"2338\n",
"60231\n",
"63632\n",
"36\n",
"49645\n",
"43\n",
"112\n",
"107\n",
"49\n",
"63853\n",
"147\n",
"50184\n",
"150\n",
"19894\n",
"641\n",
"64265\n",
"47\n",
"24879\n",
"110\n",
"1169\n",
"55\n",
"79954\n",
"2507\n",
"2369\n",
"34\n",
"9957\n",
"2721\n",
"4639\n",
"10011\n",
"53\n",
"5347\n",
"14278\n",
"0001\n",
"7385\n",
"1110\n",
"13950\n",
"73457\n",
"2077\n",
"67\n",
"87693\n",
"21133\n",
"35785\n",
"15926\n",
"40056\n",
"6300\n",
"726\n",
"83\n",
"21553\n",
"804\n",
"20276\n",
"1354\n",
"3924\n",
"00100\n"
],
"output": [
"10080\n",
"-1\n",
"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000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]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Chilly Willy loves playing with numbers. He only knows prime numbers that are digits yet. These numbers are 2, 3, 5 and 7. But Willy grew rather bored of such numbers, so he came up with a few games that were connected with them.
Chilly Willy wants to find the minimum number of length n, such that it is simultaneously divisible by all numbers Willy already knows (2, 3, 5 and 7). Help him with that.
A number's length is the number of digits in its decimal representation without leading zeros.
Input
A single input line contains a single integer n (1 ≤ n ≤ 105).
Output
Print a single integer — the answer to the problem without leading zeroes, or "-1" (without the quotes), if the number that meet the problem condition does not exist.
Examples
Input
1
Output
-1
Input
5
Output
10080
### Input:
5
### Output:
10080
### Input:
1
### Output:
-1
### Code:
n = int(input())
if n < 3:
print(-1)
else:
t = 10**(n-1)
print(t+210-t%210)
|
272_C. Dima and Staircase_3112 | Dima's got a staircase that consists of n stairs. The first stair is at height a1, the second one is at a2, the last one is at an (1 ≤ a1 ≤ a2 ≤ ... ≤ an).
Dima decided to play with the staircase, so he is throwing rectangular boxes at the staircase from above. The i-th box has width wi and height hi. Dima throws each box vertically down on the first wi stairs of the staircase, that is, the box covers stairs with numbers 1, 2, ..., wi. Each thrown box flies vertically down until at least one of the two following events happen:
* the bottom of the box touches the top of a stair;
* the bottom of the box touches the top of a box, thrown earlier.
We only consider touching of the horizontal sides of stairs and boxes, at that touching with the corners isn't taken into consideration. Specifically, that implies that a box with width wi cannot touch the stair number wi + 1.
You are given the description of the staircase and the sequence in which Dima threw the boxes at it. For each box, determine how high the bottom of the box after landing will be. Consider a box to fall after the previous one lands.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of stairs in the staircase. The second line contains a non-decreasing sequence, consisting of n integers, a1, a2, ..., an (1 ≤ ai ≤ 109; ai ≤ ai + 1).
The next line contains integer m (1 ≤ m ≤ 105) — the number of boxes. Each of the following m lines contains a pair of integers wi, hi (1 ≤ wi ≤ n; 1 ≤ hi ≤ 109) — the size of the i-th thrown box.
The numbers in the lines are separated by spaces.
Output
Print m integers — for each box the height, where the bottom of the box will be after landing. Print the answers for the boxes in the order, in which the boxes are given in the input.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
5
1 2 3 6 6
4
1 1
3 1
1 1
4 3
Output
1
3
4
6
Input
3
1 2 3
2
1 1
3 1
Output
1
3
Input
1
1
5
1 2
1 10
1 10
1 10
1 10
Output
1
3
13
23
33
Note
The first sample are shown on the picture.
<image> | # https://codeforces.com/problemset/problem/272/C
# we just check if the box dropped falls above the previous box or on stair number(1...w)
# the box is dropped from the top and hence we need to check the heights from the top -
# which height is suitable and higher
m = int(input())
arr = list(map(int, input().split()))
t = int(input())
for i in range(t):
w, h = map(int, input().split())
p = max(arr[0], arr[w - 1]) # checking which height is higher
print(p)
# increase the height for the next box to drop - can only drop above the
arr[0] = p + h
# current box
| {
"input": [
"1\n1\n5\n1 2\n1 10\n1 10\n1 10\n1 10\n",
"3\n1 2 3\n2\n1 1\n3 1\n",
"5\n1 2 3 6 6\n4\n1 1\n3 1\n1 1\n4 3\n",
"2\n1 6\n5\n2 6\n1 2\n1 1\n1 2\n1 7\n",
"3\n2 10 15\n1\n1 830\n",
"3\n1 6 8\n5\n3 4\n3 9\n3 3\n1 2\n1 6\n",
"7\n8 13 19 21 25 30 32\n3\n5 4\n6 5\n1 2\n",
"1\n1000000000\n6\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n",
"1\n8\n1\n1 42\n",
"5\n4 7 10 12 12\n9\n3 9\n2 1\n3 5\n4 7\n1 1\n5 1\n1 7\n2 4\n4 10\n",
"5\n1 2 3 6 6\n25\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n",
"8\n6 10 18 23 30 31 31 33\n1\n5 3\n",
"1\n9\n8\n1 4\n1 10\n1 9\n1 9\n1 7\n1 1\n1 9\n1 2\n",
"1\n1\n1\n1 1\n",
"3\n1 6 8\n5\n3 4\n3 9\n3 3\n1 4\n1 6\n",
"7\n8 13 19 21 25 30 32\n3\n5 2\n6 5\n1 2\n",
"5\n1 2 3 6 6\n25\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000100000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n",
"8\n6 10 18 23 30 31 11 33\n1\n5 3\n",
"1\n9\n8\n1 4\n1 20\n1 9\n1 9\n1 7\n1 1\n1 9\n1 2\n",
"1\n1\n1\n1 0\n",
"1\n1\n2\n1 2\n1 10\n1 10\n1 10\n1 10\n",
"5\n1 2 3 6 6\n4\n1 2\n3 1\n1 1\n4 3\n",
"3\n1 6 8\n5\n3 4\n3 16\n3 3\n1 4\n1 6\n",
"7\n8 13 19 21 25 30 32\n3\n5 2\n4 5\n1 2\n",
"5\n1 2 3 6 6\n25\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000100000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000010\n1 1000000000\n1 1000000000\n1 1000000000\n",
"5\n1 2 3 6 6\n4\n1 2\n3 1\n1 1\n2 3\n",
"5\n1 2 3 6 6\n25\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000100000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000001000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000010\n1 1000000000\n1 1000000000\n1 1000000000\n",
"5\n1 2 3 6 6\n4\n1 2\n3 0\n1 1\n2 3\n",
"7\n4 13 19 21 25 30 32\n1\n5 2\n4 5\n1 2\n",
"1\n2\n2\n1 2\n1 6\n4 14\n1 5\n1 0\n",
"2\n1 6\n5\n2 6\n1 2\n1 1\n1 2\n1 8\n",
"3\n4 10 15\n1\n1 830\n",
"3\n1 6 8\n5\n3 8\n3 9\n3 3\n1 2\n1 6\n",
"5\n7 7 10 12 12\n9\n3 9\n2 1\n3 5\n4 7\n1 1\n5 1\n1 7\n2 4\n4 10\n",
"8\n6 10 18 23 51 31 31 33\n1\n5 3\n",
"7\n8 13 19 21 25 59 32\n3\n5 2\n6 5\n1 2\n",
"3\n1 6 8\n5\n1 4\n3 16\n3 3\n1 4\n1 6\n",
"5\n1 2 3 6 6\n4\n1 2\n3 2\n1 1\n2 3\n",
"5\n1 2 3 6 6\n25\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000100000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000001000\n1 1000000000\n1 1000000100\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000000\n1 1000000010\n1 1000000000\n1 1000000000\n1 1000000000\n",
"8\n6 10 18 23 27 31 11 36\n1\n5 2\n",
"1\n2\n1\n1 0\n",
"5\n1 2 3 12 6\n4\n2 2\n3 0\n1 1\n2 3\n",
"7\n5 13 19 21 23 30 29\n1\n5 2\n4 5\n2 2\n",
"8\n6 10 18 23 30 31 11 33\n1\n5 2\n",
"1\n1\n1\n1 -1\n",
"1\n1\n2\n1 2\n1 10\n1 10\n1 5\n1 10\n",
"3\n0 6 8\n5\n3 4\n3 16\n3 3\n1 4\n1 6\n",
"7\n4 13 19 21 25 30 32\n3\n5 2\n4 5\n1 2\n",
"8\n6 10 18 23 30 31 11 36\n1\n5 2\n",
"1\n1\n1\n1 -2\n",
"1\n1\n2\n1 2\n1 10\n1 10\n1 5\n1 0\n",
"8\n12 10 18 23 30 31 11 36\n1\n5 2\n",
"1\n1\n2\n1 2\n1 10\n2 10\n1 5\n1 0\n",
"5\n1 2 3 12 6\n4\n1 2\n3 0\n1 1\n2 3\n",
"7\n4 13 19 21 25 30 29\n1\n5 2\n4 5\n1 2\n",
"8\n3 10 18 23 30 31 11 36\n1\n5 2\n",
"1\n1\n2\n1 2\n1 6\n2 10\n1 5\n1 0\n",
"7\n5 13 19 21 25 30 29\n1\n5 2\n4 5\n1 2\n",
"8\n3 10 18 23 30 4 11 36\n1\n5 2\n",
"1\n1\n2\n1 2\n1 6\n2 10\n1 5\n1 1\n",
"7\n5 13 19 21 25 30 29\n1\n5 2\n4 5\n2 2\n",
"1\n1\n2\n1 2\n1 6\n2 14\n1 5\n1 1\n",
"7\n5 13 19 21 25 30 38\n1\n5 2\n4 5\n2 2\n",
"1\n1\n2\n1 2\n1 6\n4 14\n1 5\n1 1\n",
"1\n1\n2\n1 2\n1 6\n4 14\n1 5\n1 0\n",
"1\n2\n2\n1 2\n1 6\n4 0\n1 5\n1 0\n",
"7\n8 13 19 21 25 30 32\n1\n5 4\n6 5\n1 2\n",
"5\n1 2 3 6 8\n4\n1 1\n3 1\n1 1\n4 3\n",
"3\n1 6 8\n5\n3 4\n3 9\n1 3\n1 4\n1 6\n",
"8\n6 10 18 12 30 31 11 33\n1\n5 2\n",
"1\n1\n2\n1 2\n1 10\n1 10\n1 14\n1 10\n",
"7\n8 13 19 19 25 30 32\n3\n5 2\n4 5\n1 2\n",
"8\n6 10 18 23 30 31 12 33\n1\n5 2\n",
"3\n0 0 8\n5\n3 4\n3 16\n3 3\n1 4\n1 6\n",
"7\n4 13 19 21 25 31 32\n3\n5 2\n4 5\n1 2\n",
"1\n2\n2\n1 2\n1 10\n1 10\n1 5\n1 0\n",
"7\n4 13 19 21 25 30 32\n1\n5 4\n4 5\n1 2\n",
"8\n12 10 18 26 30 31 11 36\n1\n5 2\n",
"1\n1\n2\n1 2\n1 10\n2 10\n1 5\n1 1\n",
"8\n3 10 10 23 30 31 11 36\n1\n5 2\n",
"1\n1\n2\n1 2\n1 6\n2 7\n1 5\n1 0\n",
"7\n1 13 19 21 25 30 29\n1\n5 2\n4 5\n1 2\n",
"1\n1\n2\n1 2\n1 0\n2 10\n1 5\n1 1\n"
],
"output": [
"1\n3\n13\n23\n33\n",
"1\n3\n",
"1\n3\n4\n6\n",
"6\n12\n14\n15\n17\n",
"2\n",
"8\n12\n21\n24\n26\n",
"25\n30\n35\n",
"1000000000\n2000000000\n3000000000\n4000000000\n5000000000\n6000000000\n",
"8\n",
"10\n19\n20\n25\n32\n33\n34\n41\n45\n",
"1\n1000000001\n2000000001\n3000000001\n4000000001\n5000000001\n6000000001\n7000000001\n8000000001\n9000000001\n10000000001\n11000000001\n12000000001\n13000000001\n14000000001\n15000000001\n16000000001\n17000000001\n18000000001\n19000000001\n20000000001\n21000000001\n22000000001\n23000000001\n24000000001\n",
"30\n",
"9\n13\n23\n32\n41\n48\n49\n58\n",
"1\n",
"8\n12\n21\n24\n28\n",
"25\n30\n35\n",
"1\n1000000001\n2000000001\n3000000001\n4000100001\n5000100001\n6000100001\n7000100001\n8000100001\n9000100001\n10000100001\n11000100001\n12000100001\n13000100001\n14000100001\n15000100001\n16000100001\n17000100001\n18000100001\n19000100001\n20000100001\n21000100001\n22000100001\n23000100001\n24000100001\n",
"30\n",
"9\n13\n33\n42\n51\n58\n59\n68\n",
"1\n",
"1\n3\n",
"1\n3\n4\n6\n",
"8\n12\n28\n31\n35\n",
"25\n27\n32\n",
"1\n1000000001\n2000000001\n3000000001\n4000100001\n5000100001\n6000100001\n7000100001\n8000100001\n9000100001\n10000100001\n11000100001\n12000100001\n13000100001\n14000100001\n15000100001\n16000100001\n17000100001\n18000100001\n19000100001\n20000100001\n21000100001\n22000100011\n23000100011\n24000100011\n",
"1\n3\n4\n5\n",
"1\n1000000001\n2000000001\n3000000001\n4000100001\n5000100001\n6000100001\n7000100001\n8000101001\n9000101001\n10000101001\n11000101001\n12000101001\n13000101001\n14000101001\n15000101001\n16000101001\n17000101001\n18000101001\n19000101001\n20000101001\n21000101001\n22000101011\n23000101011\n24000101011\n",
"1\n3\n3\n4\n",
"25\n",
"2\n4\n",
"6\n12\n14\n15\n17\n",
"4\n",
"8\n16\n25\n28\n30\n",
"10\n19\n20\n25\n32\n33\n34\n41\n45\n",
"51\n",
"25\n59\n64\n",
"1\n8\n24\n27\n31\n",
"1\n3\n5\n6\n",
"1\n1000000001\n2000000001\n3000000001\n4000100001\n5000100001\n6000100001\n7000100001\n8000101001\n9000101001\n10000101101\n11000101101\n12000101101\n13000101101\n14000101101\n15000101101\n16000101101\n17000101101\n18000101101\n19000101101\n20000101101\n21000101101\n22000101111\n23000101111\n24000101111\n",
"27\n",
"2\n",
"2\n4\n4\n5\n",
"23\n",
"30\n",
"1\n",
"1\n3\n",
"8\n12\n28\n31\n35\n",
"25\n27\n32\n",
"30\n",
"1\n",
"1\n3\n",
"30\n",
"1\n3\n",
"1\n3\n3\n4\n",
"25\n",
"30\n",
"1\n3\n",
"25\n",
"30\n",
"1\n3\n",
"25\n",
"1\n3\n",
"25\n",
"1\n3\n",
"1\n3\n",
"2\n4\n",
"25\n",
"1\n3\n4\n6\n",
"8\n12\n21\n24\n28\n",
"30\n",
"1\n3\n",
"25\n27\n32\n",
"30\n",
"8\n12\n28\n31\n35\n",
"25\n27\n32\n",
"2\n4\n",
"25\n",
"30\n",
"1\n3\n",
"30\n",
"1\n3\n",
"25\n",
"1\n3\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Dima's got a staircase that consists of n stairs. The first stair is at height a1, the second one is at a2, the last one is at an (1 ≤ a1 ≤ a2 ≤ ... ≤ an).
Dima decided to play with the staircase, so he is throwing rectangular boxes at the staircase from above. The i-th box has width wi and height hi. Dima throws each box vertically down on the first wi stairs of the staircase, that is, the box covers stairs with numbers 1, 2, ..., wi. Each thrown box flies vertically down until at least one of the two following events happen:
* the bottom of the box touches the top of a stair;
* the bottom of the box touches the top of a box, thrown earlier.
We only consider touching of the horizontal sides of stairs and boxes, at that touching with the corners isn't taken into consideration. Specifically, that implies that a box with width wi cannot touch the stair number wi + 1.
You are given the description of the staircase and the sequence in which Dima threw the boxes at it. For each box, determine how high the bottom of the box after landing will be. Consider a box to fall after the previous one lands.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of stairs in the staircase. The second line contains a non-decreasing sequence, consisting of n integers, a1, a2, ..., an (1 ≤ ai ≤ 109; ai ≤ ai + 1).
The next line contains integer m (1 ≤ m ≤ 105) — the number of boxes. Each of the following m lines contains a pair of integers wi, hi (1 ≤ wi ≤ n; 1 ≤ hi ≤ 109) — the size of the i-th thrown box.
The numbers in the lines are separated by spaces.
Output
Print m integers — for each box the height, where the bottom of the box will be after landing. Print the answers for the boxes in the order, in which the boxes are given in the input.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
5
1 2 3 6 6
4
1 1
3 1
1 1
4 3
Output
1
3
4
6
Input
3
1 2 3
2
1 1
3 1
Output
1
3
Input
1
1
5
1 2
1 10
1 10
1 10
1 10
Output
1
3
13
23
33
Note
The first sample are shown on the picture.
<image>
### Input:
1
1
5
1 2
1 10
1 10
1 10
1 10
### Output:
1
3
13
23
33
### Input:
3
1 2 3
2
1 1
3 1
### Output:
1
3
### Code:
# https://codeforces.com/problemset/problem/272/C
# we just check if the box dropped falls above the previous box or on stair number(1...w)
# the box is dropped from the top and hence we need to check the heights from the top -
# which height is suitable and higher
m = int(input())
arr = list(map(int, input().split()))
t = int(input())
for i in range(t):
w, h = map(int, input().split())
p = max(arr[0], arr[w - 1]) # checking which height is higher
print(p)
# increase the height for the next box to drop - can only drop above the
arr[0] = p + h
# current box
|
319_C. Kalila and Dimna in the Logging Industry_3118 | Kalila and Dimna are two jackals living in a huge jungle. One day they decided to join a logging factory in order to make money.
The manager of logging factory wants them to go to the jungle and cut n trees with heights a1, a2, ..., an. They bought a chain saw from a shop. Each time they use the chain saw on the tree number i, they can decrease the height of this tree by one unit. Each time that Kalila and Dimna use the chain saw, they need to recharge it. Cost of charging depends on the id of the trees which have been cut completely (a tree is cut completely if its height equal to 0). If the maximum id of a tree which has been cut completely is i (the tree that have height ai in the beginning), then the cost of charging the chain saw would be bi. If no tree is cut completely, Kalila and Dimna cannot charge the chain saw. The chainsaw is charged in the beginning. We know that for each i < j, ai < aj and bi > bj and also bn = 0 and a1 = 1. Kalila and Dimna want to cut all the trees completely, with minimum cost.
They want you to help them! Will you?
Input
The first line of input contains an integer n (1 ≤ n ≤ 105). The second line of input contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109). The third line of input contains n integers b1, b2, ..., bn (0 ≤ bi ≤ 109).
It's guaranteed that a1 = 1, bn = 0, a1 < a2 < ... < an and b1 > b2 > ... > bn.
Output
The only line of output must contain the minimum cost of cutting all the trees completely.
Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
5
1 2 3 4 5
5 4 3 2 0
Output
25
Input
6
1 2 3 10 20 30
6 5 4 3 2 0
Output
138 | n = int(input())
a = [0] + [int(x) for x in input().split()]
b = [0] + [int(x) for x in input().split()]
q = [0 for i in range(n + 1)]
f = [0 for _ in range(n + 1)]
l, r, q[1] = 1, 1, 1
for i in range(2, n + 1):
while l < r and f[q[l + 1]] - f[q[l]] < a[i] * (b[q[l]] - b[q[l + 1]]):
l += 1
f[i] = f[q[l]] + b[q[l]] * a[i]
while l < r and (f[q[r]] - f[q[r - 1]]) * (b[q[r]] - b[i]) >= (f[i] - f[q[r]]) * (b[q[r - 1]] - b[q[r]]):
r -= 1
r += 1
q[r] = i
print(f[n])
| {
"input": [
"5\n1 2 3 4 5\n5 4 3 2 0\n",
"6\n1 2 3 10 20 30\n6 5 4 3 2 0\n",
"6\n2 2 3 10 20 30\n6 5 4 3 2 0\n",
"5\n1 4 3 4 5\n5 4 3 2 0\n",
"6\n1 2 3 10 20 25\n6 5 4 3 2 0\n",
"6\n1 1 2 10 20 25\n6 5 4 3 2 0\n",
"5\n1 2 3 4 5\n9 4 3 2 0\n",
"5\n1 2 3 4 5\n6 4 3 2 0\n",
"6\n2 2 3 5 20 30\n6 5 4 3 2 0\n",
"6\n1 2 3 10 20 39\n6 5 4 3 2 0\n",
"6\n2 1 4 10 26 30\n6 5 4 3 2 0\n",
"6\n1 2 3 10 20 30\n7 5 4 3 2 0\n",
"6\n1 1 4 20 20 25\n6 5 4 3 2 0\n",
"5\n1 2 3 4 5\n7 4 3 2 0\n",
"5\n0 2 5 4 5\n8 4 3 2 0\n",
"5\n1 2 5 4 5\n5 4 3 2 0\n",
"5\n0 2 5 4 5\n5 4 3 2 0\n",
"6\n1 1 3 10 20 25\n6 5 4 3 2 0\n",
"5\n0 1 5 4 5\n5 4 3 2 0\n",
"5\n1 4 3 5 5\n5 4 3 2 0\n",
"6\n2 1 3 10 20 30\n6 5 4 3 2 0\n",
"6\n1 1 2 20 20 25\n6 5 4 3 2 0\n",
"6\n1 1 2 11 20 25\n6 5 4 3 2 0\n",
"5\n1 4 2 5 5\n5 4 3 2 0\n",
"6\n2 1 3 10 26 30\n6 5 4 3 2 0\n",
"6\n2 1 3 15 26 30\n6 5 4 3 2 0\n",
"6\n2 2 3 14 20 30\n6 5 4 3 2 0\n",
"5\n1 4 2 4 5\n5 4 3 2 0\n",
"5\n1 2 5 3 5\n5 4 3 2 0\n",
"6\n2 2 3 10 20 25\n6 5 4 3 2 0\n",
"5\n0 4 2 4 5\n5 4 3 2 0\n",
"6\n1 2 3 10 22 39\n6 5 4 3 2 0\n",
"5\n0 2 5 3 5\n5 4 3 2 0\n",
"6\n0 1 4 10 26 30\n6 5 4 3 2 0\n",
"6\n2 1 3 10 26 30\n6 5 4 3 1 0\n",
"6\n3 1 4 10 26 30\n6 5 4 3 2 0\n",
"5\n1 2 5 4 5\n5 4 3 1 0\n",
"5\n2 2 5 4 5\n5 4 3 2 0\n",
"6\n0 1 2 10 20 25\n6 5 4 3 2 0\n",
"6\n0 1 2 11 20 25\n6 5 4 3 2 0\n",
"6\n2 2 3 24 20 30\n6 5 4 3 2 0\n",
"6\n0 2 3 10 20 39\n6 5 4 3 2 0\n"
],
"output": [
"25\n",
"138\n",
"138\n",
"25\n",
"118\n",
"112\n",
"38\n",
"30\n",
"120\n",
"174\n",
"144\n",
"141\n",
"124\n",
"34\n",
"36\n",
"25\n",
"25\n",
"118\n",
"25\n",
"25\n",
"138\n",
"112\n",
"112\n",
"25\n",
"138\n",
"138\n",
"138\n",
"25\n",
"25\n",
"118\n",
"25\n",
"174\n",
"25\n",
"144\n",
"138\n",
"144\n",
"25\n",
"25\n",
"112\n",
"112\n",
"138\n",
"174\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kalila and Dimna are two jackals living in a huge jungle. One day they decided to join a logging factory in order to make money.
The manager of logging factory wants them to go to the jungle and cut n trees with heights a1, a2, ..., an. They bought a chain saw from a shop. Each time they use the chain saw on the tree number i, they can decrease the height of this tree by one unit. Each time that Kalila and Dimna use the chain saw, they need to recharge it. Cost of charging depends on the id of the trees which have been cut completely (a tree is cut completely if its height equal to 0). If the maximum id of a tree which has been cut completely is i (the tree that have height ai in the beginning), then the cost of charging the chain saw would be bi. If no tree is cut completely, Kalila and Dimna cannot charge the chain saw. The chainsaw is charged in the beginning. We know that for each i < j, ai < aj and bi > bj and also bn = 0 and a1 = 1. Kalila and Dimna want to cut all the trees completely, with minimum cost.
They want you to help them! Will you?
Input
The first line of input contains an integer n (1 ≤ n ≤ 105). The second line of input contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109). The third line of input contains n integers b1, b2, ..., bn (0 ≤ bi ≤ 109).
It's guaranteed that a1 = 1, bn = 0, a1 < a2 < ... < an and b1 > b2 > ... > bn.
Output
The only line of output must contain the minimum cost of cutting all the trees completely.
Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
5
1 2 3 4 5
5 4 3 2 0
Output
25
Input
6
1 2 3 10 20 30
6 5 4 3 2 0
Output
138
### Input:
5
1 2 3 4 5
5 4 3 2 0
### Output:
25
### Input:
6
1 2 3 10 20 30
6 5 4 3 2 0
### Output:
138
### Code:
n = int(input())
a = [0] + [int(x) for x in input().split()]
b = [0] + [int(x) for x in input().split()]
q = [0 for i in range(n + 1)]
f = [0 for _ in range(n + 1)]
l, r, q[1] = 1, 1, 1
for i in range(2, n + 1):
while l < r and f[q[l + 1]] - f[q[l]] < a[i] * (b[q[l]] - b[q[l + 1]]):
l += 1
f[i] = f[q[l]] + b[q[l]] * a[i]
while l < r and (f[q[r]] - f[q[r - 1]]) * (b[q[r]] - b[i]) >= (f[i] - f[q[r]]) * (b[q[r - 1]] - b[q[r]]):
r -= 1
r += 1
q[r] = i
print(f[n])
|
343_C. Read Time_3122 | Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel.
When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation.
<image>
Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read.
Input
The first line of the input contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≤ hi ≤ 1010, hi < hi + 1) — the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≤ pi ≤ 1010, pi < pi + 1) - the numbers of tracks to read.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier.
Output
Print a single number — the minimum time required, in seconds, to read all the needed tracks.
Examples
Input
3 4
2 5 6
1 3 6 8
Output
2
Input
3 3
1 2 3
1 2 3
Output
0
Input
1 2
165
142 200
Output
81
Note
The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way:
1. during the first second move the 1-st head to the left and let it stay there;
2. move the second head to the left twice;
3. move the third head to the right twice (note that the 6-th track has already been read at the beginning).
One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. | import sys
from itertools import *
from math import *
def solve():
n, m = map(int, input().split())
h = list(map(int, input().split()))
p = list(map(int, input().split()))
ss, ll = 0, int(2.2e10)
while ss < ll:
avg = (ss + ll) // 2
works = True
hidx = 0
pidx = 0
while hidx < len(h) and pidx < len(p):
leftget = p[pidx]
curpos = h[hidx]
if curpos - leftget > avg:
works = False
break
getbacktime = max(0, 2*(curpos - leftget))
alsotoright = max(0, avg - getbacktime)
leftime = max(0, curpos - leftget)
remtime = max(0, (avg - leftime) // 2)
furthestright = curpos + max(alsotoright, remtime)
while pidx < len(p) and p[pidx] <= furthestright: pidx += 1
hidx += 1
if pidx != len(p): works = False
if works: ll = avg
else: ss = avg + 1
print(ss)
if sys.hexversion == 50594544 : sys.stdin = open("test.txt")
solve() | {
"input": [
"3 4\n2 5 6\n1 3 6 8\n",
"3 3\n1 2 3\n1 2 3\n",
"1 2\n165\n142 200\n",
"10 11\n1 909090909 1818181817 2727272725 3636363633 4545454541 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535\n",
"2 4\n3 12\n1 7 8 14\n",
"3 3\n2 3 4\n1 3 5\n",
"3 3\n1 2 3\n2 3 4\n",
"1 1\n10000000000\n1\n",
"10 10\n389151626 1885767612 2609703695 3054567325 4421751790 5636236054 6336088034 7961001379 8631992167 9836923433\n389144165 389158510 1885760728 1885775073 2609696234 2609710579 3054559864 3054574209 4421744329 4421758674\n",
"1 1\n1\n10000000000\n",
"2 1\n1 10\n9\n",
"2 4\n4500000000 5500000000\n5 499999999 5000000001 9999999995\n",
"3 19\n7 10 13\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\n",
"10 10\n331462447 1369967506 1504296131 2061390288 2309640071 3006707770 4530801731 4544099460 7357049371 9704808257\n754193799 3820869903 4594383880 5685752675 6303322854 6384906441 7863448848 8542634752 9573124462 9665646063\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10000000000\n",
"3 12\n477702277 4717363935 8947981095\n477702276 477702304 477702312 477702317 4717363895 4717363896 4717363920 4717363936 8947981094 8947981111 8947981112 8947981135\n",
"10 10\n9999999991 9999999992 9999999993 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 7 8 9 10\n",
"1 2\n5000000000\n1 10000000000\n",
"2 4\n3 12\n1 7 14 14\n",
"2 1\n2 10\n9\n",
"2 4\n4500000000 5500000000\n2 499999999 5000000001 9999999995\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10001000000\n",
"10 10\n9999999991 9999999992 13416547534 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 7 8 9 10\n",
"1 2\n3948760531\n1 10000000000\n",
"1 2\n165\n68 200\n",
"2 4\n6 12\n1 7 14 14\n",
"2 1\n1 10\n12\n",
"2 4\n4500000000 5500000000\n2 499999999 55881109 9999999995\n",
"10 10\n9999999991 9999999992 13416547534 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n2 2 3 4 5 6 7 8 9 10\n",
"1 2\n5013946231\n1 10000000000\n",
"3 3\n1 2 3\n1 2 8\n",
"1 2\n165\n61 200\n",
"2 4\n7 12\n1 7 14 14\n",
"1 2\n1882251602\n1 10000000000\n",
"1 2\n165\n115 200\n",
"2 1\n0 9\n12\n",
"1 2\n165\n103 200\n",
"2 1\n-1 12\n12\n",
"10 11\n1 909090909 1818181817 2727272725 3636363633 3960725271 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535\n",
"1 1\n10000000000\n2\n",
"10 10\n389151626 1885767612 2609703695 3054567325 4421751790 5636236054 6336088034 7961001379 12698961867 9836923433\n389144165 389158510 1885760728 1885775073 2609696234 2609710579 3054559864 3054574209 4421744329 4421758674\n",
"1 1\n1\n10000100000\n",
"10 10\n69852655 1369967506 1504296131 2061390288 2309640071 3006707770 4530801731 4544099460 7357049371 9704808257\n754193799 3820869903 4594383880 5685752675 6303322854 6384906441 7863448848 8542634752 9573124462 9665646063\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100100 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10000000000\n",
"1 2\n3948760531\n2 10000000000\n",
"1 2\n180\n61 200\n",
"2 4\n4 12\n1 7 14 14\n",
"1 2\n271\n103 200\n",
"1 1\n10001000000\n2\n",
"3 3\n1 2 3\n1 2 4\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 338816409 6000000000 8000000000 10001000000\n",
"2 1\n0 10\n12\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100001 1000000 4999999999 5000000000 338816409 6000000000 8000000000 10001000000\n",
"2 4\n7 12\n1 1 14 14\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100001 1000000 625460102 5000000000 338816409 6000000000 8000000000 10001000000\n",
"2 1\n-1 9\n12\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100001 1000000 625460102 5123061340 338816409 6000000000 8000000000 10001000000\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100001 1000000 625460102 5123061340 338816409 6000000000 9089250183 10001000000\n",
"10 10\n9999999991 9999999992 9999999993 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 3 5 6 7 8 9 10\n",
"3 4\n2 5 6\n1 3 6 11\n",
"2 4\n3 12\n1 7 14 20\n",
"2 1\n2 17\n9\n",
"2 4\n4500000000 5500000000\n2 499999999 300818092 9999999995\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000001 4999999999 5000000000 5000000001 6000000000 8000000000 10001000000\n",
"10 10\n9999999991 9999999992 13416547534 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 2 8 9 10\n",
"3 3\n2 2 3\n1 2 4\n",
"2 1\n1 4\n12\n",
"2 4\n4500000000 5500000000\n2 418070964 55881109 9999999995\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 55862920 6000000000 8000000000 10001000000\n",
"3 3\n1 2 3\n1 2 10\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100101 1000000 4999999999 5000000000 338816409 6000000000 8000000000 10001000000\n",
"2 4\n7 12\n1 1 14 19\n",
"2 1\n1 9\n12\n",
"3 10\n4999999999 5000000000 5000000001\n1 1000 100001 1000000 625460102 5000000000 338816409 6000000000 7389396062 10001000000\n",
"2 1\n-1 7\n12\n",
"3 10\n4999999999 5000000000 5000000001\n1 1100 100001 1000000 625460102 5123061340 338816409 6000000000 8000000000 10001000000\n",
"2 1\n-1 12\n15\n",
"10 11\n1 909090909 1688988503 2727272725 3636363633 3960725271 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535\n"
],
"output": [
"2\n",
"0\n",
"81\n",
"1363636362\n",
"8\n",
"1\n",
"1\n",
"9999999999\n",
"21229\n",
"9999999999\n",
"1\n",
"5499999993\n",
"6\n",
"1840806981\n",
"4999999999\n",
"42\n",
"9999999990\n",
"14999999998\n",
"8\n",
"1\n",
"5499999993\n",
"5000999999\n",
"9999999990\n",
"13948760529\n",
"167\n",
"7\n",
"2\n",
"4499999998\n",
"9999999989\n",
"14986053768\n",
"5\n",
"174\n",
"6\n",
"11882251600\n",
"120\n",
"3\n",
"132\n",
"0\n",
"1363636362\n",
"9999999998\n",
"21229\n",
"10000099999\n",
"1840806981\n",
"4999999999\n",
"13948760527\n",
"159\n",
"9\n",
"168\n",
"10000999998\n",
"1\n",
"5000999999\n",
"2\n",
"5000999999\n",
"6\n",
"5000999999\n",
"3\n",
"5000999999\n",
"5000999999\n",
"9999999990\n",
"5\n",
"8\n",
"7\n",
"4499999998\n",
"5000999999\n",
"9999999990\n",
"1\n",
"8\n",
"4499999998\n",
"5000999999\n",
"7\n",
"5000999999\n",
"7\n",
"3\n",
"5000999999\n",
"5\n",
"5000999999\n",
"3\n",
"1363636362\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel.
When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation.
<image>
Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read.
Input
The first line of the input contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≤ hi ≤ 1010, hi < hi + 1) — the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≤ pi ≤ 1010, pi < pi + 1) - the numbers of tracks to read.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier.
Output
Print a single number — the minimum time required, in seconds, to read all the needed tracks.
Examples
Input
3 4
2 5 6
1 3 6 8
Output
2
Input
3 3
1 2 3
1 2 3
Output
0
Input
1 2
165
142 200
Output
81
Note
The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way:
1. during the first second move the 1-st head to the left and let it stay there;
2. move the second head to the left twice;
3. move the third head to the right twice (note that the 6-th track has already been read at the beginning).
One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
### Input:
3 4
2 5 6
1 3 6 8
### Output:
2
### Input:
3 3
1 2 3
1 2 3
### Output:
0
### Code:
import sys
from itertools import *
from math import *
def solve():
n, m = map(int, input().split())
h = list(map(int, input().split()))
p = list(map(int, input().split()))
ss, ll = 0, int(2.2e10)
while ss < ll:
avg = (ss + ll) // 2
works = True
hidx = 0
pidx = 0
while hidx < len(h) and pidx < len(p):
leftget = p[pidx]
curpos = h[hidx]
if curpos - leftget > avg:
works = False
break
getbacktime = max(0, 2*(curpos - leftget))
alsotoright = max(0, avg - getbacktime)
leftime = max(0, curpos - leftget)
remtime = max(0, (avg - leftime) // 2)
furthestright = curpos + max(alsotoright, remtime)
while pidx < len(p) and p[pidx] <= furthestright: pidx += 1
hidx += 1
if pidx != len(p): works = False
if works: ll = avg
else: ss = avg + 1
print(ss)
if sys.hexversion == 50594544 : sys.stdin = open("test.txt")
solve() |
366_E. Dima and Magic Guitar_3125 | Dima loves Inna very much. He decided to write a song for her. Dima has a magic guitar with n strings and m frets. Dima makes the guitar produce sounds like that: to play a note, he needs to hold one of the strings on one of the frets and then pull the string. When Dima pulls the i-th string holding it on the j-th fret the guitar produces a note, let's denote it as aij. We know that Dima's guitar can produce k distinct notes. It is possible that some notes can be produced in multiple ways. In other words, it is possible that aij = apq at (i, j) ≠ (p, q).
Dima has already written a song — a sequence of s notes. In order to play the song, you need to consecutively produce the notes from the song on the guitar. You can produce each note in any available way. Dima understood that there are many ways to play a song and he wants to play it so as to make the song look as complicated as possible (try to act like Cobein).
We'll represent a way to play a song as a sequence of pairs (xi, yi) (1 ≤ i ≤ s), such that the xi-th string on the yi-th fret produces the i-th note from the song. The complexity of moving between pairs (x1, y1) and (x2, y2) equals <image> + <image>. The complexity of a way to play a song is the maximum of complexities of moving between adjacent pairs.
Help Dima determine the maximum complexity of the way to play his song! The guy's gotta look cool!
Input
The first line of the input contains four integers n, m, k and s (1 ≤ n, m ≤ 2000, 1 ≤ k ≤ 9, 2 ≤ s ≤ 105).
Then follow n lines, each containing m integers aij (1 ≤ aij ≤ k). The number in the i-th row and the j-th column (aij) means a note that the guitar produces on the i-th string and the j-th fret.
The last line of the input contains s integers qi (1 ≤ qi ≤ k) — the sequence of notes of the song.
Output
In a single line print a single number — the maximum possible complexity of the song.
Examples
Input
4 6 5 7
3 1 2 2 3 1
3 2 2 2 5 5
4 2 2 2 5 3
3 2 2 1 4 3
2 3 1 4 1 5 1
Output
8
Input
4 4 9 5
4 7 9 5
1 2 1 7
8 3 4 9
5 7 7 2
7 1 9 2 5
Output
4 | def solution() : # 最大的距离来自于角落附近的点
n,m,k,s = map(int, input().split())
dis = lambda a,b : abs(a[0] - b[0]) + abs(a[1] - b[1])
corner = [(0,0), (0,m-1), (n-1,0), (n-1,m-1)]
vertex = [[(n,m), (n,-1), (-1,m), (-1,-1)] for _ in range(k+1)]
for i in range(n) :
for j,note in enumerate(map(int, input().split())) :
vertex[note] = [
(i,j) if dis((i,j), c) < dis(v, c) else v
for v,c in zip(vertex[note], corner)]
maxdis = [[-1] * (k+1) for _ in range(k+1)]
pairs = [(0,3),(3,0),(1,2),(2,1)]
for i in range(1, k+1) :
for j in range(i, k+1) :
vi,vj = vertex[i],vertex[j]
maxdis[i][j] = max(dis(vi[a], vj[b]) for a,b in pairs)
maxdis[j][i] = maxdis[i][j]
s = list(map(int, input().split()))
print(max(maxdis[s[i]][s[i+1]] for i in range(len(s) - 1)))
solution() | {
"input": [
"4 6 5 7\n3 1 2 2 3 1\n3 2 2 2 5 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 4 9 5\n4 7 9 5\n1 2 1 7\n8 3 4 9\n5 7 7 2\n7 1 9 2 5\n",
"10 1 9 5\n1\n2\n3\n4\n5\n6\n7\n8\n9\n1\n1 1 9 2 3\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"1 10 9 5\n1 2 3 4 5 6 7 8 9 1\n1 1 9 2 3\n",
"5 5 2 2\n2 2 2 1 2\n2 1 2 2 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n1 1\n",
"5 5 2 2\n2 1 2 2 2\n2 2 2 2 2\n2 2 2 2 1\n2 2 2 2 2\n1 2 2 2 2\n1 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"1 10 9 5\n1 2 3 3 5 6 7 8 9 1\n1 1 9 2 3\n",
"5 5 2 2\n2 2 2 1 1\n2 1 2 2 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n1 1\n",
"4 6 5 7\n3 1 4 2 3 1\n3 2 2 2 5 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 4 9 5\n4 7 9 5\n1 2 1 7\n8 3 4 9\n5 7 7 2\n7 1 9 1 5\n",
"11 11 9 11\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 4 1 1\n3 3 3 1 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 4 1\n1 2 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"5 5 2 2\n2 2 2 1 2\n2 1 2 2 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 1 1\n1 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 2 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"1 10 9 5\n1 2 3 3 5 6 7 6 9 1\n1 1 9 2 3\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 4 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"5 5 2 2\n2 2 2 1 1\n2 1 2 1 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n1 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 2 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 4 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"10 1 9 5\n1\n2\n3\n4\n5\n6\n7\n8\n9\n1\n1 1 9 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 2 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"1 10 9 5\n1 2 3 4 5 6 7 8 9 1\n1 1 9 1 3\n",
"4 6 5 7\n3 1 2 2 3 1\n3 2 2 2 2 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n0 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 2 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 2 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 2 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 2\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"4 6 5 7\n3 1 4 2 3 1\n3 2 2 2 5 5\n4 3 2 2 5 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 2 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 2 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 2 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 4 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"5 5 2 2\n2 2 2 1 1\n2 1 2 1 2\n1 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n1 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 2 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n2 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 4 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 2 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 2 2 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 2\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 2 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"4 6 5 7\n3 1 4 2 3 1\n3 2 2 2 5 5\n4 3 2 2 1 3\n3 2 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 6 5 7\n3 1 4 2 3 1\n3 2 2 2 5 5\n4 3 2 2 1 3\n3 4 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 6 5 7\n3 1 3 2 3 1\n3 2 2 2 5 5\n4 3 2 2 1 3\n3 4 2 1 4 3\n2 3 1 4 1 5 1\n",
"4 6 5 7\n3 1 3 2 3 1\n3 2 2 2 5 5\n4 3 2 2 1 3\n3 4 2 1 4 3\n2 4 1 4 1 5 1\n",
"4 6 5 7\n5 1 3 2 3 1\n3 2 2 2 5 5\n4 3 2 2 1 3\n3 4 2 1 4 3\n2 4 1 4 1 5 1\n",
"10 1 9 5\n1\n2\n3\n4\n5\n2\n7\n8\n9\n1\n1 1 9 2 3\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"1 10 9 5\n1 2 3 4 5 6 7 8 9 1\n1 1 9 3 3\n",
"5 5 2 2\n2 1 2 2 1\n2 2 2 2 2\n2 2 2 2 1\n2 2 2 2 2\n1 2 2 2 2\n1 1\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 2 1 1 3 1 1\n1 1 1 1 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 2 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 2 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"11 11 9 11\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 2 1\n1 1 1 1 1 1 1 1 3 1 1\n1 1 1 2 1 1 1 3 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1\n1 1 1 2 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 2 1 1\n3 3 3 3 3 3 3 3 3 2 2\n",
"5 5 2 2\n2 2 2 1 1\n2 1 2 2 2\n2 2 2 2 2\n1 2 2 2 2\n2 2 2 2 1\n2 1\n",
"4 6 5 7\n3 1 4 2 3 1\n3 2 2 2 5 5\n4 2 2 2 5 3\n3 2 2 1 4 3\n2 1 1 4 1 5 1\n"
],
"output": [
"8\n",
"4\n",
"9\n",
"14\n",
"9\n",
"6\n",
"6\n",
"14\n",
"9\n",
"7\n",
"8\n",
"4\n",
"16\n",
"13\n",
"6\n",
"14\n",
"14\n",
"14\n",
"14\n",
"14\n",
"9\n",
"14\n",
"14\n",
"7\n",
"14\n",
"14\n",
"9\n",
"14\n",
"9\n",
"8\n",
"14\n",
"14\n",
"14\n",
"14\n",
"8\n",
"14\n",
"14\n",
"14\n",
"7\n",
"14\n",
"14\n",
"14\n",
"14\n",
"8\n",
"8\n",
"8\n",
"7\n",
"7\n",
"9\n",
"14\n",
"9\n",
"8\n",
"14\n",
"14\n",
"8\n",
"7\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Dima loves Inna very much. He decided to write a song for her. Dima has a magic guitar with n strings and m frets. Dima makes the guitar produce sounds like that: to play a note, he needs to hold one of the strings on one of the frets and then pull the string. When Dima pulls the i-th string holding it on the j-th fret the guitar produces a note, let's denote it as aij. We know that Dima's guitar can produce k distinct notes. It is possible that some notes can be produced in multiple ways. In other words, it is possible that aij = apq at (i, j) ≠ (p, q).
Dima has already written a song — a sequence of s notes. In order to play the song, you need to consecutively produce the notes from the song on the guitar. You can produce each note in any available way. Dima understood that there are many ways to play a song and he wants to play it so as to make the song look as complicated as possible (try to act like Cobein).
We'll represent a way to play a song as a sequence of pairs (xi, yi) (1 ≤ i ≤ s), such that the xi-th string on the yi-th fret produces the i-th note from the song. The complexity of moving between pairs (x1, y1) and (x2, y2) equals <image> + <image>. The complexity of a way to play a song is the maximum of complexities of moving between adjacent pairs.
Help Dima determine the maximum complexity of the way to play his song! The guy's gotta look cool!
Input
The first line of the input contains four integers n, m, k and s (1 ≤ n, m ≤ 2000, 1 ≤ k ≤ 9, 2 ≤ s ≤ 105).
Then follow n lines, each containing m integers aij (1 ≤ aij ≤ k). The number in the i-th row and the j-th column (aij) means a note that the guitar produces on the i-th string and the j-th fret.
The last line of the input contains s integers qi (1 ≤ qi ≤ k) — the sequence of notes of the song.
Output
In a single line print a single number — the maximum possible complexity of the song.
Examples
Input
4 6 5 7
3 1 2 2 3 1
3 2 2 2 5 5
4 2 2 2 5 3
3 2 2 1 4 3
2 3 1 4 1 5 1
Output
8
Input
4 4 9 5
4 7 9 5
1 2 1 7
8 3 4 9
5 7 7 2
7 1 9 2 5
Output
4
### Input:
4 6 5 7
3 1 2 2 3 1
3 2 2 2 5 5
4 2 2 2 5 3
3 2 2 1 4 3
2 3 1 4 1 5 1
### Output:
8
### Input:
4 4 9 5
4 7 9 5
1 2 1 7
8 3 4 9
5 7 7 2
7 1 9 2 5
### Output:
4
### Code:
def solution() : # 最大的距离来自于角落附近的点
n,m,k,s = map(int, input().split())
dis = lambda a,b : abs(a[0] - b[0]) + abs(a[1] - b[1])
corner = [(0,0), (0,m-1), (n-1,0), (n-1,m-1)]
vertex = [[(n,m), (n,-1), (-1,m), (-1,-1)] for _ in range(k+1)]
for i in range(n) :
for j,note in enumerate(map(int, input().split())) :
vertex[note] = [
(i,j) if dis((i,j), c) < dis(v, c) else v
for v,c in zip(vertex[note], corner)]
maxdis = [[-1] * (k+1) for _ in range(k+1)]
pairs = [(0,3),(3,0),(1,2),(2,1)]
for i in range(1, k+1) :
for j in range(i, k+1) :
vi,vj = vertex[i],vertex[j]
maxdis[i][j] = max(dis(vi[a], vj[b]) for a,b in pairs)
maxdis[j][i] = maxdis[i][j]
s = list(map(int, input().split()))
print(max(maxdis[s[i]][s[i+1]] for i in range(len(s) - 1)))
solution() |
38_D. Vasya the Architect_3129 | Once Vasya played bricks. All the bricks in the set had regular cubical shape. Vasya vas a talented architect, however the tower he built kept falling apart.
Let us consider the building process. Vasya takes a brick and puts it on top of the already built tower so that the sides of the brick are parallel to the sides of the bricks he has already used. Let's introduce a Cartesian coordinate system on the horizontal plane, where Vasya puts the first brick. Then the projection of brick number i on the plane is a square with sides parallel to the axes of coordinates with opposite corners in points (xi, 1, yi, 1) and (xi, 2, yi, 2). The bricks are cast from homogeneous plastic and the weight of a brick a × a × a is a3 grams.
It is guaranteed that Vasya puts any brick except the first one on the previous one, that is the area of intersection of the upper side of the previous brick and the lower side of the next brick is always positive.
We (Vasya included) live in a normal world where the laws of physical statics work. And that is why, perhaps, if we put yet another brick, the tower will collapse under its own weight. Vasya puts the cubes consecutively one on top of the other until at least one cube loses the balance and falls down. If it happens, Vasya gets upset and stops the construction. Print the number of bricks in the maximal stable tower, that is the maximal number m satisfying the condition that all the towers consisting of bricks 1, 2, ..., k for every integer k from 1 to m remain stable.
Input
The first input file contains an integer n (1 ≤ n ≤ 100) which is the number of bricks. Each of the next n lines contains four numbers xi, 1, yi, 1, xi, 2, yi, 2 (xi, 1 ≠ xi, 2, |xi, 1 - xi, 2| = |yi, 1 - yi, 2|) which are the coordinates of the opposite angles of the base of the brick number i. The coordinates are integers and their absolute value does not exceed 50.
The cubes are given in the order Vasya puts them. It is guaranteed that the area of intersection of the upper side of the brick number i - 1 and the lower side of the brick number i is strictly strictly greater than zero for all i ≥ 2.
Output
Print the number of bricks in the maximal stable tower.
Examples
Input
2
0 0 3 3
1 0 4 3
Output
2
Input
2
0 0 3 3
2 0 5 3
Output
1
Input
3
0 0 3 3
1 0 4 3
2 0 5 3
Output
3 | a=[list(map(int,input().split())) for i in range(int(input()))]
n=len(a)
z=n
for i in range(n):
if i!=0:
c=[(a[i][0]+a[i][2])/2,(a[i][1]+a[i][3])/2]
m=abs(a[i][0]-a[i][2])**3
for j in range(i-1,-1,-1):
x1,y1,x2,y2=min(a[j][0],a[j][2]),min(a[j][1],a[j][3]),max(a[j][0],a[j][2]),max(a[j][1],a[j][3])
if not(x1<=c[0]<=x2 and y1<=c[1]<=y2):
z=i
break
x=c[0]+((a[j][0]+a[j][2])/2-c[0])*((abs(a[j][0]-a[j][2])**3)/(m+abs(a[j][0]-a[j][2])**3))
y=c[1]+((a[j][1]+a[j][3])/2-c[1])*((abs(a[j][0]-a[j][2])**3)/(m+abs(a[j][0]-a[j][2])**3))
c=[x,y]
m+=abs(a[j][0]-a[j][2])**3
if z!=n:
break
print(z) | {
"input": [
"3\n0 0 3 3\n1 0 4 3\n2 0 5 3\n",
"2\n0 0 3 3\n1 0 4 3\n",
"2\n0 0 3 3\n2 0 5 3\n",
"7\n4 6 1 9\n-1 4 6 11\n8 13 -3 2\n-5 0 45 50\n-2 50 45 3\n45 50 -4 1\n45 50 -1 4\n",
"11\n12 12 -12 -12\n11 8 -11 -14\n-15 -11 -3 1\n-16 -3 -14 -1\n-7 -8 -21 6\n37 -6 -19 50\n-21 -12 41 50\n48 -13 -15 50\n48 -14 -16 50\n-21 -18 47 50\n40 50 -15 -5\n",
"20\n9 -3 16 4\n11 2 14 -1\n6 -6 19 7\n16 -3 9 4\n5 -7 50 38\n50 38 5 -7\n50 38 12 0\n50 38 11 -1\n10 38 50 -2\n5 -7 50 38\n50 38 7 -5\n50 38 10 -2\n50 38 12 0\n50 38 10 -2\n10 38 50 -2\n50 -5 7 38\n50 -7 5 38\n11 -1 50 38\n10 -2 50 38\n7 -5 50 38\n",
"10\n-7 7 7 -7\n-8 -11 8 5\n-1 -1 1 1\n-2 1 2 -3\n-12 -12 10 10\n47 50 3 6\n46 5 1 50\n50 50 -10 -10\n-9 50 50 -9\n-6 -6 50 50\n",
"20\n-1 -1 1 1\n-2 -2 2 2\n12 -12 -12 12\n8 -6 -10 12\n-11 47 50 -14\n43 50 -10 -3\n45 50 -12 -7\n50 46 -4 -8\n50 49 -16 -17\n-9 -4 45 50\n-14 50 50 -14\n47 50 2 5\n47 -5 -8 50\n50 47 -7 -10\n43 50 1 8\n-5 50 48 -3\n50 47 -5 -8\n-6 9 35 50\n-15 50 45 -10\n-10 50 45 -5\n",
"20\n-6 -6 6 6\n-15 -10 5 10\n-6 5 4 -5\n1 -3 -1 -5\n4 -9 -4 -1\n-1 2 5 -4\n12 -15 -10 7\n-14 7 8 -15\n50 45 -5 -10\n11 -14 50 25\n50 -14 -5 41\n-8 43 50 -15\n-10 -17 50 43\n50 -18 -11 43\n50 48 -2 -4\n0 39 50 -11\n-7 43 50 -14\n-6 -13 50 43\n50 43 -2 -9\n50 -16 -9 43\n",
"15\n-9 -9 9 9\n-2 -18 16 0\n15 -3 5 -13\n6 -7 4 -9\n17 4 -7 -20\n6 -15 4 -17\n50 -18 3 29\n50 -22 -1 29\n-3 -23 50 30\n-6 -26 50 30\n50 -26 -5 29\n50 21 11 -18\n50 23 6 -21\n50 28 6 -16\n50 -24 -3 29\n",
"8\n-2 2 2 -2\n-2 6 6 -2\n5 -2 -1 4\n9 -7 -9 11\n13 10 -9 -12\n-10 -16 50 44\n32 50 -15 3\n-13 50 34 3\n",
"20\n10 10 -10 -10\n-8 7 10 -11\n-4 -21 20 3\n14 -2 4 -12\n-2 2 22 -22\n-8 3 14 -19\n-7 5 13 -15\n1 -13 17 3\n11 -7 19 1\n0 5 24 -19\n21 -4 7 10\n-2 -7 22 17\n19 7 23 11\n14 -2 30 14\n12 13 28 -3\n50 7 16 41\n50 40 12 2\n6 41 50 -3\n50 40 0 -10\n4 39 50 -7\n",
"7\n-9 9 9 -9\n10 -5 8 -7\n7 -6 9 -8\n20 5 -2 -17\n8 -15 10 -17\n50 25 3 -22\n50 28 7 -15\n",
"1\n0 0 1 1\n",
"11\n-4 4 4 -4\n-2 -3 0 -5\n-8 -10 6 4\n-12 6 8 -14\n-4 -12 12 4\n-1 -11 1 -9\n-5 -14 5 -4\n-11 2 11 -20\n10 -10 12 -8\n7 -12 13 -6\n-6 41 50 -15\n",
"6\n-5 5 5 -5\n9 7 -3 -5\n4 0 -8 12\n-7 2 -9 0\n-9 -1 -5 3\n42 -9 -17 50\n",
"15\n-8 11 1 20\n-5 14 -2 17\n-1 18 -6 13\n0 19 -7 12\n-5 14 -2 17\n-11 8 4 23\n-2 14 -5 17\n2 21 -9 10\n-12 24 5 7\n-10 22 3 9\n31 50 -11 8\n-8 11 31 50\n-7 50 31 12\n-7 12 31 50\n-10 9 31 50\n",
"7\n1 1 -1 -1\n6 7 -6 -5\n10 -11 -12 11\n-12 -11 49 50\n-7 43 50 -14\n-17 50 37 -4\n-14 50 47 -11\n",
"15\n5 16 -6 27\n28 21 -1 50\n-2 20 28 50\n28 14 -8 50\n28 19 -3 50\n-2 50 28 20\n-5 17 28 50\n-7 15 28 50\n-4 50 28 18\n28 50 -1 21\n-3 50 28 19\n-4 50 28 18\n28 50 -8 14\n28 50 -6 16\n28 15 -7 50\n",
"10\n-9 -14 -1 -6\n-2 -13 -8 -7\n0 -15 -10 -5\n0 -15 -10 -5\n-11 -4 1 -16\n-8 -13 -2 -7\n1 -16 -11 -4\n-13 -2 3 -18\n-11 -16 1 -4\n-13 -18 3 -2\n",
"7\n-9 -9 9 9\n-8 3 0 -5\n-16 -8 6 14\n14 -11 -6 9\n5 -5 1 -9\n-11 -21 13 3\n-10 5 10 -15\n",
"5\n-6 6 6 -6\n7 -8 -5 4\n12 -11 2 -1\n50 39 -1 -12\n-3 -16 50 37\n",
"20\n12 23 -1 10\n12 23 -1 10\n11 22 0 11\n7 18 4 15\n12 10 -1 23\n9 20 2 13\n1 21 10 12\n0 11 11 22\n39 50 2 13\n3 14 39 50\n39 10 -1 50\n4 15 39 50\n39 50 4 15\n39 50 -2 9\n39 50 1 12\n-2 9 39 50\n2 50 39 13\n0 11 39 50\n-2 9 39 50\n1 12 39 50\n",
"8\n-7 -7 7 7\n-1 -5 -3 -3\n5 4 -11 -12\n8 -4 2 -10\n3 -5 1 -3\n10 -15 -10 5\n7 -14 -11 4\n-2 -10 50 42\n",
"15\n-7 -7 7 7\n-10 -16 14 8\n13 -12 5 -4\n12 -6 4 -14\n3 -17 17 -3\n21 -11 7 3\n14 0 2 -12\n-3 0 17 -20\n-2 -12 18 8\n9 -14 13 -10\n7 -15 50 28\n0 -20 50 30\n50 -14 6 30\n-4 -21 50 33\n50 33 -3 -20\n",
"20\n26 16 11 1\n11 1 26 16\n23 4 14 13\n13 14 24 3\n20 10 17 7\n25 15 12 2\n16 6 21 11\n25 15 12 2\n10 0 27 17\n22 12 15 5\n23 4 14 13\n22 5 15 12\n25 2 12 15\n12 15 25 2\n22 12 15 5\n22 5 15 12\n21 11 16 6\n26 16 11 1\n17 7 20 10\n24 3 13 14\n",
"5\n6 -2 13 -9\n17 2 2 -13\n13 -2 6 -9\n4 0 15 -11\n8 -7 11 -4\n",
"15\n1 1 -1 -1\n50 -8 -7 49\n45 50 0 5\n49 50 -8 -7\n-11 50 49 -10\n0 9 41 50\n50 50 -6 -6\n-1 46 50 -5\n1 49 50 0\n50 -8 -8 50\n7 41 50 -2\n-9 50 50 -9\n50 10 10 50\n9 41 50 0\n-4 -5 50 49\n",
"7\n24 6 11 -7\n23 -6 12 5\n16 -2 19 1\n13 4 22 -5\n12 -6 23 5\n13 32 50 -5\n50 32 11 -7\n",
"1\n-50 -50 50 50\n",
"20\n-10 17 -4 11\n1 22 -15 6\n-5 12 -9 16\n-9 16 -5 12\n-2 19 -12 9\n-10 17 -4 11\n-8 13 -6 15\n-5 12 -9 16\n-3 18 -11 10\n-1 20 -13 8\n29 9 -12 50\n29 50 -11 10\n29 9 -12 50\n29 50 -10 11\n-14 50 29 7\n-9 12 29 50\n-14 7 29 50\n29 9 -12 50\n-11 10 29 50\n-11 50 29 10\n",
"10\n27 -3 15 9\n18 0 24 6\n28 -4 14 10\n19 1 23 5\n27 -3 15 9\n19 32 50 1\n50 32 14 -4\n19 32 50 1\n15 32 50 -3\n16 -2 50 32\n",
"6\n-9 -9 9 9\n-16 9 0 -7\n7 8 -17 -16\n49 -18 -19 50\n-19 49 50 -20\n50 -17 -14 47\n",
"20\n-9 -9 9 9\n0 4 14 -10\n8 -7 10 -9\n6 -5 10 -9\n1 -2 15 -16\n20 3 0 -17\n1 -10 11 0\n-2 -18 16 0\n-1 0 17 -18\n2 1 20 -17\n50 42 -1 -9\n50 35 -1 -16\n-1 -15 50 36\n50 49 -3 -4\n50 40 -7 -17\n50 40 -8 -18\n-3 -10 50 43\n-7 -17 50 40\n-3 -13 50 40\n2 46 50 -2\n",
"15\n-14 27 -1 14\n-10 23 -5 18\n1 29 -16 12\n-9 19 -6 22\n-10 18 -5 23\n-4 17 -11 24\n22 50 -13 15\n-13 50 22 15\n22 50 -11 17\n-9 19 22 50\n-10 18 22 50\n22 19 -9 50\n-14 14 22 50\n-14 14 22 50\n-11 17 22 50\n",
"7\n-2 23 -10 15\n2 11 -14 27\n-12 25 0 13\n-8 17 -4 21\n1 26 -13 12\n-8 17 -4 21\n-7 20 -5 18\n",
"8\n12 -12 -12 12\n1 13 -13 -1\n-18 0 2 20\n31 -1 -20 50\n29 50 -30 -9\n-15 -9 44 50\n-21 -14 43 50\n45 50 -16 -11\n",
"5\n7 -10 -8 5\n4 -7 -5 2\n2 -5 -3 0\n-9 48 50 -11\n50 -4 -2 48\n",
"5\n-12 12 12 -12\n4 -12 8 -8\n10 -5 2 -13\n12 -5 -2 -19\n-7 -18 15 4\n",
"10\n-7 -7 7 7\n-16 -18 6 4\n-12 -8 4 8\n5 -13 -7 -1\n5 4 -13 -14\n7 11 -13 -9\n4 10 8 6\n8 6 0 14\n7 7 9 5\n-2 -9 16 9\n",
"11\n12 12 -12 -12\n11 13 -11 -14\n-15 -11 -3 1\n-16 -3 -14 -1\n-7 -8 -21 6\n37 -6 -19 50\n-21 -12 41 50\n48 -13 -15 50\n48 -14 -16 50\n-21 -18 47 50\n40 50 -15 -5\n",
"10\n-7 7 7 -7\n-8 -20 8 5\n-1 -1 1 1\n-2 1 2 -3\n-12 -12 10 10\n47 50 3 6\n46 5 1 50\n50 50 -10 -10\n-9 50 50 -9\n-6 -6 50 50\n",
"20\n-6 -6 6 6\n-15 -10 5 10\n-6 5 4 -5\n1 -3 -1 -5\n4 -9 -4 -1\n-1 2 5 -4\n12 -15 -10 7\n-14 7 8 -15\n50 45 -5 -10\n11 -14 50 25\n50 -14 -5 41\n-8 43 50 -15\n-10 -17 50 43\n50 -18 -11 43\n50 48 -2 -4\n0 39 50 -11\n-7 8 50 -14\n-6 -13 50 43\n50 43 -2 -9\n50 -16 -9 43\n",
"8\n-2 2 2 -2\n-2 6 6 -2\n5 -2 -1 4\n0 -7 -9 11\n13 10 -9 -12\n-10 -16 50 44\n32 50 -15 3\n-13 50 34 3\n",
"20\n10 10 -10 -10\n-8 7 10 -11\n-4 -21 20 3\n14 -2 4 -12\n-2 2 22 -22\n-8 3 14 -19\n-7 5 13 -15\n1 -13 17 3\n11 -7 19 1\n0 5 24 -19\n21 -4 7 10\n-2 -7 22 17\n19 7 23 11\n14 -2 30 14\n12 13 28 -3\n50 7 27 41\n50 40 12 2\n6 41 50 -3\n50 40 0 -10\n4 39 50 -7\n",
"1\n0 0 2 1\n",
"11\n-4 4 4 -4\n-2 -3 0 -5\n-8 -10 6 4\n-12 6 8 -14\n-4 -12 12 4\n-1 -11 1 -9\n-5 -14 5 -4\n-11 2 11 -20\n10 -10 12 -8\n7 -12 13 -4\n-6 41 50 -15\n",
"10\n-9 -14 0 -6\n-2 -13 -8 -7\n0 -15 -10 -5\n0 -15 -10 -5\n-11 -4 1 -16\n-8 -13 -2 -7\n1 -16 -11 -4\n-13 -2 3 -18\n-11 -16 1 -4\n-13 -18 3 -2\n",
"7\n-9 -9 9 9\n-8 3 0 -5\n-16 -8 6 14\n14 -11 -6 9\n5 -5 1 -9\n-11 -21 22 3\n-10 5 10 -15\n",
"5\n-6 6 6 -6\n7 -8 -5 4\n12 -11 4 -1\n50 39 -1 -12\n-3 -16 50 37\n",
"20\n26 16 11 1\n11 1 26 16\n23 4 14 13\n13 14 24 3\n20 10 17 7\n25 15 12 2\n16 6 21 11\n25 15 12 2\n10 0 27 17\n22 12 15 5\n23 4 13 13\n22 5 15 12\n25 2 12 15\n12 15 25 2\n22 12 15 5\n22 5 15 12\n21 11 16 6\n26 16 11 1\n17 7 20 10\n24 3 13 14\n",
"5\n6 0 13 -9\n17 2 2 -13\n13 -2 6 -9\n4 0 15 -11\n8 -7 11 -4\n",
"20\n-9 -9 9 9\n0 4 14 -10\n8 -7 10 -9\n6 -5 10 -9\n1 -2 15 -16\n20 3 0 -17\n1 -10 11 0\n-2 -18 16 0\n-1 0 17 -18\n2 1 20 -17\n50 42 -1 -9\n50 35 -1 -16\n-1 -15 50 36\n50 49 -3 -4\n50 40 -7 -17\n50 40 -8 -18\n-3 -10 50 43\n-7 -17 50 40\n-3 -13 50 40\n2 46 50 -3\n",
"10\n-7 -7 7 7\n-16 -6 6 4\n-12 -8 4 8\n5 -13 -7 -1\n5 4 -13 -14\n7 11 -13 -9\n4 10 8 6\n8 6 0 14\n7 7 9 5\n-2 -9 16 9\n",
"2\n0 0 4 3\n1 0 4 3\n",
"20\n2 -3 16 4\n11 2 14 -1\n6 -6 19 7\n16 -3 9 4\n5 -7 50 38\n50 38 5 -7\n50 38 12 0\n50 38 11 -1\n10 38 50 -2\n5 -7 50 38\n50 38 7 -5\n50 38 10 -2\n50 38 12 0\n50 38 10 -2\n10 38 50 -2\n50 -5 7 38\n50 -7 5 38\n11 -1 50 38\n10 -2 50 38\n7 -5 50 38\n",
"20\n-1 -1 1 1\n-2 -2 2 2\n12 -12 -12 12\n8 -6 -10 12\n-11 47 50 -14\n43 50 -10 -3\n8 50 -12 -7\n50 46 -4 -8\n50 49 -16 -17\n-9 -4 45 50\n-14 50 50 -14\n47 50 2 5\n47 -5 -8 50\n50 47 -7 -10\n43 50 1 8\n-5 50 48 -3\n50 47 -5 -8\n-6 9 35 50\n-15 50 45 -10\n-10 50 45 -5\n",
"7\n-9 9 9 -9\n10 -5 8 -7\n7 -6 9 -8\n20 5 -2 -31\n8 -15 10 -17\n50 25 3 -22\n50 28 7 -15\n",
"6\n-5 5 5 -5\n9 7 -3 -5\n4 0 -8 12\n-7 2 -9 0\n-9 -1 -2 3\n42 -9 -17 50\n",
"7\n1 1 -1 -1\n6 7 -6 -5\n10 -11 -12 11\n-12 -11 49 50\n-7 43 50 -14\n-17 50 37 -4\n-8 50 47 -11\n",
"15\n5 16 -6 27\n28 21 -1 50\n-2 20 28 50\n28 14 -8 50\n28 19 -3 50\n-2 50 28 20\n-5 17 28 50\n-7 15 28 50\n-4 50 28 18\n28 50 -1 21\n-3 50 28 19\n-4 50 28 18\n21 50 -8 14\n28 50 -6 16\n28 15 -7 50\n",
"20\n12 23 -1 10\n12 23 -1 10\n11 22 0 11\n7 18 4 15\n12 10 -1 23\n9 20 2 13\n1 21 10 12\n0 11 11 22\n39 50 2 13\n3 14 39 50\n39 10 -1 50\n4 15 39 50\n39 50 4 15\n39 50 -2 9\n39 50 1 12\n-2 9 39 50\n2 50 39 13\n0 11 39 87\n-2 9 39 50\n1 12 39 50\n",
"8\n-7 -7 7 7\n-1 -5 -5 -3\n5 4 -11 -12\n8 -4 2 -10\n3 -5 1 -3\n10 -15 -10 5\n7 -14 -11 4\n-2 -10 50 42\n",
"15\n1 1 -1 -1\n50 -8 -7 49\n45 50 0 5\n49 50 -8 -7\n-11 50 49 -10\n0 9 41 50\n50 50 -6 -6\n-1 46 50 -5\n1 49 50 0\n50 -8 -8 50\n7 41 50 -2\n-9 50 50 -9\n50 10 10 50\n9 41 50 0\n-4 -2 50 49\n",
"7\n24 6 11 -7\n23 -6 12 5\n16 -2 19 1\n13 4 22 -5\n12 -6 23 5\n13 32 50 -5\n50 32 11 -6\n",
"1\n-50 -93 50 50\n",
"10\n27 -3 15 9\n18 0 24 6\n28 -4 14 10\n19 1 23 5\n27 -3 15 9\n19 32 50 1\n10 32 14 -4\n19 32 50 1\n15 32 50 -3\n16 -2 50 32\n",
"6\n-9 -3 9 9\n-16 9 0 -7\n7 8 -17 -16\n49 -18 -19 50\n-19 49 50 -20\n50 -17 -14 47\n",
"8\n12 -12 -12 12\n1 13 -13 -1\n-18 0 2 20\n31 -1 -20 50\n29 50 -30 -9\n-15 -2 44 50\n-21 -14 43 50\n45 50 -16 -11\n",
"5\n7 -10 -8 5\n4 -7 -5 2\n2 -5 -3 0\n-9 48 50 -14\n50 -4 -2 48\n",
"5\n-12 12 12 -23\n4 -12 8 -8\n10 -5 2 -13\n12 -5 -2 -19\n-7 -18 15 4\n",
"11\n12 12 -12 -12\n11 13 -11 -14\n-15 -11 -3 1\n-16 -3 -14 -1\n-7 -8 -21 6\n37 -6 -19 50\n-21 -3 41 50\n48 -13 -15 50\n48 -14 -16 50\n-21 -18 47 50\n40 50 -15 -5\n",
"20\n2 -3 16 4\n11 2 14 -1\n6 -6 19 7\n16 -3 9 4\n5 -7 50 38\n50 38 5 -7\n50 38 12 0\n50 38 11 -1\n10 38 50 -2\n5 -7 50 38\n50 38 7 -5\n50 38 10 -2\n50 46 12 0\n50 38 10 -2\n10 38 50 -2\n50 -5 7 38\n50 -7 5 38\n11 -1 50 38\n10 -2 50 38\n7 -5 50 38\n",
"10\n-7 7 7 -1\n-8 -20 8 5\n-1 -1 1 1\n-2 1 2 -3\n-12 -12 10 10\n47 50 3 6\n46 5 1 50\n50 50 -10 -10\n-9 50 50 -9\n-6 -6 50 50\n",
"20\n-1 -1 1 1\n-2 -2 2 2\n12 -12 -12 12\n8 -6 -10 12\n-11 47 50 -14\n43 50 -10 -3\n8 50 -12 -7\n50 46 -4 -8\n50 49 -16 -17\n-9 -4 45 50\n-14 50 50 -14\n47 50 2 5\n47 -5 -8 50\n50 47 -7 -10\n43 50 1 7\n-5 50 48 -3\n50 47 -5 -8\n-6 9 35 50\n-15 50 45 -10\n-10 50 45 -5\n",
"20\n-6 -6 6 6\n-15 -10 5 10\n-6 5 4 -5\n1 -3 -1 -5\n4 -9 -4 -1\n-1 2 5 -4\n12 -15 -10 7\n-14 7 8 -15\n50 45 -5 -10\n11 -14 50 25\n50 -14 -5 41\n-8 43 50 -15\n-10 -22 50 43\n50 -18 -11 43\n50 48 -2 -4\n0 39 50 -11\n-7 8 50 -14\n-6 -13 50 43\n50 43 -2 -9\n50 -16 -9 43\n",
"20\n10 10 -10 -10\n-8 7 10 -11\n-4 -21 20 3\n14 -2 4 -12\n-2 2 22 -22\n-8 3 14 -19\n-7 5 13 -15\n1 -13 17 3\n11 -7 19 1\n0 5 24 -19\n21 -4 7 10\n-2 -7 22 17\n19 7 23 11\n14 -2 30 7\n12 13 28 -3\n50 7 27 41\n50 40 12 2\n6 41 50 -3\n50 40 0 -10\n4 39 50 -7\n",
"7\n-9 9 9 -17\n10 -5 8 -7\n7 -6 9 -8\n20 5 -2 -31\n8 -15 10 -17\n50 25 3 -22\n50 28 7 -15\n",
"1\n0 0 4 1\n",
"6\n-5 5 5 -5\n9 7 -3 -5\n5 0 -8 12\n-7 2 -9 0\n-9 -1 -2 3\n42 -9 -17 50\n",
"7\n1 1 -1 -1\n12 7 -6 -5\n10 -11 -12 11\n-12 -11 49 50\n-7 43 50 -14\n-17 50 37 -4\n-8 50 47 -11\n",
"15\n5 16 -6 27\n28 21 -1 50\n-2 20 28 50\n28 14 -8 50\n28 19 -3 50\n-2 50 28 20\n-5 17 28 50\n-7 15 28 50\n-4 50 28 18\n28 50 -1 21\n-3 50 28 19\n-4 50 28 18\n21 50 -8 14\n28 50 -6 16\n26 15 -7 50\n",
"7\n-9 -9 9 14\n-8 3 0 -5\n-16 -8 6 14\n14 -11 -6 9\n5 -5 1 -9\n-11 -21 22 3\n-10 5 10 -15\n"
],
"output": [
"3",
"2",
"1",
"3",
"4",
"4",
"5",
"4",
"8",
"6",
"5",
"13",
"5",
"1",
"6",
"5",
"10",
"3",
"1",
"10",
"6",
"3",
"8",
"5",
"10",
"20",
"5",
"1",
"5",
"1",
"10",
"5",
"3",
"10",
"6",
"7",
"3",
"3",
"5",
"9",
"4\n",
"1\n",
"8\n",
"3\n",
"13\n",
"1",
"6\n",
"10",
"5\n",
"2\n",
"20",
"5",
"10\n",
"9\n",
"2",
"4\n",
"4\n",
"3\n",
"4\n",
"3\n",
"1\n",
"8\n",
"5\n",
"1\n",
"5\n",
"1",
"5\n",
"3\n",
"3\n",
"3\n",
"5",
"4\n",
"4\n",
"1\n",
"4\n",
"8\n",
"13\n",
"3\n",
"1",
"4\n",
"1\n",
"1\n",
"5\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Once Vasya played bricks. All the bricks in the set had regular cubical shape. Vasya vas a talented architect, however the tower he built kept falling apart.
Let us consider the building process. Vasya takes a brick and puts it on top of the already built tower so that the sides of the brick are parallel to the sides of the bricks he has already used. Let's introduce a Cartesian coordinate system on the horizontal plane, where Vasya puts the first brick. Then the projection of brick number i on the plane is a square with sides parallel to the axes of coordinates with opposite corners in points (xi, 1, yi, 1) and (xi, 2, yi, 2). The bricks are cast from homogeneous plastic and the weight of a brick a × a × a is a3 grams.
It is guaranteed that Vasya puts any brick except the first one on the previous one, that is the area of intersection of the upper side of the previous brick and the lower side of the next brick is always positive.
We (Vasya included) live in a normal world where the laws of physical statics work. And that is why, perhaps, if we put yet another brick, the tower will collapse under its own weight. Vasya puts the cubes consecutively one on top of the other until at least one cube loses the balance and falls down. If it happens, Vasya gets upset and stops the construction. Print the number of bricks in the maximal stable tower, that is the maximal number m satisfying the condition that all the towers consisting of bricks 1, 2, ..., k for every integer k from 1 to m remain stable.
Input
The first input file contains an integer n (1 ≤ n ≤ 100) which is the number of bricks. Each of the next n lines contains four numbers xi, 1, yi, 1, xi, 2, yi, 2 (xi, 1 ≠ xi, 2, |xi, 1 - xi, 2| = |yi, 1 - yi, 2|) which are the coordinates of the opposite angles of the base of the brick number i. The coordinates are integers and their absolute value does not exceed 50.
The cubes are given in the order Vasya puts them. It is guaranteed that the area of intersection of the upper side of the brick number i - 1 and the lower side of the brick number i is strictly strictly greater than zero for all i ≥ 2.
Output
Print the number of bricks in the maximal stable tower.
Examples
Input
2
0 0 3 3
1 0 4 3
Output
2
Input
2
0 0 3 3
2 0 5 3
Output
1
Input
3
0 0 3 3
1 0 4 3
2 0 5 3
Output
3
### Input:
3
0 0 3 3
1 0 4 3
2 0 5 3
### Output:
3
### Input:
2
0 0 3 3
1 0 4 3
### Output:
2
### Code:
a=[list(map(int,input().split())) for i in range(int(input()))]
n=len(a)
z=n
for i in range(n):
if i!=0:
c=[(a[i][0]+a[i][2])/2,(a[i][1]+a[i][3])/2]
m=abs(a[i][0]-a[i][2])**3
for j in range(i-1,-1,-1):
x1,y1,x2,y2=min(a[j][0],a[j][2]),min(a[j][1],a[j][3]),max(a[j][0],a[j][2]),max(a[j][1],a[j][3])
if not(x1<=c[0]<=x2 and y1<=c[1]<=y2):
z=i
break
x=c[0]+((a[j][0]+a[j][2])/2-c[0])*((abs(a[j][0]-a[j][2])**3)/(m+abs(a[j][0]-a[j][2])**3))
y=c[1]+((a[j][1]+a[j][3])/2-c[1])*((abs(a[j][0]-a[j][2])**3)/(m+abs(a[j][0]-a[j][2])**3))
c=[x,y]
m+=abs(a[j][0]-a[j][2])**3
if z!=n:
break
print(z) |
40_C. Berland Square_3133 | Last year the world's largest square was built in Berland. It is known that the square can be represented as an infinite plane with an introduced Cartesian system of coordinates. On that square two sets of concentric circles were painted. Let's call the set of concentric circles with radii 1, 2, ..., K and the center in the point (z, 0) a (K, z)-set. Thus, on the square were painted a (N, x)-set and a (M, y)-set. You have to find out how many parts those sets divided the square into.
Input
The first line contains integers N, x, M, y. (1 ≤ N, M ≤ 100000, - 100000 ≤ x, y ≤ 100000, x ≠ y).
Output
Print the sought number of parts.
Examples
Input
1 0 1 1
Output
4
Input
1 0 1 2
Output
3
Input
3 3 4 7
Output
17
Note
Picture for the third sample:
<image> | def readGen(trans):
while 1:
for x in input().split():
yield(trans(x))
readint=readGen(int)
[N,x,M,y]=(next(readint) for i in range(4))
d=abs(y-x)
def interval(a,b): return range(a,b+1)
def case1(N,M,d): # d>=N
ans=0
for r in interval(1, min(M,d-N)):
ans+=1
if (M<=d-N):
return ans
for r in interval(d-N+1, min(M,d)):
ans+=2*(N+r-d)
if (M<=d):
return ans
for r in interval(d+1,min(M,d+N)):
ans+=2*(d+N-r+1)
if (M<=d+N):
return ans
for r in interval(d+N+1,M):
ans+=1
return ans
def partA(N,M,d):
ans=0
for r in interval(1,min(M,d)):
ans+=2*r-1
if (M<d+1):
return ans
for r in interval(d+1,min(M,2*d)):
ans+=2*(2*d-r)+1
return ans
def partB(N,M,d):
ans=0
bound1=min(2*d,N-d)
for r in interval(1,min(M,bound1)):
ans+=2*(r-1)+1
if (M<=bound1):
return ans
if (2*d<=N-d):
for r in interval(bound1+1,min(M,N-d)):
ans+=4*d
if (M<=N-d):
return ans
if (2*d>N-d):
for r in interval(bound1+1,min(M,2*d)):
ans+=2*(N-d)+1
if (M<=2*d):
return ans
bound2=max(2*d,N-d)
for r in interval(bound2+1,min(M,d+N)):
ans+=2*(d+N-r)+2
if (M<=d+N):
return ans
for r in interval(d+N+1,M):
ans+=1
return ans
def case2(N,M,d): # d<N
return partA(N,M,d)+partB(N,M,d)
def remain(N,M,d):
if (M>=d+N):
return 1
if (M>d):
return d+N-M+1
if (M<=d):
return N+1
def calc(N,M,d):
if (N<=d): return remain(N,M,d)+case1(N,M,d)
else: return remain(N,M,d)+case2(N,M,d)
print(calc(N,M,d))
| {
"input": [
"3 3 4 7\n",
"1 0 1 2\n",
"1 0 1 1\n",
"99085 7738 98097 -6487\n",
"1 2 2 1\n",
"93430 5720 93581 -2371\n",
"97530 -7728 92184 -755\n",
"93564 -4520 99118 -52061\n",
"100000 100 100000 70000\n",
"98405 -62879 99461 -33688\n",
"5 4 3 -2\n",
"93564 8371 99118 6409\n",
"91125 7374 92925 -5261\n",
"98445 19337 99881 -95888\n",
"96533 -7124 93876 6985\n",
"1 3 3 1\n",
"100000 0 100000 1\n",
"100000 50000 100000 -50000\n",
"98445 3623 99881 46\n",
"91125 -66336 92925 63094\n",
"1 -100000 1 100000\n",
"1 100000 1 99999\n",
"99085 -95516 98097 8735\n",
"98405 9100 99461 7679\n",
"91805 28117 90481 -94484\n",
"1 0 2 3\n",
"2 2 2 3\n",
"100000 99999 88888 77777\n",
"99442 76614 99268 94414\n",
"5 5 10 10\n",
"4 7 3 3\n",
"5 7 1 2\n",
"10 -10 5 -5\n",
"99765 -1063 95654 -21753\n",
"91436 -81744 96964 75017\n",
"2 4 5 -4\n",
"2 1 4 -7\n",
"5 2 1 -5\n",
"3 -9 3 4\n",
"100000 -100000 100000 100000\n",
"2 -4 1 9\n",
"100000 100000 100000 99999\n",
"100000 100000 100000 -100000\n",
"1 -1 5 -10\n",
"99999 100000 100000 -100000\n",
"90438 -5027 97577 4568\n",
"95017 -8444 95084 7736\n",
"94427 90088 92968 -81169\n",
"4 4 2 2\n",
"99442 -702 99268 -7694\n",
"94427 1396 92968 9890\n",
"93430 32810 93581 -71470\n",
"91805 9733 90481 574\n",
"99765 -9904 95654 3069\n",
"100000 0 100000 100000\n",
"94244 7010 97753 -7757\n",
"97448 -37940 91572 -86189\n",
"1 0 100000 1\n",
"92433 -9956 95272 5368\n",
"92433 -24467 95272 -61772\n",
"97448 7948 91572 7786\n",
"91436 -5631 96964 -3172\n",
"90444 8736 94289 8904\n",
"2 2 4 4\n",
"90438 -66110 97577 84716\n",
"2 -6 4 6\n",
"94244 -37156 97753 -9638\n",
"94925 5648 96389 1799\n",
"90444 -33699 94289 20670\n",
"3 7 4 1\n",
"94925 -69793 96389 -40126\n",
"100000 0 100000 -1\n",
"1 0 1 100\n",
"158953 7738 98097 -6487\n",
"150185 5720 93581 -2371\n",
"97530 -7728 80028 -755\n",
"23342 -4520 99118 -52061\n",
"100000 110 100000 70000\n",
"98405 -62879 99461 -17596\n",
"5 8 3 -2\n",
"93564 15176 99118 6409\n",
"61389 7374 92925 -5261\n",
"98445 19337 74939 -95888\n",
"96533 -4138 93876 6985\n",
"100000 0 110000 1\n",
"100000 67662 100000 -50000\n",
"98445 1931 99881 46\n",
"91125 -7085 92925 63094\n",
"1 -100000 2 100000\n",
"1 000000 1 99999\n",
"99085 -95516 149930 8735\n",
"144770 9100 99461 7679\n",
"91805 28117 90481 -7973\n",
"1 0 2 2\n",
"99442 76614 99268 124626\n",
"5 5 10 3\n",
"7 7 3 3\n",
"5 0 1 2\n",
"5 -10 5 -5\n",
"17797 -1063 95654 -21753\n",
"91436 -81744 96964 95191\n",
"5 2 1 -7\n",
"100000 -100000 100001 100000\n",
"101000 100000 100000 99999\n",
"100000 100000 110000 -100000\n",
"99999 100000 100001 -100000\n",
"90438 -5027 73706 4568\n",
"82210 -8444 95084 7736\n",
"94427 90088 104237 -81169\n",
"4 5 2 2\n",
"96816 -702 99268 -7694\n",
"94427 1680 92968 9890\n",
"93430 13409 93581 -71470\n",
"91805 9733 124211 574\n",
"99765 -9904 85598 3069\n",
"94244 7010 146581 -7757\n",
"97448 -37940 91572 -160015\n",
"1 0 100000 2\n",
"92433 -9956 95272 855\n",
"92433 -24467 95272 -64603\n",
"176285 7948 91572 7786\n",
"91436 -3659 96964 -3172\n",
"2 2 2 4\n",
"2 2 5 -4\n",
"3 1 4 -7\n",
"3 -5 3 4\n",
"2 -4 0 9\n",
"1 -1 5 -20\n"
],
"output": [
" 17\n",
" 3\n",
" 4\n",
"5001828332\n",
" 5\n",
"2829812541\n",
"2471317488\n",
"11509398048\n",
"13302109801\n",
"8994412616\n",
" 13\n",
" 726598901\n",
"4168799096\n",
"6905974528\n",
"4768738089\n",
" 6\n",
" 400000\n",
"10000200001\n",
" 1378384476\n",
"2983528451\n",
" 3\n",
" 4\n",
"8636367944\n",
" 555165156\n",
"3562481512\n",
" 4\n",
" 8\n",
"6790054321\n",
"6123561325\n",
" 61\n",
" 17\n",
" 8\n",
" 61\n",
"6785350980\n",
" 1001214722\n",
" 8\n",
" 7\n",
" 7\n",
" 7\n",
" 200001\n",
" 4\n",
" 400000\n",
" 200001\n",
" 7\n",
" 200000\n",
"3280869645\n",
"5366319032\n",
" 260622440\n",
" 13\n",
"2632080157\n",
"2964910460\n",
"6844605373\n",
"3085718448\n",
"4548570813\n",
"10000200001\n",
"5003962985\n",
"11221723080\n",
" 100003\n",
"5040278640\n",
"9821695665\n",
" 59292207\n",
" 887279122\n",
" 60725934\n",
" 13\n",
" 1383209737\n",
" 7\n",
"8282767876\n",
" 1426155172\n",
"11204857185\n",
" 9\n",
"8708948248\n",
" 400000\n",
"3\n",
"5177093132\n",
"2897791618\n",
"2134919994\n",
"1089797047\n",
"13302303481\n",
"11767257320\n",
"9\n",
"3117075940\n",
"2783357782\n",
"3382642666\n",
"3857637825\n",
"410000\n",
"6779746245\n",
"734971020\n",
"11054514136\n",
"4\n",
"3\n",
"16783676951\n",
"561344573\n",
"9248258385\n",
"5\n",
"12165538357\n",
"40\n",
"26\n",
"8\n",
"36\n",
"633562073\n",
"131634626\n",
"7\n",
"200003\n",
"401000\n",
"100210001\n",
"200001\n",
"2644734558\n",
"4786149125\n",
"751342314\n",
"13\n",
"2589376145\n",
"2872701340\n",
"10133426373\n",
"3195634984\n",
"4105281099\n",
"5130743119\n",
"4481822046\n",
"100003\n",
"3699886049\n",
"10226780624\n",
"59371044\n",
"177649006\n",
"9\n",
"9\n",
"8\n",
"7\n",
"3\n",
"7\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Last year the world's largest square was built in Berland. It is known that the square can be represented as an infinite plane with an introduced Cartesian system of coordinates. On that square two sets of concentric circles were painted. Let's call the set of concentric circles with radii 1, 2, ..., K and the center in the point (z, 0) a (K, z)-set. Thus, on the square were painted a (N, x)-set and a (M, y)-set. You have to find out how many parts those sets divided the square into.
Input
The first line contains integers N, x, M, y. (1 ≤ N, M ≤ 100000, - 100000 ≤ x, y ≤ 100000, x ≠ y).
Output
Print the sought number of parts.
Examples
Input
1 0 1 1
Output
4
Input
1 0 1 2
Output
3
Input
3 3 4 7
Output
17
Note
Picture for the third sample:
<image>
### Input:
3 3 4 7
### Output:
17
### Input:
1 0 1 2
### Output:
3
### Code:
def readGen(trans):
while 1:
for x in input().split():
yield(trans(x))
readint=readGen(int)
[N,x,M,y]=(next(readint) for i in range(4))
d=abs(y-x)
def interval(a,b): return range(a,b+1)
def case1(N,M,d): # d>=N
ans=0
for r in interval(1, min(M,d-N)):
ans+=1
if (M<=d-N):
return ans
for r in interval(d-N+1, min(M,d)):
ans+=2*(N+r-d)
if (M<=d):
return ans
for r in interval(d+1,min(M,d+N)):
ans+=2*(d+N-r+1)
if (M<=d+N):
return ans
for r in interval(d+N+1,M):
ans+=1
return ans
def partA(N,M,d):
ans=0
for r in interval(1,min(M,d)):
ans+=2*r-1
if (M<d+1):
return ans
for r in interval(d+1,min(M,2*d)):
ans+=2*(2*d-r)+1
return ans
def partB(N,M,d):
ans=0
bound1=min(2*d,N-d)
for r in interval(1,min(M,bound1)):
ans+=2*(r-1)+1
if (M<=bound1):
return ans
if (2*d<=N-d):
for r in interval(bound1+1,min(M,N-d)):
ans+=4*d
if (M<=N-d):
return ans
if (2*d>N-d):
for r in interval(bound1+1,min(M,2*d)):
ans+=2*(N-d)+1
if (M<=2*d):
return ans
bound2=max(2*d,N-d)
for r in interval(bound2+1,min(M,d+N)):
ans+=2*(d+N-r)+2
if (M<=d+N):
return ans
for r in interval(d+N+1,M):
ans+=1
return ans
def case2(N,M,d): # d<N
return partA(N,M,d)+partB(N,M,d)
def remain(N,M,d):
if (M>=d+N):
return 1
if (M>d):
return d+N-M+1
if (M<=d):
return N+1
def calc(N,M,d):
if (N<=d): return remain(N,M,d)+case1(N,M,d)
else: return remain(N,M,d)+case2(N,M,d)
print(calc(N,M,d))
|
438_B. The Child and Zoo_3137 | Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.
Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let's denote the largest of the written numbers as f(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).
After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?
Input
The first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi (1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.
All roads are bidirectional, each pair of areas is connected by at most one road.
Output
Output a real number — the value of <image>.
The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
4 3
10 20 30 40
1 3
2 3
4 3
Output
16.666667
Input
3 3
10 20 30
1 2
2 3
3 1
Output
13.333333
Input
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
Output
18.571429
Note
Consider the first sample. There are 12 possible situations:
* p = 1, q = 3, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 4, q = 3, f(p, q) = 30.
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 4, f(p, q) = 20.
* p = 4, q = 1, f(p, q) = 10.
Another 6 cases are symmetrical to the above. The average is <image>.
Consider the second sample. There are 6 possible situations:
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 1, q = 3, f(p, q) = 10.
Another 3 cases are symmetrical to the above. The average is <image>. | R = lambda:map(int, input().split())
n, m = R()
a = list(R())
p, f, sz =[], [], []
e = [[] for i in range(n)]
vis = [0] * n
ans = 0
def find(u):
if f[u] != u:
f[u] = find(f[u])
return f[u]
for i in range(n):
p.append([a[i], i])
f.append(i)
sz.append(1)
p.sort()
p.reverse()
for i in range(m):
u, v = R()
e[u - 1].append(v - 1)
e[v - 1].append(u - 1)
for i in range(n):
u = p[i][1]
for v in e[u]:
if (vis[v] and find(u) != find(v)):
pu, pv = u, v
if (sz[f[u]] > sz[f[v]]):
pu, pv = pv, pu
ans += p[i][0] * sz[f[pu]] * sz[f[pv]]
sz[f[pv]] += sz[f[pu]]
f[f[pu]] = f[pv]
vis[u] = 1
print("%.6f" %(2. * ans / n / (n - 1))) | {
"input": [
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"3 3\n10 20 30\n1 2\n2 3\n3 1\n",
"4 3\n10 20 30 40\n1 3\n2 3\n4 3\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"2 1\n233 2333\n1 2\n",
"10 14\n296 371 507 807 102 558 199 500 553 150\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 14\n594 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"10 14\n296 371 507 807 102 558 199 500 553 150\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"7 8\n40 20 10 30 20 72 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"4 3\n10 20 28 40\n1 3\n2 3\n4 3\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n5 4\n",
"10 14\n594 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 4\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 7\n5 7\n",
"10 14\n594 965 90 463 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 4\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 19\n13637 23955 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"2 1\n233 3568\n1 2\n",
"10 14\n594 965 90 57 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"3 3\n10 20 30\n1 2\n2 1\n3 1\n",
"10 19\n15704 19758 26631 25050 12908 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"10 14\n296 371 507 807 102 558 199 500 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 17117 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 3508\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n2 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"3 3\n4 20 30\n1 2\n2 1\n3 1\n",
"10 14\n174 371 507 807 102 558 199 500 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 17117 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 9\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n5 4\n",
"10 19\n13637 23955 19043 2500 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n4 6\n7 4\n",
"10 19\n13637 23955 19043 2500 23197 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n4 6\n7 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n4 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 44614 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"2 1\n282 2333\n1 2\n",
"10 14\n594 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 7\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 14\n296 371 507 807 112 558 199 500 553 150\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 18206 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 3074 4199\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"7 8\n40 20 10 30 20 72 40\n1 2\n2 3\n5 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n2 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n2 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 6\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n3 2\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n5 4\n4 5\n5 6\n6 7\n1 7\n5 7\n",
"10 14\n594 965 90 463 549 206 514 993 803 635\n1 2\n1 6\n3 4\n2 5\n5 4\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 19\n13637 23955 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n4 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 3508\n1 2\n1 3\n1 4\n2 5\n2 6\n2 7\n2 8\n7 9\n6 10\n5 3\n4 7\n6 4\n2 8\n5 8\n6 9\n5 4\n2 8\n1 9\n5 3\n",
"10 14\n174 371 507 807 102 558 199 500 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n7 2\n8 7\n4 6\n2 7\n5 4\n",
"10 14\n174 371 507 807 102 558 199 500 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n4 2\n8 7\n4 6\n2 7\n5 4\n",
"10 14\n174 371 507 807 102 558 199 500 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n4 1\n8 7\n4 6\n2 7\n5 4\n",
"10 14\n174 371 507 807 102 558 199 830 553 103\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n7 9\n8 10\n4 1\n8 7\n4 6\n2 7\n5 4\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n3 6\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 8\n2 9\n5 3\n",
"7 8\n40 20 10 30 20 72 40\n1 2\n4 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"4 3\n10 20 28 28\n1 3\n2 3\n4 3\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n1 3\n3 4\n4 5\n5 6\n6 7\n1 7\n5 7\n",
"7 8\n40 20 10 30 20 72 40\n1 2\n2 3\n5 4\n2 5\n5 6\n6 7\n1 4\n5 7\n"
],
"output": [
"18.5714285714\n",
"13.3333333333\n",
"16.6666666667\n",
"8241.4222222222\n",
"11616.7555555556\n",
"233.0000000000\n",
"213.9333333333\n",
"326.0888888889\n",
"11616.755556\n",
"230.088889\n",
"18.571429\n",
"16.333333\n",
"8241.422222\n",
"326.088889\n",
"20.000000\n",
"365.377778\n",
"8213.977778\n",
"233.000000\n",
"240.000000\n",
"10.000000\n",
"10045.222222\n",
"221.733333\n",
"8680.333333\n",
"11478.555556\n",
"4.000000\n",
"207.066667\n",
"8551.933333\n",
"8040.377778\n",
"8789.644444\n",
"8104.822222\n",
"12015.622222\n",
"282.000000\n",
"322.977778\n",
"232.088889\n",
"8148.422222\n",
"11225.177778\n",
"11616.755556\n",
"18.571429\n",
"8241.422222\n",
"11616.755556\n",
"11616.755556\n",
"18.571429\n",
"20.000000\n",
"365.377778\n",
"8213.977778\n",
"11478.555556\n",
"207.066667\n",
"207.066667\n",
"207.066667\n",
"207.066667\n",
"18.571429\n",
"11616.755556\n",
"18.571429\n",
"16.333333\n",
"20.000000\n",
"18.571429\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.
Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let's denote the largest of the written numbers as f(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).
After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?
Input
The first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi (1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.
All roads are bidirectional, each pair of areas is connected by at most one road.
Output
Output a real number — the value of <image>.
The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
4 3
10 20 30 40
1 3
2 3
4 3
Output
16.666667
Input
3 3
10 20 30
1 2
2 3
3 1
Output
13.333333
Input
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
Output
18.571429
Note
Consider the first sample. There are 12 possible situations:
* p = 1, q = 3, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 4, q = 3, f(p, q) = 30.
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 4, f(p, q) = 20.
* p = 4, q = 1, f(p, q) = 10.
Another 6 cases are symmetrical to the above. The average is <image>.
Consider the second sample. There are 6 possible situations:
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 1, q = 3, f(p, q) = 10.
Another 3 cases are symmetrical to the above. The average is <image>.
### Input:
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
### Output:
18.5714285714
### Input:
3 3
10 20 30
1 2
2 3
3 1
### Output:
13.3333333333
### Code:
R = lambda:map(int, input().split())
n, m = R()
a = list(R())
p, f, sz =[], [], []
e = [[] for i in range(n)]
vis = [0] * n
ans = 0
def find(u):
if f[u] != u:
f[u] = find(f[u])
return f[u]
for i in range(n):
p.append([a[i], i])
f.append(i)
sz.append(1)
p.sort()
p.reverse()
for i in range(m):
u, v = R()
e[u - 1].append(v - 1)
e[v - 1].append(u - 1)
for i in range(n):
u = p[i][1]
for v in e[u]:
if (vis[v] and find(u) != find(v)):
pu, pv = u, v
if (sz[f[u]] > sz[f[v]]):
pu, pv = pv, pu
ans += p[i][0] * sz[f[pu]] * sz[f[pv]]
sz[f[pv]] += sz[f[pu]]
f[f[pu]] = f[pv]
vis[u] = 1
print("%.6f" %(2. * ans / n / (n - 1))) |
45_I. TCMCF+++_3141 | Vasya has gotten interested in programming contests in TCMCF+++ rules. On the contest n problems were suggested and every problem had a cost — a certain integral number of points (perhaps, negative or even equal to zero). According to TCMCF+++ rules, only accepted problems can earn points and the overall number of points of a contestant was equal to the product of the costs of all the problems he/she had completed. If a person didn't solve anything, then he/she didn't even appear in final standings and wasn't considered as participant. Vasya understood that to get the maximal number of points it is not always useful to solve all the problems. Unfortunately, he understood it only after the contest was finished. Now he asks you to help him: find out what problems he had to solve to earn the maximal number of points.
Input
The first line contains an integer n (1 ≤ n ≤ 100) — the number of the suggested problems. The next line contains n space-separated integers ci ( - 100 ≤ ci ≤ 100) — the cost of the i-th task. The tasks' costs may coinсide.
Output
Print space-separated the costs of the problems that needed to be solved to get the maximal possible number of points. Do not forget, please, that it was necessary to solve at least one problem. If there are several solutions to that problem, print any of them.
Examples
Input
5
1 2 -3 3 3
Output
3 1 2 3
Input
13
100 100 100 100 100 100 100 100 100 100 100 100 100
Output
100 100 100 100 100 100 100 100 100 100 100 100 100
Input
4
-2 -2 -2 -2
Output
-2 -2 -2 -2 | import sys
input=sys.stdin.readline
n=int(input())
s=list(map(int,input().split()))
s.sort()
s.reverse()
num_manfi=0
num_sefr=0
flag=0
for i in s:
if i>0:
print(i,end=' ')
flag=1
elif i==0:
num_sefr+=1
else:
num_manfi+=1
num_manfi-=(num_manfi%2)
s.reverse()
for i in range(num_manfi):
print(s[i],end=' ')
if (not flag) and num_manfi<=0 and num_sefr>0 :
print(0,end=' ')
exit()
if (not flag) and num_sefr<=0 and num_manfi<=0 :
print(s[0])
exit()
| {
"input": [
"4\n-2 -2 -2 -2\n",
"13\n100 100 100 100 100 100 100 100 100 100 100 100 100\n",
"5\n1 2 -3 3 3\n",
"100\n-93 -100 -99 -100 -99 -100 -99 -99 -99 -100 -99 -99 -100 -98 -98 -100 -99 -100 -95 -100 -100 -99 -98 -100 -96 -99 -99 -100 -97 -98 -100 -98 -98 -93 -100 -100 -99 -100 -100 -98 -100 -98 -100 -98 -97 -99 -98 -99 -99 -99 -100 -100 -100 -100 -98 -93 -100 -100 -97 -100 -100 -100 -98 -99 -100 -95 -98 -99 -100 -100 -99 -99 -100 -98 -100 -100 -100 -100 -96 -100 -93 -97 -100 -100 -99 -93 -92 -98 -97 -94 -100 -100 -99 -98 -100 -100 -100 -99 -99 -100\n",
"2\n0 100\n",
"100\n-60 98 -34 30 48 69 -50 70 3 85 67 73 -23 64 31 98 57 84 54 81 24 37 41 -29 73 -6 3 62 -23 86 67 -8 79 38 60 64 -65 78 81 95 98 100 38 -46 -6 -4 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 -90 67 61 24 62 78 -1 96 82 23 87 9 87 2 -50 -26 30 74 52 -28 39 69 67 6 56 74 93 13 -22 23 97 70 -45\n",
"2\n100 -100\n",
"1\n1\n",
"100\n99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 99 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 96 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100\n",
"2\n100 0\n",
"4\n-2 -1 2 2\n",
"3\n2 1 -1\n",
"100\n16 -41 -52 -100 -74 -57 -57 -49 63 -71 -26 -96 -50 -49 -57 -66 -27 -32 -99 6 -24 14 -79 -57 -82 -81 17 -54 -47 3 -66 -100 2 -35 -18 -83 12 46 -37 -19 -1 30 -93 -59 57 -69 -43 -83 -91 -28 -67 -17 -18 13 -35 57 -59 -85 33 -77 -74 92 -58 -82 -59 42 29 -54 -50 -89 -39 68 -64 -86 37 -73 -68 -85 -51 -25 -31 -10 -70 32 1 -64 -47 27 -86 -7 24 -55 -73 -88 21 -3 61 -61 -44 -24\n",
"10\n-5 -5 4 1 -8 -3 -9 -2 4 4\n",
"2\n-100 100\n",
"2\n-100 0\n",
"2\n1 -1\n",
"100\n-39 -43 43 18 -21 -24 -8 -29 -32 -12 50 35 5 1 42 -24 44 37 6 25 -39 17 32 -67 49 -19 -19 50 45 17 -48 17 -11 -16 47 44 29 -29 30 1 50 -4 35 -18 0 -9 -14 31 49 34 -25 36 37 9 3 26 43 25 40 24 48 21 -18 50 -10 26 39 29 45 1 48 34 14 -48 17 0 50 33 -4 31 31 -63 10 26 22 8 50 -15 1 -1 -15 13 -47 25 3 45 22 -5 -16 32\n",
"4\n2 2 1 -1\n",
"100\n42 -14 90 5 0 62 14 36 -76 -94 69 25 -2 40 -49 62 -38 0 -96 49 -24 -92 55 18 22 42 -25 72 -52 47 78 98 80 -27 -64 -4 -38 -93 -15 40 -78 -49 -49 21 50 -13 34 0 78 84 55 -95 -52 -3 -46 -49 53 23 -49 -98 -1 47 48 -93 25 37 -71 -23 74 -58 -39 -43 -14 -57 98 -6 9 -56 88 -88 7 71 -60 95 -9 15 55 63 -75 -29 -90 -38 -61 -97 9 -40 89 92 -37 50\n",
"1\n13\n",
"1\n3\n",
"2\n0 0\n",
"2\n-2 -1\n",
"1\n-13\n",
"2\n-1 -1\n",
"2\n1 0\n",
"3\n-1 2 2\n",
"2\n-1 0\n",
"1\n-100\n",
"4\n1 0 -1 2\n",
"2\n-1 2\n",
"100\n8 -63 12 -31 48 1 11 7 -18 -25 -3 11 -23 44 31 33 -10 44 46 -62 29 5 -4 -35 -1 0 -20 34 -18 -46 -9 46 41 42 -69 18 24 48 50 13 -24 -19 37 -21 8 50 30 24 -48 36 -42 -43 31 50 -17 -29 -27 9 50 47 36 -50 6 -51 12 49 -1 -15 37 -44 -19 46 27 5 -37 17 19 39 11 42 44 43 -48 -1 31 -80 -30 -35 -19 50 35 -56 -1 20 50 -13 27 39 -20 -15\n",
"2\n0 -100\n",
"3\n-2 0 2\n",
"2\n0 -2\n",
"2\n1 1\n",
"2\n-1 1\n",
"2\n0 -1\n",
"3\n0 1 2\n",
"2\n2 2\n",
"4\n-1 -1 -2 0\n",
"10\n-3 -9 -10 -10 -9 -8 -9 -9 -8 -9\n",
"10\n9 10 9 10 10 10 1 5 10 5\n",
"2\n-1 -2\n",
"100\n43 17 39 -15 9 24 28 21 42 -56 9 12 -53 -30 -1 26 39 44 50 46 47 22 29 11 30 42 27 34 31 31 46 7 33 47 48 2 44 -19 33 32 22 23 39 34 -8 1 -18 33 43 45 47 39 -15 44 50 32 42 42 46 -13 28 35 31 -31 13 30 -10 0 9 50 24 38 24 -48 20 43 13 46 26 36 43 32 48 5 -5 39 37 41 -4 -6 -9 32 42 -3 31 37 39 48 26 38\n",
"3\n1 -1 2\n",
"100\n-74 11 -35 -39 31 -39 43 43 2 -78 -17 -16 -70 41 -96 -70 -89 48 -98 -44 47 -92 49 20 47 -23 -19 -24 7 -79 16 18 0 29 -43 -98 27 50 -65 -50 44 -66 -64 -34 -77 -38 22 18 8 30 -62 -37 -3 -80 -94 15 -50 -61 6 -97 35 24 -19 -79 -47 -4 4 38 -37 -51 -31 -24 -3 -3 -94 -99 -87 -35 48 -57 16 -2 6 -13 -5 -60 -39 -61 -42 7 -14 -4 -99 -32 31 17 -84 13 -72 -37\n",
"2\n1 2\n",
"4\n1 2 -2 1\n",
"3\n1 0 2\n",
"1\n0\n",
"3\n0 -2 -1\n",
"2\n100 100\n",
"2\n0 1\n",
"1\n100\n",
"4\n-2 0 -2 0\n",
"4\n0 0 2 -2\n",
"3\n-2 2 2\n",
"1\n-1\n",
"4\n-1 2 0 -2\n",
"100\n35 41 38 39 46 -1 19 42 34 22 0 -23 48 24 41 12 11 4 4 35 35 2 9 33 50 30 15 21 44 47 47 27 31 24 40 14 22 26 45 1 35 31 13 8 48 50 31 36 26 26 48 41 6 -19 17 17 16 3 38 42 41 35 19 31 15 -48 43 6 -32 -18 -2 41 44 29 11 46 43 48 -12 34 30 -10 -7 44 47 24 44 32 36 29 15 25 25 -19 26 46 36 37 -10 45\n",
"10\n-10 5 9 -10 2 -7 10 10 6 -9\n",
"100\n-93 -100 -99 -100 -99 -100 -99 -99 -99 -100 -99 -99 -100 -98 -98 -100 -99 -100 -95 -100 -100 -99 -98 -100 -96 -99 -99 -100 -97 -98 -100 -98 -98 -93 -100 -100 -99 -100 -100 -98 -100 -98 -100 -98 -97 -99 -98 -99 -99 -99 -100 -100 -100 -100 -98 -93 -100 -100 -97 -100 -100 -100 -98 -126 -100 -95 -98 -99 -100 -100 -99 -99 -100 -98 -100 -100 -100 -100 -96 -100 -93 -97 -100 -100 -99 -93 -92 -98 -97 -94 -100 -100 -99 -98 -100 -100 -100 -99 -99 -100\n",
"2\n1 100\n",
"100\n-60 98 -34 30 48 69 -50 70 3 85 67 73 -23 64 31 98 57 84 54 81 24 37 41 -29 73 -6 3 62 -23 86 67 -8 79 38 60 120 -65 78 81 95 98 100 38 -46 -6 -4 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 -90 67 61 24 62 78 -1 96 82 23 87 9 87 2 -50 -26 30 74 52 -28 39 69 67 6 56 74 93 13 -22 23 97 70 -45\n",
"2\n101 -100\n",
"1\n-2\n",
"100\n99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 99 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 104 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100\n",
"2\n100 -1\n",
"4\n-2 -1 2 0\n",
"3\n2 1 -2\n",
"100\n16 -41 -52 -100 -74 -57 -57 -49 63 -71 -26 -96 -50 -49 -57 -66 -27 -32 -99 6 -24 14 -79 -57 -82 -81 17 -54 -47 3 -66 -100 2 -35 -18 -83 12 46 -37 -19 -1 30 -93 -59 57 -69 -43 -83 -91 -28 -67 -17 -18 13 -35 57 -59 -85 33 -77 -74 92 -58 -82 -59 42 29 -54 -50 -89 -39 68 -64 -86 37 -73 -68 -85 -51 -25 -31 -8 -70 32 1 -64 -47 27 -86 -7 24 -55 -73 -88 21 -3 61 -61 -44 -24\n",
"10\n-5 -5 4 1 -8 -3 -11 -2 4 4\n",
"2\n-100 000\n",
"2\n-100 -1\n",
"2\n-2 1\n",
"100\n-39 -43 43 18 -21 -24 -8 -29 -32 -12 50 35 5 1 42 -24 44 37 6 25 -39 17 32 -67 49 -19 -19 50 45 17 -48 17 -11 -16 47 44 29 -29 30 1 50 -4 35 -18 0 -9 -14 31 49 34 -25 36 37 9 3 26 43 25 40 24 48 21 -18 50 -10 26 39 29 45 1 48 34 14 -48 16 0 50 33 -4 31 31 -63 10 26 22 8 50 -15 1 -1 -15 13 -47 25 3 45 22 -5 -16 32\n",
"100\n42 -14 90 5 0 62 14 36 -76 -94 69 25 -2 40 -49 62 -38 0 -96 49 -24 -92 55 18 22 42 -25 72 -52 47 78 98 80 -27 -64 -4 -38 -93 -15 40 -78 -49 -49 21 50 -13 34 0 78 84 55 -95 -52 -3 -46 -49 53 23 -49 -98 -1 47 48 -93 16 37 -71 -23 74 -58 -39 -43 -14 -57 98 -6 9 -56 88 -88 7 71 -60 95 -9 15 55 63 -75 -29 -90 -38 -61 -97 9 -40 89 92 -37 50\n",
"1\n11\n",
"1\n2\n",
"2\n-2 -2\n",
"1\n-14\n",
"2\n-1 4\n",
"4\n1 -1 -1 2\n",
"100\n8 -63 12 -31 48 1 11 7 -18 -25 -3 11 -23 44 31 33 -10 44 46 -62 29 5 -4 -35 -1 0 -20 34 -18 -46 -9 46 41 42 -69 18 24 48 50 13 -24 -19 37 -21 8 50 30 24 -48 36 -42 -43 31 50 -17 -29 -27 9 50 47 36 -50 6 -51 12 49 -1 -15 37 -44 -19 46 27 5 -37 17 19 39 11 42 44 43 -48 -1 31 -80 -30 -35 -19 50 35 -56 -1 20 36 -13 27 39 -20 -15\n",
"2\n0 3\n",
"2\n-1 -4\n",
"3\n1 1 2\n",
"2\n2 4\n",
"4\n-1 0 -2 0\n",
"10\n-3 -9 -10 -6 -9 -8 -9 -9 -8 -9\n",
"10\n9 11 9 10 10 10 1 5 10 5\n",
"2\n-1 -3\n",
"100\n43 17 39 -15 9 24 28 21 42 -56 9 12 -53 -30 -1 26 39 44 50 55 47 22 29 11 30 42 27 34 31 31 46 7 33 47 48 2 44 -19 33 32 22 23 39 34 -8 1 -18 33 43 45 47 39 -15 44 50 32 42 42 46 -13 28 35 31 -31 13 30 -10 0 9 50 24 38 24 -48 20 43 13 46 26 36 43 32 48 5 -5 39 37 41 -4 -6 -9 32 42 -3 31 37 39 48 26 38\n",
"3\n2 -1 2\n",
"100\n-74 11 -35 -39 31 -39 43 43 2 -78 -17 -16 -70 41 -96 -70 -89 48 -98 -44 47 -92 49 20 47 -23 -19 -24 7 -79 16 18 0 29 -43 -98 27 50 -65 -50 44 -66 -64 -34 -77 -38 22 18 8 30 -16 -37 -3 -80 -94 15 -50 -61 6 -97 35 24 -19 -79 -47 -4 4 38 -37 -51 -31 -24 -3 -3 -94 -99 -87 -35 48 -57 16 -2 6 -13 -5 -60 -39 -61 -42 7 -14 -4 -99 -32 31 17 -84 13 -72 -37\n",
"2\n1 3\n",
"4\n1 2 -3 1\n",
"3\n1 0 1\n",
"3\n1 -2 -1\n",
"4\n-2 0 -4 0\n",
"3\n-2 1 2\n",
"1\n5\n",
"4\n-2 2 0 -2\n",
"100\n35 41 38 39 46 -1 19 42 34 22 1 -23 48 24 41 12 11 4 4 35 35 2 9 33 50 30 15 21 44 47 47 27 31 24 40 14 22 26 45 1 35 31 13 8 48 50 31 36 26 26 48 41 6 -19 17 17 16 3 38 42 41 35 19 31 15 -48 43 6 -32 -18 -2 41 44 29 11 46 43 48 -12 34 30 -10 -7 44 47 24 44 32 36 29 15 25 25 -19 26 46 36 37 -10 45\n",
"10\n-10 5 2 -10 2 -7 10 10 6 -9\n",
"13\n100 000 100 100 100 100 100 100 100 100 100 100 100\n",
"5\n1 2 -3 3 6\n",
"100\n-93 -100 -99 -100 -99 -100 -99 -99 -99 -100 -99 -99 -100 -98 -98 -100 -99 -100 -95 -100 -100 -99 -98 -100 -96 -99 -99 -100 -97 -98 -100 -98 -98 -93 -100 -100 -99 -100 -100 -98 -100 -98 -100 -98 -97 -99 -98 -99 -99 -99 -100 -100 -100 -100 -98 -93 -100 -100 -97 -100 -100 -100 -98 -126 -100 -95 -98 -99 -100 -100 -99 -99 -100 -98 -100 -100 -100 -31 -96 -100 -93 -97 -100 -100 -99 -93 -92 -98 -97 -94 -100 -100 -99 -98 -100 -100 -100 -99 -99 -100\n",
"2\n1 101\n",
"100\n-60 98 -34 30 48 69 -50 70 3 85 67 73 -23 64 31 98 57 84 54 81 24 37 37 -29 73 -6 3 62 -23 86 67 -8 79 38 60 120 -65 78 81 95 98 100 38 -46 -6 -4 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 -90 67 61 24 62 78 -1 96 82 23 87 9 87 2 -50 -26 30 74 52 -28 39 69 67 6 56 74 93 13 -22 23 97 70 -45\n",
"1\n-4\n",
"100\n99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 40 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 104 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100\n",
"100\n16 -41 -52 -100 -74 -57 -57 -49 63 -71 -26 -96 -50 -49 -57 -66 -27 -32 -99 6 -24 14 -79 -57 -82 -81 18 -54 -47 3 -66 -100 2 -35 -18 -83 12 46 -37 -19 -1 30 -93 -59 57 -69 -43 -83 -91 -28 -67 -17 -18 13 -35 57 -59 -85 33 -77 -74 92 -58 -82 -59 42 29 -54 -50 -89 -39 68 -64 -86 37 -73 -68 -85 -51 -25 -31 -8 -70 32 1 -64 -47 27 -86 -7 24 -55 -73 -88 21 -3 61 -61 -44 -24\n",
"4\n0 2 1 -1\n",
"2\n2 -1\n",
"2\n0 -4\n",
"2\n2 0\n",
"3\n-1 0 2\n",
"2\n-2 2\n",
"2\n0 -101\n",
"3\n-2 0 4\n",
"2\n0 2\n",
"2\n2 -2\n",
"1\n4\n",
"2\n000 100\n",
"2\n-3 -1\n",
"1\n101\n",
"4\n-2 0 -2 -2\n",
"2\n001 -100\n",
"2\n101 -1\n",
"4\n-2 0 2 0\n",
"3\n2 2 -1\n"
],
"output": [
"-2 -2 -2 -2\n",
"100 100 100 100 100 100 100 100 100 100 100 100 100\n",
"1 2 3 3\n",
"-100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -97 -97 -97 -97 -97 -96 -96 -95 -95 -94 -93 -93 -93 -93 -93 -92\n",
"100\n",
"98 30 48 69 70 3 85 67 73 64 31 98 57 84 54 81 24 37 41 73 3 62 86 67 79 38 60 64 78 81 95 98 100 38 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 67 61 24 62 78 96 82 23 87 9 87 2 30 74 52 39 69 67 6 56 74 93 13 23 97 70 -90 -65 -60 -50 -50 -46 -45 -34 -29 -28 -26 -23 -23 -22 -8 -6 -6 -4 ",
"100\n",
"1\n",
"99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 99 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 96 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100\n",
"100\n",
"2 2 -2 -1 ",
"2 1\n",
"16 63 6 14 17 3 2 12 46 30 57 13 57 33 92 42 29 68 37 32 1 27 24 21 61 -100 -100 -99 -96 -93 -91 -89 -88 -86 -86 -85 -85 -83 -83 -82 -82 -81 -79 -77 -74 -74 -73 -73 -71 -70 -69 -68 -67 -66 -66 -64 -64 -61 -59 -59 -59 -58 -57 -57 -57 -57 -55 -54 -54 -52 -51 -50 -50 -49 -49 -47 -47 -44 -43 -41 -39 -37 -35 -35 -32 -31 -28 -27 -26 -25 -24 -24 -19 -18 -18 -17 -10 -7 -3 ",
"4 1 4 4 -9 -8 -5 -5 -3 -2 ",
"100\n",
"0\n",
"1\n",
"43 18 50 35 5 1 42 44 37 6 25 17 32 49 50 45 17 17 47 44 29 30 1 50 35 31 49 34 36 37 9 3 26 43 25 40 24 48 21 50 26 39 29 45 1 48 34 14 17 50 33 31 31 10 26 22 8 50 1 13 25 3 45 22 32 -67 -63 -48 -48 -47 -43 -39 -39 -32 -29 -29 -25 -24 -24 -21 -19 -19 -18 -18 -16 -16 -15 -15 -14 -12 -11 -10 -9 -8 -5 -4 -4 ",
"2 2 1\n",
"42 90 5 62 14 36 69 25 40 62 49 55 18 22 42 72 47 78 98 80 40 21 50 34 78 84 55 53 23 47 48 25 37 74 98 9 88 7 71 95 15 55 63 9 89 92 50 -98 -97 -96 -95 -94 -93 -93 -92 -90 -88 -78 -76 -75 -71 -64 -61 -60 -58 -57 -56 -52 -52 -49 -49 -49 -49 -49 -46 -43 -40 -39 -38 -38 -38 -37 -29 -27 -25 -24 -23 -15 -14 -14 -13 -9 -6 -4 -3 -2 -1 ",
"13\n",
"3\n",
"0\n",
"-2 -1\n",
"-13\n",
"-1 -1\n",
"1\n",
"2 2\n",
"0\n",
"-100\n",
"1 2\n",
"2\n",
"8 12 48 1 11 7 11 44 31 33 44 46 29 5 34 46 41 42 18 24 48 50 13 37 8 50 30 24 36 31 50 9 50 47 36 6 12 49 37 46 27 5 17 19 39 11 42 44 43 31 50 35 20 50 27 39 -80 -69 -63 -62 -56 -51 -50 -48 -48 -46 -44 -43 -42 -37 -35 -35 -31 -30 -29 -27 -25 -24 -23 -21 -20 -20 -19 -19 -19 -18 -18 -17 -15 -15 -13 -10 -9 -4 -3 -1 -1 -1 ",
"0\n",
"2\n",
"0\n",
"1 1\n",
"1\n",
"0\n",
"1 2\n",
"2 2\n",
"-2 -1\n",
"-10 -10 -9 -9 -9 -9 -9 -8 -8 -3\n",
"9 10 9 10 10 10 1 5 10 5\n",
"-2 -1\n",
"43 17 39 9 24 28 21 42 9 12 26 39 44 50 46 47 22 29 11 30 42 27 34 31 31 46 7 33 47 48 2 44 33 32 22 23 39 34 1 33 43 45 47 39 44 50 32 42 42 46 28 35 31 13 30 9 50 24 38 24 20 43 13 46 26 36 43 32 48 5 39 37 41 32 42 31 37 39 48 26 38 -56 -53 -48 -31 -30 -19 -18 -15 -15 -13 -10 -9 -8 -6 -5 -4 -3 -1 ",
"1 2\n",
"11 31 43 43 2 41 48 47 49 20 47 7 16 18 29 27 50 44 22 18 8 30 15 6 35 24 4 38 48 16 6 7 31 17 13 -99 -99 -98 -98 -97 -96 -94 -94 -92 -89 -87 -84 -80 -79 -79 -78 -77 -74 -72 -70 -70 -66 -65 -64 -62 -61 -61 -60 -57 -51 -50 -50 -47 -44 -43 -42 -39 -39 -39 -38 -37 -37 -37 -35 -35 -34 -32 -31 -24 -24 -23 -19 -19 -17 -16 -14 -13 -5 -4 -4 -3 -3 -3 -2 ",
"1 2\n",
"1 2 1\n",
"1 2\n",
"0\n",
"-2 -1\n",
"100 100\n",
"1\n",
"100\n",
"-2 -2\n",
"2\n",
"2 2\n",
"-1\n",
"2 -2 -1\n",
"35 41 38 39 46 19 42 34 22 48 24 41 12 11 4 4 35 35 2 9 33 50 30 15 21 44 47 47 27 31 24 40 14 22 26 45 1 35 31 13 8 48 50 31 36 26 26 48 41 6 17 17 16 3 38 42 41 35 19 31 15 43 6 41 44 29 11 46 43 48 34 30 44 47 24 44 32 36 29 15 25 25 26 46 36 37 45 -48 -32 -23 -19 -19 -18 -12 -10 -10 -7 -2 -1 ",
"5 9 2 10 10 6 -10 -10 -9 -7 ",
"-126 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -97 -97 -97 -97 -97 -96 -96 -95 -95 -94 -93 -93 -93 -93 -93 -92 ",
"1 100 ",
"98 30 48 69 70 3 85 67 73 64 31 98 57 84 54 81 24 37 41 73 3 62 86 67 79 38 60 120 78 81 95 98 100 38 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 67 61 24 62 78 96 82 23 87 9 87 2 30 74 52 39 69 67 6 56 74 93 13 23 97 70 -90 -65 -60 -50 -50 -46 -45 -34 -29 -28 -26 -23 -23 -22 -8 -6 -6 -4 ",
"101 ",
"-2",
"99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 99 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 104 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100 ",
"100 ",
"2 -2 -1 ",
"2 1 ",
"16 63 6 14 17 3 2 12 46 30 57 13 57 33 92 42 29 68 37 32 1 27 24 21 61 -100 -100 -99 -96 -93 -91 -89 -88 -86 -86 -85 -85 -83 -83 -82 -82 -81 -79 -77 -74 -74 -73 -73 -71 -70 -69 -68 -67 -66 -66 -64 -64 -61 -59 -59 -59 -58 -57 -57 -57 -57 -55 -54 -54 -52 -51 -50 -50 -49 -49 -47 -47 -44 -43 -41 -39 -37 -35 -35 -32 -31 -28 -27 -26 -25 -24 -24 -19 -18 -18 -17 -8 -7 -3 ",
"4 1 4 4 -11 -8 -5 -5 -3 -2 ",
"0\n",
"-100 -1 ",
"1 ",
"43 18 50 35 5 1 42 44 37 6 25 17 32 49 50 45 17 17 47 44 29 30 1 50 35 31 49 34 36 37 9 3 26 43 25 40 24 48 21 50 26 39 29 45 1 48 34 14 16 50 33 31 31 10 26 22 8 50 1 13 25 3 45 22 32 -67 -63 -48 -48 -47 -43 -39 -39 -32 -29 -29 -25 -24 -24 -21 -19 -19 -18 -18 -16 -16 -15 -15 -14 -12 -11 -10 -9 -8 -5 -4 -4 ",
"42 90 5 62 14 36 69 25 40 62 49 55 18 22 42 72 47 78 98 80 40 21 50 34 78 84 55 53 23 47 48 16 37 74 98 9 88 7 71 95 15 55 63 9 89 92 50 -98 -97 -96 -95 -94 -93 -93 -92 -90 -88 -78 -76 -75 -71 -64 -61 -60 -58 -57 -56 -52 -52 -49 -49 -49 -49 -49 -46 -43 -40 -39 -38 -38 -38 -37 -29 -27 -25 -24 -23 -15 -14 -14 -13 -9 -6 -4 -3 -2 -1 ",
"11 ",
"2 ",
"-2 -2 ",
"-14",
"4 ",
"1 2 -1 -1 ",
"8 12 48 1 11 7 11 44 31 33 44 46 29 5 34 46 41 42 18 24 48 50 13 37 8 50 30 24 36 31 50 9 50 47 36 6 12 49 37 46 27 5 17 19 39 11 42 44 43 31 50 35 20 36 27 39 -80 -69 -63 -62 -56 -51 -50 -48 -48 -46 -44 -43 -42 -37 -35 -35 -31 -30 -29 -27 -25 -24 -23 -21 -20 -20 -19 -19 -19 -18 -18 -17 -15 -15 -13 -10 -9 -4 -3 -1 -1 -1 ",
"3 ",
"-4 -1 ",
"1 1 2 ",
"2 4 ",
"-2 -1 ",
"-10 -9 -9 -9 -9 -9 -8 -8 -6 -3 ",
"9 11 9 10 10 10 1 5 10 5 ",
"-3 -1 ",
"43 17 39 9 24 28 21 42 9 12 26 39 44 50 55 47 22 29 11 30 42 27 34 31 31 46 7 33 47 48 2 44 33 32 22 23 39 34 1 33 43 45 47 39 44 50 32 42 42 46 28 35 31 13 30 9 50 24 38 24 20 43 13 46 26 36 43 32 48 5 39 37 41 32 42 31 37 39 48 26 38 -56 -53 -48 -31 -30 -19 -18 -15 -15 -13 -10 -9 -8 -6 -5 -4 -3 -1 ",
"2 2 ",
"11 31 43 43 2 41 48 47 49 20 47 7 16 18 29 27 50 44 22 18 8 30 15 6 35 24 4 38 48 16 6 7 31 17 13 -99 -99 -98 -98 -97 -96 -94 -94 -92 -89 -87 -84 -80 -79 -79 -78 -77 -74 -72 -70 -70 -66 -65 -64 -61 -61 -60 -57 -51 -50 -50 -47 -44 -43 -42 -39 -39 -39 -38 -37 -37 -37 -35 -35 -34 -32 -31 -24 -24 -23 -19 -19 -17 -16 -16 -14 -13 -5 -4 -4 -3 -3 -3 -2 ",
"1 3 ",
"1 2 1 ",
"1 1 ",
"1 -2 -1 ",
"-4 -2 ",
"1 2 ",
"5 ",
"2 -2 -2 ",
"35 41 38 39 46 19 42 34 22 1 48 24 41 12 11 4 4 35 35 2 9 33 50 30 15 21 44 47 47 27 31 24 40 14 22 26 45 1 35 31 13 8 48 50 31 36 26 26 48 41 6 17 17 16 3 38 42 41 35 19 31 15 43 6 41 44 29 11 46 43 48 34 30 44 47 24 44 32 36 29 15 25 25 26 46 36 37 45 -48 -32 -23 -19 -19 -18 -12 -10 -10 -7 -2 -1 ",
"5 2 2 10 10 6 -10 -10 -9 -7 ",
"100 100 100 100 100 100 100 100 100 100 100 100 ",
"1 2 3 6 ",
"-126 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -99 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -98 -97 -97 -97 -97 -97 -96 -96 -95 -95 -94 -93 -93 -93 -93 -93 -92 -31 ",
"1 101 ",
"98 30 48 69 70 3 85 67 73 64 31 98 57 84 54 81 24 37 37 73 3 62 86 67 79 38 60 120 78 81 95 98 100 38 14 18 58 95 94 57 21 66 8 26 89 99 74 46 69 75 97 54 29 79 1 67 61 24 62 78 96 82 23 87 9 87 2 30 74 52 39 69 67 6 56 74 93 13 23 97 70 -90 -65 -60 -50 -50 -46 -45 -34 -29 -28 -26 -23 -23 -22 -8 -6 -6 -4 ",
"-4",
"99 100 100 99 99 96 100 100 100 98 98 99 100 99 98 98 97 99 99 100 94 100 99 98 97 100 98 99 100 99 97 91 40 95 95 97 99 99 100 98 100 99 99 100 99 100 100 93 96 104 93 99 99 99 100 96 100 97 92 100 100 100 97 100 100 99 98 98 95 97 96 92 97 100 100 90 98 100 100 99 100 98 99 99 100 97 94 99 100 100 99 99 99 100 99 100 96 99 98 100 ",
"16 63 6 14 18 3 2 12 46 30 57 13 57 33 92 42 29 68 37 32 1 27 24 21 61 -100 -100 -99 -96 -93 -91 -89 -88 -86 -86 -85 -85 -83 -83 -82 -82 -81 -79 -77 -74 -74 -73 -73 -71 -70 -69 -68 -67 -66 -66 -64 -64 -61 -59 -59 -59 -58 -57 -57 -57 -57 -55 -54 -54 -52 -51 -50 -50 -49 -49 -47 -47 -44 -43 -41 -39 -37 -35 -35 -32 -31 -28 -27 -26 -25 -24 -24 -19 -18 -18 -17 -8 -7 -3 ",
"2 1 ",
"2 ",
"0\n",
"2 ",
"2 ",
"2 ",
"0\n",
"4 ",
"2 ",
"2 ",
"4 ",
"100 ",
"-3 -1 ",
"101 ",
"-2 -2 ",
"1 ",
"101 ",
"2 ",
"2 2 "
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vasya has gotten interested in programming contests in TCMCF+++ rules. On the contest n problems were suggested and every problem had a cost — a certain integral number of points (perhaps, negative or even equal to zero). According to TCMCF+++ rules, only accepted problems can earn points and the overall number of points of a contestant was equal to the product of the costs of all the problems he/she had completed. If a person didn't solve anything, then he/she didn't even appear in final standings and wasn't considered as participant. Vasya understood that to get the maximal number of points it is not always useful to solve all the problems. Unfortunately, he understood it only after the contest was finished. Now he asks you to help him: find out what problems he had to solve to earn the maximal number of points.
Input
The first line contains an integer n (1 ≤ n ≤ 100) — the number of the suggested problems. The next line contains n space-separated integers ci ( - 100 ≤ ci ≤ 100) — the cost of the i-th task. The tasks' costs may coinсide.
Output
Print space-separated the costs of the problems that needed to be solved to get the maximal possible number of points. Do not forget, please, that it was necessary to solve at least one problem. If there are several solutions to that problem, print any of them.
Examples
Input
5
1 2 -3 3 3
Output
3 1 2 3
Input
13
100 100 100 100 100 100 100 100 100 100 100 100 100
Output
100 100 100 100 100 100 100 100 100 100 100 100 100
Input
4
-2 -2 -2 -2
Output
-2 -2 -2 -2
### Input:
4
-2 -2 -2 -2
### Output:
-2 -2 -2 -2
### Input:
13
100 100 100 100 100 100 100 100 100 100 100 100 100
### Output:
100 100 100 100 100 100 100 100 100 100 100 100 100
### Code:
import sys
input=sys.stdin.readline
n=int(input())
s=list(map(int,input().split()))
s.sort()
s.reverse()
num_manfi=0
num_sefr=0
flag=0
for i in s:
if i>0:
print(i,end=' ')
flag=1
elif i==0:
num_sefr+=1
else:
num_manfi+=1
num_manfi-=(num_manfi%2)
s.reverse()
for i in range(num_manfi):
print(s[i],end=' ')
if (not flag) and num_manfi<=0 and num_sefr>0 :
print(0,end=' ')
exit()
if (not flag) and num_sefr<=0 and num_manfi<=0 :
print(s[0])
exit()
|
483_C. Diverse Permutation_3145 | Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.
Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.
Input
The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).
Output
Print n integers forming the permutation. If there are multiple answers, print any of them.
Examples
Input
3 2
Output
1 3 2
Input
3 1
Output
1 2 3
Input
5 2
Output
1 3 2 4 5
Note
By |x| we denote the absolute value of number x. | from collections import Counter
import string
import math
import sys
# sys.setrecursionlimit(10**6)
from fractions import Fraction
def array_int():
return [int(i) for i in sys.stdin.readline().split()]
def vary(arrber_of_variables):
if arrber_of_variables==1:
return int(sys.stdin.readline())
if arrber_of_variables>=2:
return map(int,sys.stdin.readline().split())
def makedict(var):
return dict(Counter(var))
testcases=1
# testcases=vary(1)
for _ in range(testcases):
n,k=vary(2)
temp=k
num=[i for i in range(1,n+1)]
j=0
for i in range(k+1):
if i%2==0:
print(num[j],end=" ")
j+=1
else:
print(num[k],end=" ")
k-=1
for i in range(temp+1,n):
print(num[i],end=" ")
| {
"input": [
"5 2\n",
"3 1\n",
"3 2\n",
"29857 9843\n",
"10 3\n",
"2 1\n",
"10931 8824\n",
"4 2\n",
"6591 407\n",
"10 9\n",
"5 4\n",
"3222 311\n",
"27687 4031\n",
"23347 20494\n",
"10 4\n",
"7 5\n",
"25517 1767\n",
"4 1\n",
"9 8\n",
"1111 122\n",
"32342 1221\n",
"32244 222\n",
"29857 17420\n",
"10 5\n",
"10931 2897\n",
"8 2\n",
"8270 407\n",
"11 9\n",
"5 3\n",
"3222 440\n",
"27687 5695\n",
"32714 20494\n",
"10 2\n",
"7 3\n",
"14584 1767\n",
"6 2\n",
"18 8\n",
"1111 216\n",
"29075 1221\n",
"6 1\n",
"29857 17977\n",
"13 5\n",
"10931 269\n",
"15 2\n",
"15944 407\n",
"17 9\n",
"7 6\n",
"3222 329\n",
"25342 20494\n",
"4922 1767\n",
"18 4\n",
"29075 321\n",
"7 2\n",
"10931 279\n",
"15 3\n",
"15944 228\n",
"17 2\n",
"3222 274\n",
"8513 1767\n",
"31502 321\n",
"7 4\n",
"10931 518\n",
"15944 138\n",
"3222 20\n",
"5523 1767\n",
"31502 493\n",
"6 4\n",
"10931 939\n",
"9143 138\n",
"3222 27\n",
"8397 1767\n",
"11 4\n",
"15862 939\n",
"9143 246\n",
"1703 27\n",
"8397 3172\n",
"21 4\n",
"18247 939\n",
"13819 246\n",
"536 27\n",
"5538 3172\n",
"18 6\n",
"23297 939\n",
"13819 269\n",
"536 17\n",
"13819 127\n",
"820 17\n",
"13819 72\n",
"820 24\n",
"1560 72\n",
"820 20\n",
"1560 123\n",
"1317 20\n",
"1560 98\n",
"1862 20\n",
"1560 167\n",
"266 20\n",
"3004 167\n",
"266 13\n",
"2442 167\n",
"286 13\n",
"2442 219\n",
"205 13\n",
"2442 125\n",
"139 13\n",
"636 125\n",
"139 22\n",
"636 69\n",
"139 6\n",
"636 6\n",
"154 6\n",
"519 6\n",
"519 3\n",
"29857 13332\n",
"12063 8824\n",
"6591 102\n",
"3222 241\n",
"27687 7987\n",
"23347 22557\n",
"6 3\n",
"7 1\n",
"3510 1767\n"
],
"output": [
"1 3 2 4 5 ",
"1 2 3 \n",
"1 3 2 ",
"1 9844 2 9843 3 9842 4 9841 5 9840 6 9839 7 9838 8 9837 9 9836 10 9835 11 9834 12 9833 13 9832 14 9831 15 9830 16 9829 17 9828 18 9827 19 9826 20 9825 21 9824 22 9823 23 9822 24 9821 25 9820 26 9819 27 9818 28 9817 29 9816 30 9815 31 9814 32 9813 33 9812 34 9811 35 9810 36 9809 37 9808 38 9807 39 9806 40 9805 41 9804 42 9803 43 9802 44 9801 45 9800 46 9799 47 9798 48 9797 49 9796 50 9795 51 9794 52 9793 53 9792 54 9791 55 9790 56 9789 57 9788 58 9787 59 9786 60 9785 61 9784 62 9783 63 9782 64 9781 65 9780 66 9779 67 9778 68 9777 69 9776 70 9775 71 9774 72 9773 73 9772 74 9771 75 9770 76 9769 77 9768 78 9767 79 9766 80 9765 81 9764 82 9763 83 9762 84 9761 85 9760 86 9759 87 9758 88 9757 89 9756 90 9755 91 9754 92 9753 93 9752 94 9751 95 9750 96 9749 97 9748 98 9747 99 9746 100 9745 101 9744 102 9743 103 9742 104 9741 105 9740 106 9739 107 9738 108 9737 109 9736 110 9735 111 9734 112 9733 113 9732 114 9731 115 9730 116 9729 117 9728 118 9727 119 9726 120 9725 121 9724 122 9723 123 9722 124 9721 125 9720 126 9719 127 9718 128 9717 129 9716 130 9715 131 9714 132 9713 133 9712 134 9711 135 9710 136 9709 137 9708 138 9707 139 9706 140 9705 141 9704 142 9703 143 9702 144 9701 145 9700 146 9699 147 9698 148 9697 149 9696 150 9695 151 9694 152 9693 153 9692 154 9691 155 9690 156 9689 157 9688 158 9687 159 9686 160 9685 161 9684 162 9683 163 9682 164 9681 165 9680 166 9679 167 9678 168 9677 169 9676 170 9675 171 9674 172 9673 173 9672 174 9671 175 9670 176 9669 177 9668 178 9667 179 9666 180 9665 181 9664 182 9663 183 9662 184 9661 185 9660 186 9659 187 9658 188 9657 189 9656 190 9655 191 9654 192 9653 193 9652 194 9651 195 9650 196 9649 197 9648 198 9647 199 9646 200 9645 201 9644 202 9643 203 9642 204 9641 205 9640 206 9639 207 9638 208 9637 209 9636 210 9635 211 9634 212 9633 213 9632 214 9631 215 9630 216 9629 217 9628 218 9627 219 9626 220 9625 221 9624 222 9623 223 9622 224 9621 225 9620 226 9619 227 9618 228 9617 229 9616 230 9615 231 9614 232 9613 233 9612 234 9611 235 9610 236 9609 237 9608 238 9607 239 9606 240 9605 241 9604 242 9603 243 9602 244 9601 245 9600 246 9599 247 9598 248 9597 249 9596 250 9595 251 9594 252 9593 253 9592 254 9591 255 9590 256 9589 257 9588 258 9587 259 9586 260 9585 261 9584 262 9583 263 9582 264 9581 265 9580 266 9579 267 9578 268 9577 269 9576 270 9575 271 9574 272 9573 273 9572 274 9571 275 9570 276 9569 277 9568 278 9567 279 9566 280 9565 281 9564 282 9563 283 9562 284 9561 285 9560 286 9559 287 9558 288 9557 289 9556 290 9555 291 9554 292 9553 293 9552 294 9551 295 9550 296 9549 297 9548 298 9547 299 9546 300 9545 301 9544 302 9543 303 9542 304 9541 305 9540 306 9539 307 9538 308 9537 309 9536 310 9535 311 9534 312 9533 313 9532 314 9531 315 9530 316 9529 317 9528 318 9527 319 9526 320 9525 321 9524 322 9523 323 9522 324 9521 325 9520 326 9519 327 9518 328 9517 329 9516 330 9515 331 9514 332 9513 333 9512 334 9511 335 9510 336 9509 337 9508 338 9507 339 9506 340 9505 341 9504 342 9503 343 9502 344 9501 345 9500 346 9499 347 9498 348 9497 349 9496 350 9495 351 9494 352 9493 353 9492 354 9491 355 9490 356 9489 357 9488 358 9487 359 9486 360 9485 361 9484 362 9483 363 9482 364 9481 365 9480 366 9479 367 9478 368 9477 369 9476 370 9475 371 9474 372 9473 373 9472 374 9471 375 9470 376 9469 377 9468 378 9467 379 9466 380 9465 381 9464 382 9463 383 9462 384 9461 385 9460 386 9459 387 9458 388 9457 389 9456 390 9455 391 9454 392 9453 393 9452 394 9451 395 9450 396 9449 397 9448 398 9447 399 9446 400 9445 401 9444 402 9443 403 9442 404 9441 405 9440 406 9439 407 9438 408 9437 409 9436 410 9435 411 9434 412 9433 413 9432 414 9431 415 9430 416 9429 417 9428 418 9427 419 9426 420 9425 421 9424 422 9423 423 9422 424 9421 425 9420 426 9419 427 9418 428 9417 429 9416 430 9415 431 9414 432 9413 433 9412 434 9411 435 9410 436 9409 437 9408 438 9407 439 9406 440 9405 441 9404 442 9403 443 9402 444 9401 445 9400 446 9399 447 9398 448 9397 449 9396 450 9395 451 9394 452 9393 453 9392 454 9391 455 9390 456 9389 457 9388 458 9387 459 9386 460 9385 461 9384 462 9383 463 9382 464 9381 465 9380 466 9379 467 9378 468 9377 469 9376 470 9375 471 9374 472 9373 473 9372 474 9371 475 9370 476 9369 477 9368 478 9367 479 9366 480 9365 481 9364 482 9363 483 9362 484 9361 485 9360 486 9359 487 9358 488 9357 489 9356 490 9355 491 9354 492 9353 493 9352 494 9351 495 9350 496 9349 497 9348 498 9347 499 9346 500 9345 501 9344 502 9343 503 9342 504 9341 505 9340 506 9339 507 9338 508 9337 509 9336 510 9335 511 9334 512 9333 513 9332 514 9331 515 9330 516 9329 517 9328 518 9327 519 9326 520 9325 521 9324 522 9323 523 9322 524 9321 525 9320 526 9319 527 9318 528 9317 529 9316 530 9315 531 9314 532 9313 533 9312 534 9311 535 9310 536 9309 537 9308 538 9307 539 9306 540 9305 541 9304 542 9303 543 9302 544 9301 545 9300 546 9299 547 9298 548 9297 549 9296 550 9295 551 9294 552 9293 553 9292 554 9291 555 9290 556 9289 557 9288 558 9287 559 9286 560 9285 561 9284 562 9283 563 9282 564 9281 565 9280 566 9279 567 9278 568 9277 569 9276 570 9275 571 9274 572 9273 573 9272 574 9271 575 9270 576 9269 577 9268 578 9267 579 9266 580 9265 581 9264 582 9263 583 9262 584 9261 585 9260 586 9259 587 9258 588 9257 589 9256 590 9255 591 9254 592 9253 593 9252 594 9251 595 9250 596 9249 597 9248 598 9247 599 9246 600 9245 601 9244 602 9243 603 9242 604 9241 605 9240 606 9239 607 9238 608 9237 609 9236 610 9235 611 9234 612 9233 613 9232 614 9231 615 9230 616 9229 617 9228 618 9227 619 9226 620 9225 621 9224 622 9223 623 9222 624 9221 625 9220 626 9219 627 9218 628 9217 629 9216 630 9215 631 9214 632 9213 633 9212 634 9211 635 9210 636 9209 637 9208 638 9207 639 9206 640 9205 641 9204 642 9203 643 9202 644 9201 645 9200 646 9199 647 9198 648 9197 649 9196 650 9195 651 9194 652 9193 653 9192 654 9191 655 9190 656 9189 657 9188 658 9187 659 9186 660 9185 661 9184 662 9183 663 9182 664 9181 665 9180 666 9179 667 9178 668 9177 669 9176 670 9175 671 9174 672 9173 673 9172 674 9171 675 9170 676 9169 677 9168 678 9167 679 9166 680 9165 681 9164 682 9163 683 9162 684 9161 685 9160 686 9159 687 9158 688 9157 689 9156 690 9155 691 9154 692 9153 693 9152 694 9151 695 9150 696 9149 697 9148 698 9147 699 9146 700 9145 701 9144 702 9143 703 9142 704 9141 705 9140 706 9139 707 9138 708 9137 709 9136 710 9135 711 9134 712 9133 713 9132 714 9131 715 9130 716 9129 717 9128 718 9127 719 9126 720 9125 721 9124 722 9123 723 9122 724 9121 725 9120 726 9119 727 9118 728 9117 729 9116 730 9115 731 9114 732 9113 733 9112 734 9111 735 9110 736 9109 737 9108 738 9107 739 9106 740 9105 741 9104 742 9103 743 9102 744 9101 745 9100 746 9099 747 9098 748 9097 749 9096 750 9095 751 9094 752 9093 753 9092 754 9091 755 9090 756 9089 757 9088 758 9087 759 9086 760 9085 761 9084 762 9083 763 9082 764 9081 765 9080 766 9079 767 9078 768 9077 769 9076 770 9075 771 9074 772 9073 773 9072 774 9071 775 9070 776 9069 777 9068 778 9067 779 9066 780 9065 781 9064 782 9063 783 9062 784 9061 785 9060 786 9059 787 9058 788 9057 789 9056 790 9055 791 9054 792 9053 793 9052 794 9051 795 9050 796 9049 797 9048 798 9047 799 9046 800 9045 801 9044 802 9043 803 9042 804 9041 805 9040 806 9039 807 9038 808 9037 809 9036 810 9035 811 9034 812 9033 813 9032 814 9031 815 9030 816 9029 817 9028 818 9027 819 9026 820 9025 821 9024 822 9023 823 9022 824 9021 825 9020 826 9019 827 9018 828 9017 829 9016 830 9015 831 9014 832 9013 833 9012 834 9011 835 9010 836 9009 837 9008 838 9007 839 9006 840 9005 841 9004 842 9003 843 9002 844 9001 845 9000 846 8999 847 8998 848 8997 849 8996 850 8995 851 8994 852 8993 853 8992 854 8991 855 8990 856 8989 857 8988 858 8987 859 8986 860 8985 861 8984 862 8983 863 8982 864 8981 865 8980 866 8979 867 8978 868 8977 869 8976 870 8975 871 8974 872 8973 873 8972 874 8971 875 8970 876 8969 877 8968 878 8967 879 8966 880 8965 881 8964 882 8963 883 8962 884 8961 885 8960 886 8959 887 8958 888 8957 889 8956 890 8955 891 8954 892 8953 893 8952 894 8951 895 8950 896 8949 897 8948 898 8947 899 8946 900 8945 901 8944 902 8943 903 8942 904 8941 905 8940 906 8939 907 8938 908 8937 909 8936 910 8935 911 8934 912 8933 913 8932 914 8931 915 8930 916 8929 917 8928 918 8927 919 8926 920 8925 921 8924 922 8923 923 8922 924 8921 925 8920 926 8919 927 8918 928 8917 929 8916 930 8915 931 8914 932 8913 933 8912 934 8911 935 8910 936 8909 937 8908 938 8907 939 8906 940 8905 941 8904 942 8903 943 8902 944 8901 945 8900 946 8899 947 8898 948 8897 949 8896 950 8895 951 8894 952 8893 953 8892 954 8891 955 8890 956 8889 957 8888 958 8887 959 8886 960 8885 961 8884 962 8883 963 8882 964 8881 965 8880 966 8879 967 8878 968 8877 969 8876 970 8875 971 8874 972 8873 973 8872 974 8871 975 8870 976 8869 977 8868 978 8867 979 8866 980 8865 981 8864 982 8863 983 8862 984 8861 985 8860 986 8859 987 8858 988 8857 989 8856 990 8855 991 8854 992 8853 993 8852 994 8851 995 8850 996 8849 997 8848 998 8847 999 8846 1000 8845 1001 8844 1002 8843 1003 8842 1004 8841 1005 8840 1006 8839 1007 8838 1008 8837 1009 8836 1010 8835 1011 8834 1012 8833 1013 8832 1014 8831 1015 8830 1016 8829 1017 8828 1018 8827 1019 8826 1020 8825 1021 8824 1022 8823 1023 8822 1024 8821 1025 8820 1026 8819 1027 8818 1028 8817 1029 8816 1030 8815 1031 8814 1032 8813 1033 8812 1034 8811 1035 8810 1036 8809 1037 8808 1038 8807 1039 8806 1040 8805 1041 8804 1042 8803 1043 8802 1044 8801 1045 8800 1046 8799 1047 8798 1048 8797 1049 8796 1050 8795 1051 8794 1052 8793 1053 8792 1054 8791 1055 8790 1056 8789 1057 8788 1058 8787 1059 8786 1060 8785 1061 8784 1062 8783 1063 8782 1064 8781 1065 8780 1066 8779 1067 8778 1068 8777 1069 8776 1070 8775 1071 8774 1072 8773 1073 8772 1074 8771 1075 8770 1076 8769 1077 8768 1078 8767 1079 8766 1080 8765 1081 8764 1082 8763 1083 8762 1084 8761 1085 8760 1086 8759 1087 8758 1088 8757 1089 8756 1090 8755 1091 8754 1092 8753 1093 8752 1094 8751 1095 8750 1096 8749 1097 8748 1098 8747 1099 8746 1100 8745 1101 8744 1102 8743 1103 8742 1104 8741 1105 8740 1106 8739 1107 8738 1108 8737 1109 8736 1110 8735 1111 8734 1112 8733 1113 8732 1114 8731 1115 8730 1116 8729 1117 8728 1118 8727 1119 8726 1120 8725 1121 8724 1122 8723 1123 8722 1124 8721 1125 8720 1126 8719 1127 8718 1128 8717 1129 8716 1130 8715 1131 8714 1132 8713 1133 8712 1134 8711 1135 8710 1136 8709 1137 8708 1138 8707 1139 8706 1140 8705 1141 8704 1142 8703 1143 8702 1144 8701 1145 8700 1146 8699 1147 8698 1148 8697 1149 8696 1150 8695 1151 8694 1152 8693 1153 8692 1154 8691 1155 8690 1156 8689 1157 8688 1158 8687 1159 8686 1160 8685 1161 8684 1162 8683 1163 8682 1164 8681 1165 8680 1166 8679 1167 8678 1168 8677 1169 8676 1170 8675 1171 8674 1172 8673 1173 8672 1174 8671 1175 8670 1176 8669 1177 8668 1178 8667 1179 8666 1180 8665 1181 8664 1182 8663 1183 8662 1184 8661 1185 8660 1186 8659 1187 8658 1188 8657 1189 8656 1190 8655 1191 8654 1192 8653 1193 8652 1194 8651 1195 8650 1196 8649 1197 8648 1198 8647 1199 8646 1200 8645 1201 8644 1202 8643 1203 8642 1204 8641 1205 8640 1206 8639 1207 8638 1208 8637 1209 8636 1210 8635 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"1 2 \n",
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"1 3 2 4 ",
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"1 10 2 9 3 8 4 7 5 6 \n",
"1 5 2 4 3 \n",
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3222 ",
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23463 23464 23465 23466 23467 23468 23469 23470 23471 23472 23473 23474 23475 23476 23477 23478 23479 23480 23481 23482 23483 23484 23485 23486 23487 23488 23489 23490 23491 23492 23493 23494 23495 23496 23497 23498 23499 23500 23501 23502 23503 23504 23505 23506 23507 23508 23509 23510 23511 23512 23513 23514 23515 23516 23517 23518 23519 23520 23521 23522 23523 23524 23525 23526 23527 23528 23529 23530 23531 23532 23533 23534 23535 23536 23537 23538 23539 23540 23541 23542 23543 23544 23545 23546 23547 23548 23549 23550 23551 23552 23553 23554 23555 23556 23557 23558 23559 23560 23561 23562 23563 23564 23565 23566 23567 23568 23569 23570 23571 23572 23573 23574 23575 23576 23577 23578 23579 23580 23581 23582 23583 23584 23585 23586 23587 23588 23589 23590 23591 23592 23593 23594 23595 23596 23597 23598 23599 23600 23601 23602 23603 23604 23605 23606 23607 23608 23609 23610 23611 23612 23613 23614 23615 23616 23617 23618 23619 23620 23621 23622 23623 23624 23625 23626 23627 23628 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23961 23962 23963 23964 23965 23966 23967 23968 23969 23970 23971 23972 23973 23974 23975 23976 23977 23978 23979 23980 23981 23982 23983 23984 23985 23986 23987 23988 23989 23990 23991 23992 23993 23994 23995 23996 23997 23998 23999 24000 24001 24002 24003 24004 24005 24006 24007 24008 24009 24010 24011 24012 24013 24014 24015 24016 24017 24018 24019 24020 24021 24022 24023 24024 24025 24026 24027 24028 24029 24030 24031 24032 24033 24034 24035 24036 24037 24038 24039 24040 24041 24042 24043 24044 24045 24046 24047 24048 24049 24050 24051 24052 24053 24054 24055 24056 24057 24058 24059 24060 24061 24062 24063 24064 24065 24066 24067 24068 24069 24070 24071 24072 24073 24074 24075 24076 24077 24078 24079 24080 24081 24082 24083 24084 24085 24086 24087 24088 24089 24090 24091 24092 24093 24094 24095 24096 24097 24098 24099 24100 24101 24102 24103 24104 24105 24106 24107 24108 24109 24110 24111 24112 24113 24114 24115 24116 24117 24118 24119 24120 24121 24122 24123 24124 24125 24126 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24293 24294 24295 24296 24297 24298 24299 24300 24301 24302 24303 24304 24305 24306 24307 24308 24309 24310 24311 24312 24313 24314 24315 24316 24317 24318 24319 24320 24321 24322 24323 24324 24325 24326 24327 24328 24329 24330 24331 24332 24333 24334 24335 24336 24337 24338 24339 24340 24341 24342 24343 24344 24345 24346 24347 24348 24349 24350 24351 24352 24353 24354 24355 24356 24357 24358 24359 24360 24361 24362 24363 24364 24365 24366 24367 24368 24369 24370 24371 24372 24373 24374 24375 24376 24377 24378 24379 24380 24381 24382 24383 24384 24385 24386 24387 24388 24389 24390 24391 24392 24393 24394 24395 24396 24397 24398 24399 24400 24401 24402 24403 24404 24405 24406 24407 24408 24409 24410 24411 24412 24413 24414 24415 24416 24417 24418 24419 24420 24421 24422 24423 24424 24425 24426 24427 24428 24429 24430 24431 24432 24433 24434 24435 24436 24437 24438 24439 24440 24441 24442 24443 24444 24445 24446 24447 24448 24449 24450 24451 24452 24453 24454 24455 24456 24457 24458 24459 24460 24461 24462 24463 24464 24465 24466 24467 24468 24469 24470 24471 24472 24473 24474 24475 24476 24477 24478 24479 24480 24481 24482 24483 24484 24485 24486 24487 24488 24489 24490 24491 24492 24493 24494 24495 24496 24497 24498 24499 24500 24501 24502 24503 24504 24505 24506 24507 24508 24509 24510 24511 24512 24513 24514 24515 24516 24517 24518 24519 24520 24521 24522 24523 24524 24525 24526 24527 24528 24529 24530 24531 24532 24533 24534 24535 24536 24537 24538 24539 24540 24541 24542 24543 24544 24545 24546 24547 24548 24549 24550 24551 24552 24553 24554 24555 24556 24557 24558 24559 24560 24561 24562 24563 24564 24565 24566 24567 24568 24569 24570 24571 24572 24573 24574 24575 24576 24577 24578 24579 24580 24581 24582 24583 24584 24585 24586 24587 24588 24589 24590 24591 24592 24593 24594 24595 24596 24597 24598 24599 24600 24601 24602 24603 24604 24605 24606 24607 24608 24609 24610 24611 24612 24613 24614 24615 24616 24617 24618 24619 24620 24621 24622 24623 24624 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24791 24792 24793 24794 24795 24796 24797 24798 24799 24800 24801 24802 24803 24804 24805 24806 24807 24808 24809 24810 24811 24812 24813 24814 24815 24816 24817 24818 24819 24820 24821 24822 24823 24824 24825 24826 24827 24828 24829 24830 24831 24832 24833 24834 24835 24836 24837 24838 24839 24840 24841 24842 24843 24844 24845 24846 24847 24848 24849 24850 24851 24852 24853 24854 24855 24856 24857 24858 24859 24860 24861 24862 24863 24864 24865 24866 24867 24868 24869 24870 24871 24872 24873 24874 24875 24876 24877 24878 24879 24880 24881 24882 24883 24884 24885 24886 24887 24888 24889 24890 24891 24892 24893 24894 24895 24896 24897 24898 24899 24900 24901 24902 24903 24904 24905 24906 24907 24908 24909 24910 24911 24912 24913 24914 24915 24916 24917 24918 24919 24920 24921 24922 24923 24924 24925 24926 24927 24928 24929 24930 24931 24932 24933 24934 24935 24936 24937 24938 24939 24940 24941 24942 24943 24944 24945 24946 24947 24948 24949 24950 24951 24952 24953 24954 24955 24956 24957 24958 24959 24960 24961 24962 24963 24964 24965 24966 24967 24968 24969 24970 24971 24972 24973 24974 24975 24976 24977 24978 24979 24980 24981 24982 24983 24984 24985 24986 24987 24988 24989 24990 24991 24992 24993 24994 24995 24996 24997 24998 24999 25000 25001 25002 25003 25004 25005 25006 25007 25008 25009 25010 25011 25012 25013 25014 25015 25016 25017 25018 25019 25020 25021 25022 25023 25024 25025 25026 25027 25028 25029 25030 25031 25032 25033 25034 25035 25036 25037 25038 25039 25040 25041 25042 25043 25044 25045 25046 25047 25048 25049 25050 25051 25052 25053 25054 25055 25056 25057 25058 25059 25060 25061 25062 25063 25064 25065 25066 25067 25068 25069 25070 25071 25072 25073 25074 25075 25076 25077 25078 25079 25080 25081 25082 25083 25084 25085 25086 25087 25088 25089 25090 25091 25092 25093 25094 25095 25096 25097 25098 25099 25100 25101 25102 25103 25104 25105 25106 25107 25108 25109 25110 25111 25112 25113 25114 25115 25116 25117 25118 25119 25120 25121 25122 25123 25124 25125 25126 25127 25128 25129 25130 25131 25132 25133 25134 25135 25136 25137 25138 25139 25140 25141 25142 25143 25144 25145 25146 25147 25148 25149 25150 25151 25152 25153 25154 25155 25156 25157 25158 25159 25160 25161 25162 25163 25164 25165 25166 25167 25168 25169 25170 25171 25172 25173 25174 25175 25176 25177 25178 25179 25180 25181 25182 25183 25184 25185 25186 25187 25188 25189 25190 25191 25192 25193 25194 25195 25196 25197 25198 25199 25200 25201 25202 25203 25204 25205 25206 25207 25208 25209 25210 25211 25212 25213 25214 25215 25216 25217 25218 25219 25220 25221 25222 25223 25224 25225 25226 25227 25228 25229 25230 25231 25232 25233 25234 25235 25236 25237 25238 25239 25240 25241 25242 25243 25244 25245 25246 25247 25248 25249 25250 25251 25252 25253 25254 25255 25256 25257 25258 25259 25260 25261 25262 25263 25264 25265 25266 25267 25268 25269 25270 25271 25272 25273 25274 25275 25276 25277 25278 25279 25280 25281 25282 25283 25284 25285 25286 25287 25288 25289 25290 25291 25292 25293 25294 25295 25296 25297 25298 25299 25300 25301 25302 25303 25304 25305 25306 25307 25308 25309 25310 25311 25312 25313 25314 25315 25316 25317 25318 25319 25320 25321 25322 25323 25324 25325 25326 25327 25328 25329 25330 25331 25332 25333 25334 25335 25336 25337 25338 25339 25340 25341 25342 25343 25344 25345 25346 25347 25348 25349 25350 25351 25352 25353 25354 25355 25356 25357 25358 25359 25360 25361 25362 25363 25364 25365 25366 25367 25368 25369 25370 25371 25372 25373 25374 25375 25376 25377 25378 25379 25380 25381 25382 25383 25384 25385 25386 25387 25388 25389 25390 25391 25392 25393 25394 25395 25396 25397 25398 25399 25400 25401 25402 25403 25404 25405 25406 25407 25408 25409 25410 25411 25412 25413 25414 25415 25416 25417 25418 25419 25420 25421 25422 25423 25424 25425 25426 25427 25428 25429 25430 25431 25432 25433 25434 25435 25436 25437 25438 25439 25440 25441 25442 25443 25444 25445 25446 25447 25448 25449 25450 25451 25452 25453 25454 25455 25456 25457 25458 25459 25460 25461 25462 25463 25464 25465 25466 25467 25468 25469 25470 25471 25472 25473 25474 25475 25476 25477 25478 25479 25480 25481 25482 25483 25484 25485 25486 25487 25488 25489 25490 25491 25492 25493 25494 25495 25496 25497 25498 25499 25500 25501 25502 25503 25504 25505 25506 25507 25508 25509 25510 25511 25512 25513 25514 25515 25516 25517 ",
"1 2 3 4 \n",
"1 9 2 8 3 7 4 6 5 \n",
"1 123 2 122 3 121 4 120 5 119 6 118 7 117 8 116 9 115 10 114 11 113 12 112 13 111 14 110 15 109 16 108 17 107 18 106 19 105 20 104 21 103 22 102 23 101 24 100 25 99 26 98 27 97 28 96 29 95 30 94 31 93 32 92 33 91 34 90 35 89 36 88 37 87 38 86 39 85 40 84 41 83 42 82 43 81 44 80 45 79 46 78 47 77 48 76 49 75 50 74 51 73 52 72 53 71 54 70 55 69 56 68 57 67 58 66 59 65 60 64 61 63 62 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 ",
"1 1222 2 1221 3 1220 4 1219 5 1218 6 1217 7 1216 8 1215 9 1214 10 1213 11 1212 12 1211 13 1210 14 1209 15 1208 16 1207 17 1206 18 1205 19 1204 20 1203 21 1202 22 1201 23 1200 24 1199 25 1198 26 1197 27 1196 28 1195 29 1194 30 1193 31 1192 32 1191 33 1190 34 1189 35 1188 36 1187 37 1186 38 1185 39 1184 40 1183 41 1182 42 1181 43 1180 44 1179 45 1178 46 1177 47 1176 48 1175 49 1174 50 1173 51 1172 52 1171 53 1170 54 1169 55 1168 56 1167 57 1166 58 1165 59 1164 60 1163 61 1162 62 1161 63 1160 64 1159 65 1158 66 1157 67 1156 68 1155 69 1154 70 1153 71 1152 72 1151 73 1150 74 1149 75 1148 76 1147 77 1146 78 1145 79 1144 80 1143 81 1142 82 1141 83 1140 84 1139 85 1138 86 1137 87 1136 88 1135 89 1134 90 1133 91 1132 92 1131 93 1130 94 1129 95 1128 96 1127 97 1126 98 1125 99 1124 100 1123 101 1122 102 1121 103 1120 104 1119 105 1118 106 1117 107 1116 108 1115 109 1114 110 1113 111 1112 112 1111 113 1110 114 1109 115 1108 116 1107 117 1106 118 1105 119 1104 120 1103 121 1102 122 1101 123 1100 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29828 29829 29830 29831 29832 29833 29834 29835 29836 29837 29838 29839 29840 29841 29842 29843 29844 29845 29846 29847 29848 29849 29850 29851 29852 29853 29854 29855 29856 29857 29858 29859 29860 29861 29862 29863 29864 29865 29866 29867 29868 29869 29870 29871 29872 29873 29874 29875 29876 29877 29878 29879 29880 29881 29882 29883 29884 29885 29886 29887 29888 29889 29890 29891 29892 29893 29894 29895 29896 29897 29898 29899 29900 29901 29902 29903 29904 29905 29906 29907 29908 29909 29910 29911 29912 29913 29914 29915 29916 29917 29918 29919 29920 29921 29922 29923 29924 29925 29926 29927 29928 29929 29930 29931 29932 29933 29934 29935 29936 29937 29938 29939 29940 29941 29942 29943 29944 29945 29946 29947 29948 29949 29950 29951 29952 29953 29954 29955 29956 29957 29958 29959 29960 29961 29962 29963 29964 29965 29966 29967 29968 29969 29970 29971 29972 29973 29974 29975 29976 29977 29978 29979 29980 29981 29982 29983 29984 29985 29986 29987 29988 29989 29990 29991 29992 29993 29994 29995 29996 29997 29998 29999 30000 30001 30002 30003 30004 30005 30006 30007 30008 30009 30010 30011 30012 30013 30014 30015 30016 30017 30018 30019 30020 30021 30022 30023 30024 30025 30026 30027 30028 30029 30030 30031 30032 30033 30034 30035 30036 30037 30038 30039 30040 30041 30042 30043 30044 30045 30046 30047 30048 30049 30050 30051 30052 30053 30054 30055 30056 30057 30058 30059 30060 30061 30062 30063 30064 30065 30066 30067 30068 30069 30070 30071 30072 30073 30074 30075 30076 30077 30078 30079 30080 30081 30082 30083 30084 30085 30086 30087 30088 30089 30090 30091 30092 30093 30094 30095 30096 30097 30098 30099 30100 30101 30102 30103 30104 30105 30106 30107 30108 30109 30110 30111 30112 30113 30114 30115 30116 30117 30118 30119 30120 30121 30122 30123 30124 30125 30126 30127 30128 30129 30130 30131 30132 30133 30134 30135 30136 30137 30138 30139 30140 30141 30142 30143 30144 30145 30146 30147 30148 30149 30150 30151 30152 30153 30154 30155 30156 30157 30158 30159 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30326 30327 30328 30329 30330 30331 30332 30333 30334 30335 30336 30337 30338 30339 30340 30341 30342 30343 30344 30345 30346 30347 30348 30349 30350 30351 30352 30353 30354 30355 30356 30357 30358 30359 30360 30361 30362 30363 30364 30365 30366 30367 30368 30369 30370 30371 30372 30373 30374 30375 30376 30377 30378 30379 30380 30381 30382 30383 30384 30385 30386 30387 30388 30389 30390 30391 30392 30393 30394 30395 30396 30397 30398 30399 30400 30401 30402 30403 30404 30405 30406 30407 30408 30409 30410 30411 30412 30413 30414 30415 30416 30417 30418 30419 30420 30421 30422 30423 30424 30425 30426 30427 30428 30429 30430 30431 30432 30433 30434 30435 30436 30437 30438 30439 30440 30441 30442 30443 30444 30445 30446 30447 30448 30449 30450 30451 30452 30453 30454 30455 30456 30457 30458 30459 30460 30461 30462 30463 30464 30465 30466 30467 30468 30469 30470 30471 30472 30473 30474 30475 30476 30477 30478 30479 30480 30481 30482 30483 30484 30485 30486 30487 30488 30489 30490 30491 30492 30493 30494 30495 30496 30497 30498 30499 30500 30501 30502 30503 30504 30505 30506 30507 30508 30509 30510 30511 30512 30513 30514 30515 30516 30517 30518 30519 30520 30521 30522 30523 30524 30525 30526 30527 30528 30529 30530 30531 30532 30533 30534 30535 30536 30537 30538 30539 30540 30541 30542 30543 30544 30545 30546 30547 30548 30549 30550 30551 30552 30553 30554 30555 30556 30557 30558 30559 30560 30561 30562 30563 30564 30565 30566 30567 30568 30569 30570 30571 30572 30573 30574 30575 30576 30577 30578 30579 30580 30581 30582 30583 30584 30585 30586 30587 30588 30589 30590 30591 30592 30593 30594 30595 30596 30597 30598 30599 30600 30601 30602 30603 30604 30605 30606 30607 30608 30609 30610 30611 30612 30613 30614 30615 30616 30617 30618 30619 30620 30621 30622 30623 30624 30625 30626 30627 30628 30629 30630 30631 30632 30633 30634 30635 30636 30637 30638 30639 30640 30641 30642 30643 30644 30645 30646 30647 30648 30649 30650 30651 30652 30653 30654 30655 30656 30657 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30990 30991 30992 30993 30994 30995 30996 30997 30998 30999 31000 31001 31002 31003 31004 31005 31006 31007 31008 31009 31010 31011 31012 31013 31014 31015 31016 31017 31018 31019 31020 31021 31022 31023 31024 31025 31026 31027 31028 31029 31030 31031 31032 31033 31034 31035 31036 31037 31038 31039 31040 31041 31042 31043 31044 31045 31046 31047 31048 31049 31050 31051 31052 31053 31054 31055 31056 31057 31058 31059 31060 31061 31062 31063 31064 31065 31066 31067 31068 31069 31070 31071 31072 31073 31074 31075 31076 31077 31078 31079 31080 31081 31082 31083 31084 31085 31086 31087 31088 31089 31090 31091 31092 31093 31094 31095 31096 31097 31098 31099 31100 31101 31102 31103 31104 31105 31106 31107 31108 31109 31110 31111 31112 31113 31114 31115 31116 31117 31118 31119 31120 31121 31122 31123 31124 31125 31126 31127 31128 31129 31130 31131 31132 31133 31134 31135 31136 31137 31138 31139 31140 31141 31142 31143 31144 31145 31146 31147 31148 31149 31150 31151 31152 31153 31154 31155 31156 31157 31158 31159 31160 31161 31162 31163 31164 31165 31166 31167 31168 31169 31170 31171 31172 31173 31174 31175 31176 31177 31178 31179 31180 31181 31182 31183 31184 31185 31186 31187 31188 31189 31190 31191 31192 31193 31194 31195 31196 31197 31198 31199 31200 31201 31202 31203 31204 31205 31206 31207 31208 31209 31210 31211 31212 31213 31214 31215 31216 31217 31218 31219 31220 31221 31222 31223 31224 31225 31226 31227 31228 31229 31230 31231 31232 31233 31234 31235 31236 31237 31238 31239 31240 31241 31242 31243 31244 31245 31246 31247 31248 31249 31250 31251 31252 31253 31254 31255 31256 31257 31258 31259 31260 31261 31262 31263 31264 31265 31266 31267 31268 31269 31270 31271 31272 31273 31274 31275 31276 31277 31278 31279 31280 31281 31282 31283 31284 31285 31286 31287 31288 31289 31290 31291 31292 31293 31294 31295 31296 31297 31298 31299 31300 31301 31302 31303 31304 31305 31306 31307 31308 31309 31310 31311 31312 31313 31314 31315 31316 31317 31318 31319 31320 31321 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31986 31987 31988 31989 31990 31991 31992 31993 31994 31995 31996 31997 31998 31999 32000 32001 32002 32003 32004 32005 32006 32007 32008 32009 32010 32011 32012 32013 32014 32015 32016 32017 32018 32019 32020 32021 32022 32023 32024 32025 32026 32027 32028 32029 32030 32031 32032 32033 32034 32035 32036 32037 32038 32039 32040 32041 32042 32043 32044 32045 32046 32047 32048 32049 32050 32051 32052 32053 32054 32055 32056 32057 32058 32059 32060 32061 32062 32063 32064 32065 32066 32067 32068 32069 32070 32071 32072 32073 32074 32075 32076 32077 32078 32079 32080 32081 32082 32083 32084 32085 32086 32087 32088 32089 32090 32091 32092 32093 32094 32095 32096 32097 32098 32099 32100 32101 32102 32103 32104 32105 32106 32107 32108 32109 32110 32111 32112 32113 32114 32115 32116 32117 32118 32119 32120 32121 32122 32123 32124 32125 32126 32127 32128 32129 32130 32131 32132 32133 32134 32135 32136 32137 32138 32139 32140 32141 32142 32143 32144 32145 32146 32147 32148 32149 32150 32151 32152 32153 32154 32155 32156 32157 32158 32159 32160 32161 32162 32163 32164 32165 32166 32167 32168 32169 32170 32171 32172 32173 32174 32175 32176 32177 32178 32179 32180 32181 32182 32183 32184 32185 32186 32187 32188 32189 32190 32191 32192 32193 32194 32195 32196 32197 32198 32199 32200 32201 32202 32203 32204 32205 32206 32207 32208 32209 32210 32211 32212 32213 32214 32215 32216 32217 32218 32219 32220 32221 32222 32223 32224 32225 32226 32227 32228 32229 32230 32231 32232 32233 32234 32235 32236 32237 32238 32239 32240 32241 32242 32243 32244 32245 32246 32247 32248 32249 32250 32251 32252 32253 32254 32255 32256 32257 32258 32259 32260 32261 32262 32263 32264 32265 32266 32267 32268 32269 32270 32271 32272 32273 32274 32275 32276 32277 32278 32279 32280 32281 32282 32283 32284 32285 32286 32287 32288 32289 32290 32291 32292 32293 32294 32295 32296 32297 32298 32299 32300 32301 32302 32303 32304 32305 32306 32307 32308 32309 32310 32311 32312 32313 32314 32315 32316 32317 32318 32319 32320 32321 32322 32323 32324 32325 32326 32327 32328 32329 32330 32331 32332 32333 32334 32335 32336 32337 32338 32339 32340 32341 32342 32343 32344 32345 32346 32347 32348 32349 32350 32351 32352 32353 32354 32355 32356 32357 32358 32359 32360 32361 32362 32363 32364 32365 32366 32367 32368 32369 32370 32371 32372 32373 32374 32375 32376 32377 32378 32379 32380 32381 32382 32383 32384 32385 32386 32387 32388 32389 32390 32391 32392 32393 32394 32395 32396 32397 32398 32399 32400 32401 32402 32403 32404 32405 32406 32407 32408 32409 32410 32411 32412 32413 32414 32415 32416 32417 32418 32419 32420 32421 32422 32423 32424 32425 32426 32427 32428 32429 32430 32431 32432 32433 32434 32435 32436 32437 32438 32439 32440 32441 32442 32443 32444 32445 32446 32447 32448 32449 32450 32451 32452 32453 32454 32455 32456 32457 32458 32459 32460 32461 32462 32463 32464 32465 32466 32467 32468 32469 32470 32471 32472 32473 32474 32475 32476 32477 32478 32479 32480 32481 32482 32483 32484 32485 32486 32487 32488 32489 32490 32491 32492 32493 32494 32495 32496 32497 32498 32499 32500 32501 32502 32503 32504 32505 32506 32507 32508 32509 32510 32511 32512 32513 32514 32515 32516 32517 32518 32519 32520 32521 32522 32523 32524 32525 32526 32527 32528 32529 32530 32531 32532 32533 32534 32535 32536 32537 32538 32539 32540 32541 32542 32543 32544 32545 32546 32547 32548 32549 32550 32551 32552 32553 32554 32555 32556 32557 32558 32559 32560 32561 32562 32563 32564 32565 32566 32567 32568 32569 32570 32571 32572 32573 32574 32575 32576 32577 32578 32579 32580 32581 32582 32583 32584 32585 32586 32587 32588 32589 32590 32591 32592 32593 32594 32595 32596 32597 32598 32599 32600 32601 32602 32603 32604 32605 32606 32607 32608 32609 32610 32611 32612 32613 32614 32615 32616 32617 32618 32619 32620 32621 32622 32623 32624 32625 32626 32627 32628 32629 32630 32631 32632 32633 32634 32635 32636 32637 32638 32639 32640 32641 32642 32643 32644 32645 32646 32647 32648 32649 32650 32651 32652 32653 32654 32655 32656 32657 32658 32659 32660 32661 32662 32663 32664 32665 32666 32667 32668 32669 32670 32671 32672 32673 32674 32675 32676 32677 32678 32679 32680 32681 32682 32683 32684 32685 32686 32687 32688 32689 32690 32691 32692 32693 32694 32695 32696 32697 32698 32699 32700 32701 32702 32703 32704 32705 32706 32707 32708 32709 32710 32711 32712 32713 32714 ",
"1 3 2 4 5 6 7 8 9 10 ",
"1 4 2 3 5 6 7 ",
"1 1768 2 1767 3 1766 4 1765 5 1764 6 1763 7 1762 8 1761 9 1760 10 1759 11 1758 12 1757 13 1756 14 1755 15 1754 16 1753 17 1752 18 1751 19 1750 20 1749 21 1748 22 1747 23 1746 24 1745 25 1744 26 1743 27 1742 28 1741 29 1740 30 1739 31 1738 32 1737 33 1736 34 1735 35 1734 36 1733 37 1732 38 1731 39 1730 40 1729 41 1728 42 1727 43 1726 44 1725 45 1724 46 1723 47 1722 48 1721 49 1720 50 1719 51 1718 52 1717 53 1716 54 1715 55 1714 56 1713 57 1712 58 1711 59 1710 60 1709 61 1708 62 1707 63 1706 64 1705 65 1704 66 1703 67 1702 68 1701 69 1700 70 1699 71 1698 72 1697 73 1696 74 1695 75 1694 76 1693 77 1692 78 1691 79 1690 80 1689 81 1688 82 1687 83 1686 84 1685 85 1684 86 1683 87 1682 88 1681 89 1680 90 1679 91 1678 92 1677 93 1676 94 1675 95 1674 96 1673 97 1672 98 1671 99 1670 100 1669 101 1668 102 1667 103 1666 104 1665 105 1664 106 1663 107 1662 108 1661 109 1660 110 1659 111 1658 112 1657 113 1656 114 1655 115 1654 116 1653 117 1652 118 1651 119 1650 120 1649 121 1648 122 1647 123 1646 124 1645 125 1644 126 1643 127 1642 128 1641 129 1640 130 1639 131 1638 132 1637 133 1636 134 1635 135 1634 136 1633 137 1632 138 1631 139 1630 140 1629 141 1628 142 1627 143 1626 144 1625 145 1624 146 1623 147 1622 148 1621 149 1620 150 1619 151 1618 152 1617 153 1616 154 1615 155 1614 156 1613 157 1612 158 1611 159 1610 160 1609 161 1608 162 1607 163 1606 164 1605 165 1604 166 1603 167 1602 168 1601 169 1600 170 1599 171 1598 172 1597 173 1596 174 1595 175 1594 176 1593 177 1592 178 1591 179 1590 180 1589 181 1588 182 1587 183 1586 184 1585 185 1584 186 1583 187 1582 188 1581 189 1580 190 1579 191 1578 192 1577 193 1576 194 1575 195 1574 196 1573 197 1572 198 1571 199 1570 200 1569 201 1568 202 1567 203 1566 204 1565 205 1564 206 1563 207 1562 208 1561 209 1560 210 1559 211 1558 212 1557 213 1556 214 1555 215 1554 216 1553 217 1552 218 1551 219 1550 220 1549 221 1548 222 1547 223 1546 224 1545 225 1544 226 1543 227 1542 228 1541 229 1540 230 1539 231 1538 232 1537 233 1536 234 1535 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"1 5 2 4 3 6 7 ",
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1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 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13223 112 13222 113 13221 114 13220 115 13219 116 13218 117 13217 118 13216 119 13215 120 13214 121 13213 122 13212 123 13211 124 13210 125 13209 126 13208 127 13207 128 13206 129 13205 130 13204 131 13203 132 13202 133 13201 134 13200 135 13199 136 13198 137 13197 138 13196 139 13195 140 13194 141 13193 142 13192 143 13191 144 13190 145 13189 146 13188 147 13187 148 13186 149 13185 150 13184 151 13183 152 13182 153 13181 154 13180 155 13179 156 13178 157 13177 158 13176 159 13175 160 13174 161 13173 162 13172 163 13171 164 13170 165 13169 166 13168 167 13167 168 13166 169 13165 170 13164 171 13163 172 13162 173 13161 174 13160 175 13159 176 13158 177 13157 178 13156 179 13155 180 13154 181 13153 182 13152 183 13151 184 13150 185 13149 186 13148 187 13147 188 13146 189 13145 190 13144 191 13143 192 13142 193 13141 194 13140 195 13139 196 13138 197 13137 198 13136 199 13135 200 13134 201 13133 202 13132 203 13131 204 13130 205 13129 206 13128 207 13127 208 13126 209 13125 210 13124 211 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3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 "
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.
Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.
Input
The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).
Output
Print n integers forming the permutation. If there are multiple answers, print any of them.
Examples
Input
3 2
Output
1 3 2
Input
3 1
Output
1 2 3
Input
5 2
Output
1 3 2 4 5
Note
By |x| we denote the absolute value of number x.
### Input:
5 2
### Output:
1 3 2 4 5
### Input:
3 1
### Output:
1 2 3
### Code:
from collections import Counter
import string
import math
import sys
# sys.setrecursionlimit(10**6)
from fractions import Fraction
def array_int():
return [int(i) for i in sys.stdin.readline().split()]
def vary(arrber_of_variables):
if arrber_of_variables==1:
return int(sys.stdin.readline())
if arrber_of_variables>=2:
return map(int,sys.stdin.readline().split())
def makedict(var):
return dict(Counter(var))
testcases=1
# testcases=vary(1)
for _ in range(testcases):
n,k=vary(2)
temp=k
num=[i for i in range(1,n+1)]
j=0
for i in range(k+1):
if i%2==0:
print(num[j],end=" ")
j+=1
else:
print(num[k],end=" ")
k-=1
for i in range(temp+1,n):
print(num[i],end=" ")
|
507_C. Guess Your Way Out!_3149 | Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node.
Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≤ n ≤ 2h, the player doesn't know where the exit is so he has to guess his way out!
Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:
* Character 'L' means "go to the left child of the current node";
* Character 'R' means "go to the right child of the current node";
* If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node;
* If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command;
* If he reached a leaf node that is not the exit, he returns to the parent of the current node;
* If he reaches an exit, the game is finished.
Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?
Input
Input consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2h).
Output
Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.
Examples
Input
1 2
Output
2
Input
2 3
Output
5
Input
3 6
Output
10
Input
10 1024
Output
2046
Note
A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one.
Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit.
<image> | import sys
def main():
rdl = list(map(int,input().split()))
obx(rdl[0],rdl[1],0,1)
def obx(lvl, ind, kl, current):
if lvl ==0:
print(int(kl))
sys.exit()
all = 0
for i in range(lvl+1):
all += 2**i
all -= 1
if ind > (2**(lvl))/2:
if current == 1:
kl += all / 2 + 1
else:
kl += 1
current *= -1
obx(lvl-1,ind-(2**lvl)/2,kl,current)
else:
if current == -1:
kl += all/2+1
else:
kl += 1
current *= -1
obx(lvl-1,ind,kl,current)
main() | {
"input": [
"1 2\n",
"10 1024\n",
"3 6\n",
"2 3\n",
"49 295606900104348\n",
"1 1\n",
"29 113463931\n",
"40 615535158153\n",
"50 905353992267944\n",
"22 3343393\n",
"20 589266\n",
"19 12783\n",
"30 414940886\n",
"32 3786259360\n",
"35 12080044014\n",
"13 4796\n",
"50 562949953421312\n",
"33 2599588275\n",
"16 21395\n",
"13 154\n",
"14 2334\n",
"24 14428281\n",
"7 31\n",
"21 1687606\n",
"35 31233562499\n",
"42 1042128038474\n",
"24 3543583\n",
"11 349\n",
"28 72803174\n",
"10 359\n",
"50 375299968947542\n",
"45 17519319833295\n",
"39 457181784666\n",
"4 14\n",
"17 80239\n",
"29 19827102\n",
"38 99361414961\n",
"20 742273\n",
"50 844424930131968\n",
"12 955\n",
"31 1819651953\n",
"18 153276\n",
"11 550\n",
"38 262402936512\n",
"8 19\n",
"12 2715\n",
"29 524109003\n",
"8 204\n",
"4 13\n",
"50 1125899906842624\n",
"10 577\n",
"40 874338951117\n",
"15 15512\n",
"3 5\n",
"9 43\n",
"25 678676\n",
"33 2696188969\n",
"3 8\n",
"46 34999315964173\n",
"6 40\n",
"50 1\n",
"27 109473899\n",
"22 3809417\n",
"19 13130\n",
"30 310686113\n",
"32 1974078185\n",
"13 1486\n",
"50 865276010242491\n",
"33 3120492793\n",
"28 21395\n",
"13 98\n",
"16 2334\n",
"24 720510\n",
"7 48\n",
"21 1890748\n",
"42 1454146769415\n",
"40 3543583\n",
"11 14\n",
"28 106984283\n",
"50 570076444813889\n",
"8 14\n",
"29 7131063\n",
"38 117354504358\n",
"13 955\n",
"31 1270150511\n",
"18 216017\n",
"11 19\n",
"38 90275483043\n",
"9 19\n",
"12 2442\n",
"5 13\n",
"10 50\n",
"15 26098\n",
"3 1\n",
"9 17\n",
"33 678676\n",
"3 3\n",
"46 46821697614159\n",
"6 45\n",
"9 1\n",
"27 27445737\n",
"3 4\n",
"13 147\n",
"33 3847539484\n",
"28 1168\n",
"8 98\n",
"13 2334\n",
"43 720510\n",
"7 53\n",
"21 588140\n",
"42 2844706328971\n",
"40 3307405\n",
"11 26\n",
"28 11483602\n",
"50 774178672041300\n",
"29 7444530\n",
"24 216017\n",
"38 162204501579\n",
"18 19\n",
"12 3307\n",
"5 17\n",
"16 50\n",
"15 15212\n",
"9 13\n",
"41 678676\n",
"5 3\n",
"6 58\n",
"14 1\n",
"27 48974904\n",
"6 4\n",
"13 207\n",
"33 7345333483\n",
"28 924\n",
"8 54\n",
"17 2334\n",
"43 9221\n",
"14 53\n",
"21 171538\n",
"40 2419461\n",
"28 7136641\n",
"29 6206402\n",
"24 401960\n",
"14 19\n",
"38 180588510466\n",
"17 19\n",
"12 1627\n",
"5 26\n",
"14 50\n",
"15 18949\n",
"2 2\n",
"9 6\n",
"49 678676\n",
"7 3\n",
"9 58\n",
"27 14496059\n",
"6 7\n",
"17 207\n",
"16 924\n",
"30 2334\n",
"43 7927\n",
"7 19\n",
"2 1\n"
],
"output": [
"2\n",
"2046\n",
"10\n",
"5\n",
"820858833984106\n",
"1\n",
"347736449\n",
"1572205271927\n",
"1871650493613618\n",
"7009189\n",
"1505684\n",
"503251\n",
"372407442\n",
"8003335020\n",
"2415167450\n",
"10298\n",
"562949953421312\n",
"1357401405\n",
"2899\n",
"7770\n",
"9440\n",
"26969983\n",
"95\n",
"3522472\n",
"60951693197\n",
"3195908899134\n",
"10865127\n",
"1057\n",
"50649698\n",
"91\n",
"50\n",
"17381304930499\n",
"830699159852\n",
"26\n",
"177237\n",
"478963048\n",
"28342263489\n",
"1182599\n",
"1407374883553280\n",
"2871\n",
"3412135549\n",
"328766\n",
"408\n",
"519008349260\n",
"205\n",
"4185\n",
"1052258991\n",
"422\n",
"27\n",
"2251799813685246\n",
"1345\n",
"1800799608767\n",
"14926\n",
"11\n",
"391\n",
"31527640\n",
"505562011\n",
"14\n",
"34646522010881\n",
"88\n",
"1125899906842623\n",
"209022797\n",
"7446127\n",
"502318\n",
"141700399\n",
"1627513051\n",
"4528\n",
"1909734402989387\n",
"905768705\n",
"268372819\n",
"8032\n",
"58592\n",
"14744962\n",
"18\n",
"3839292\n",
"35665512973\n",
"1099505715687\n",
"2028\n",
"90139167\n",
"1677245864919377\n",
"236\n",
"524988209\n",
"77454057000\n",
"6967\n",
"2736971871\n",
"402327\n",
"1997\n",
"4068763953\n",
"461\n",
"5482\n",
"13\n",
"944\n",
"53746\n",
"7\n",
"465\n",
"8587907800\n",
"3\n",
"70649864678473\n",
"77\n",
"511\n",
"85501397\n",
"4\n",
"7759\n",
"3489833704\n",
"268431988\n",
"96\n",
"1248\n",
"8796090989954\n",
"39\n",
"455758\n",
"4694418230653\n",
"1099505952629\n",
"2008\n",
"235845018\n",
"1336844846897188\n",
"527259574\n",
"16393113\n",
"350905120053\n",
"262093\n",
"6855\n",
"47\n",
"65456\n",
"12876\n",
"493\n",
"2199021228760\n",
"27\n",
"118\n",
"16383\n",
"12725174\n",
"60\n",
"7857\n",
"13447910099\n",
"268434264\n",
"166\n",
"124128\n",
"8796092994553\n",
"16295\n",
"1596886\n",
"1099504468735\n",
"256561545\n",
"521939912\n",
"16095648\n",
"16333\n",
"282994276620\n",
"131021\n",
"1305\n",
"54\n",
"16304\n",
"41465\n",
"2\n",
"500\n",
"562949951394520\n",
"123\n",
"440\n",
"110668991\n",
"55\n",
"130737\n",
"64344\n",
"1073734880\n",
"8796093013227\n",
"77\n",
"3\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Amr bought a new video game "Guess Your Way Out!". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node.
Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≤ n ≤ 2h, the player doesn't know where the exit is so he has to guess his way out!
Amr follows simple algorithm to choose the path. Let's consider infinite command string "LRLRLRLRL..." (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:
* Character 'L' means "go to the left child of the current node";
* Character 'R' means "go to the right child of the current node";
* If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node;
* If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command;
* If he reached a leaf node that is not the exit, he returns to the parent of the current node;
* If he reaches an exit, the game is finished.
Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?
Input
Input consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2h).
Output
Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.
Examples
Input
1 2
Output
2
Input
2 3
Output
5
Input
3 6
Output
10
Input
10 1024
Output
2046
Note
A perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one.
Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit.
<image>
### Input:
1 2
### Output:
2
### Input:
10 1024
### Output:
2046
### Code:
import sys
def main():
rdl = list(map(int,input().split()))
obx(rdl[0],rdl[1],0,1)
def obx(lvl, ind, kl, current):
if lvl ==0:
print(int(kl))
sys.exit()
all = 0
for i in range(lvl+1):
all += 2**i
all -= 1
if ind > (2**(lvl))/2:
if current == 1:
kl += all / 2 + 1
else:
kl += 1
current *= -1
obx(lvl-1,ind-(2**lvl)/2,kl,current)
else:
if current == -1:
kl += all/2+1
else:
kl += 1
current *= -1
obx(lvl-1,ind,kl,current)
main() |
556_D. Case of Fugitive_3152 | Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.
The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≤ i ≤ n - 1.
To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≤ x ≤ ri, li + 1 ≤ y ≤ ri + 1 and y - x = a.
The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.
Input
The first line contains integers n (2 ≤ n ≤ 2·105) and m (1 ≤ m ≤ 2·105) — the number of islands and bridges.
Next n lines each contain two integers li and ri (1 ≤ li ≤ ri ≤ 1018) — the coordinates of the island endpoints.
The last line contains m integer numbers a1, a2, ..., am (1 ≤ ai ≤ 1018) — the lengths of the bridges that Andrewid got.
Output
If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi.
If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case.
Examples
Input
4 4
1 4
7 8
9 10
12 14
4 5 3 8
Output
Yes
2 3 1
Input
2 2
11 14
17 18
2 9
Output
No
Input
2 1
1 1
1000000000000000000 1000000000000000000
999999999999999999
Output
Yes
1
Note
In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14.
In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist. | #!/usr/bin/env python
# 556D_fug.py - Codeforces.com 556D Fug quiz
#
# Copyright (C) 2015 Sergey
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Input
The first line contains integers n and m - the number of islands and bridges.
Next n lines each contain two integers li and ri - the coordinates of the
island endpoints.
The last line contains m integer numbers a1..am - the lengths of the bridges
that Andrewid got.
Output
If it is impossible to place a bridge between each pair of adjacent islands
in the required manner, print on a single line "No" (without the quotes)
, otherwise print in the first line "Yes" (without the quotes), and in the
second line print n-1 numbers b1, bn-1, which mean that between islands
i and i+1 there must be used a bridge number bi.
If there are multiple correct answers, print any of them. Note that in this
problem it is necessary to print "Yes" and "No" in correct case
"""
# Standard modules
import unittest
import sys
import re
# Additional modules
import bisect
###############################################################################
# Fastlist Class
###############################################################################
class Fastlist(object):
""" Fastlist representation """
def __init__(self, l=[], load=5000, sorted=0):
self._load = load
self._sorted = sorted
self._lists = []
self._starts = []
self._mins = []
self._insert_list()
self._irev = 0
self.extend(l)
def _index_location(self, index):
if len(self._lists[0]) == 0:
raise IndexError("List index out of range")
if index == 0:
return (0, 0)
if index == -1:
return (len(self._lists) - 1, len(self._lists[-1]) - 1)
if self._sorted:
raise RuntimeError("No index access to the sorted list, exc 0, -1")
length = len(self)
if index < 0:
index = length + index
if index >= length:
raise IndexError("List index out of range")
il = bisect.bisect_right(self._starts, index) - 1
return (il, index - self._starts[il])
def _insert_list(self, il=None):
if il is None:
il = len(self._lists)
self._lists.insert(il, [])
if self._sorted:
if il == 0:
self._mins.insert(il, None)
else:
self._mins.insert(il, self._lists[il-1][-1])
else:
if il == 0:
self._starts.insert(il, 0)
else:
start = self._starts[il-1] + len(self._lists[il-1])
self._starts.insert(il, start)
def _del_list(self, il):
del self._lists[il]
if self._sorted:
del self._mins[il]
else:
del self._starts[il]
def _rebalance(self, il):
illen = len(self._lists[il])
if illen >= self._load * 2:
self._insert_list(il)
self._even_lists(il)
if illen <= self._load * 0.2:
if il != 0:
self._even_lists(il-1)
elif len(self._lists) > 1:
self._even_lists(il)
def _even_lists(self, il):
tot = len(self._lists[il]) + len(self._lists[il+1])
if tot < self._load * 1:
self._lists[il] += self._lists[il+1]
self._del_list(il+1)
if self._sorted:
self._mins[il] = self._lists[il][0]
else:
half = tot//2
ltot = self._lists[il] + self._lists[il+1]
self._lists[il] = ltot[:half]
self._lists[il+1] = ltot[half:]
if self._sorted:
self._mins[il] = self._lists[il][0]
self._mins[il+1] = self._lists[il+1][0]
else:
self._starts[il+1] = self._starts[il] + len(self._lists[il])
def _obj_location(self, obj, l=0):
if not self._sorted:
raise RuntimeError("No by value access to an unserted list")
il = 0
if len(self._mins) > 1 and obj > self._mins[0]:
if l:
il = bisect.bisect_left(self._mins, obj) - 1
else:
il = bisect.bisect_right(self._mins, obj) - 1
if l:
ii = bisect.bisect_left(self._lists[il], obj)
else:
ii = bisect.bisect_right(self._lists[il], obj)
if ii == len(self._lists[il]) and il != len(self._lists) - 1:
ii = 0
il += 1
return (il, ii)
def insert(self, index, obj):
(il, ii) = self._index_location(index)
self._lists[il].insert(ii, obj)
for j in range(il + 1, len(self._starts)):
self._starts[j] += 1
self._rebalance(il)
def append(self, obj):
if len(self._lists[-1]) >= self._load:
self._insert_list()
self._lists[-1].append(obj)
if self._sorted and self._mins[0] is None:
self._mins[0] = self._lists[0][0]
def extend(self, iter):
for n in iter:
self.append(n)
def pop(self, index=None):
if index is None:
index = -1
(il, ii) = self._index_location(index)
item = self._lists[il].pop(ii)
if self._sorted:
if ii == 0 and len(self._lists[il]) > 0:
self._mins[il] = self._lists[il][0]
else:
for j in range(il + 1, len(self._starts)):
self._starts[j] -= 1
self._rebalance(il)
return item
def clear(self):
self._lists.clear()
self._starts.clear()
self._mins.clear()
self._insert_list()
def as_list(self):
return sum(self._lists, [])
def insort(self, obj, l=0):
(il, ii) = self._obj_location(obj, l)
self._lists[il].insert(ii, obj)
if ii == 0:
self._mins[il] = obj
self._rebalance(il)
def add(self, obj):
if self._sorted:
self.insort(obj)
else:
self.append(obj)
def insort_left(self, obj):
self.insort(obj, l=1)
def lower_bound(self, obj):
(self._il, self._ii) = self._obj_location(obj, l=1)
return self
def upper_bound(self, obj):
(self._il, self._ii) = self._obj_location(obj)
return self
def __str__(self):
return str(self.as_list())
def __setitem__(self, index, obj):
if isinstance(index, int):
(il, ii) = self._index_location(index)
self._lists[il][ii] = obj
elif isinstance(index, slice):
raise RuntimeError("Slice assignment is not supported")
def __getitem__(self, index):
if isinstance(index, int):
(il, ii) = self._index_location(index)
return self._lists[il][ii]
elif isinstance(index, slice):
rg = index.indices(len(self))
if rg[0] == 0 and rg[1] == len(self) and rg[2] == 1:
return self.as_list()
return [self.__getitem__(index) for index in range(*rg)]
def __iadd__(self, obj):
if self._sorted:
[self.insort(n) for n in obj]
else:
[self.append(n) for n in obj]
return self
def __delitem__(self, index):
if isinstance(index, int):
self.pop(index)
elif isinstance(index, slice):
rg = index.indices(len(self))
[self.__delitem__(rg[0]) for i in range(*rg)]
def __len__(self):
if self._sorted:
return sum([len(l) for l in self._lists])
return self._starts[-1] + len(self._lists[-1])
def __contains__(self, obj):
if self._sorted:
it = self.lower_bound(obj)
return not it.iter_end() and obj == it.iter_getitem()
else:
for n in self:
if obj == n:
return True
return False
def __bool__(self):
return len(self._lists[0]) != 0
def __iter__(self):
self._il = self._ii = self._irev = 0
return self
def __reversed__(self):
self._il = len(self._lists) - 1
self._ii = len(self._lists[self._il]) - 1
self._irev = 1
return self
def __next__(self):
if self._il in (-1, len(self._lists)) or len(self._lists[0]) == 0:
raise StopIteration("Iteration stopped")
item = self._lists[self._il][self._ii]
if not self._irev:
self._ii += 1
if self._ii == len(self._lists[self._il]):
self._il += 1
self._ii = 0
else:
self._ii -= 1
if self._ii == 0:
self._il -= 1
self._ii = len(self._lists[self._il])
return item
def iter_getitem(self):
return self._lists[self._il][self._ii]
def iter_end(self):
return (self._il == len(self._lists) - 1 and
self._ii == len(self._lists[self._il]))
def iter_del(self):
self.iter_pop()
def iter_pop(self):
item = self._lists[self._il].pop(self._ii)
if self._sorted:
if self._ii == 0 and len(self._lists[self._il]) > 0:
self._mins[self._il] = self._lists[self._il][0]
else:
for j in range(self._il + 1, len(self._starts)):
self._starts[j] -= 1
self._rebalance(self._il)
return item
###############################################################################
# Fug Class
###############################################################################
class Fug:
""" Fug representation """
def __init__(self, args):
""" Default constructor """
self.gsrt = args[0]
self.asrt = args[1]
self.gn = args[2]
self.result = [0]*self.gn
self.a = Fastlist(self.asrt, load=500, sorted=1)
def calculate(self):
""" Main calcualtion function of the class """
for i in range(self.gn):
g = self.gsrt[i]
it = self.a.lower_bound((g[1], 0))
if not it.iter_end():
alb = it.iter_getitem()
if alb[0] > g[0]:
return "No"
self.result[g[2]] = alb[1]+1
it.iter_del()
else:
return "No"
answer = "Yes\n" + " ".join(str(n) for n in self.result)
return answer
###############################################################################
# Executable code
###############################################################################
def get_inputs(test_inputs=None):
it = iter(test_inputs.split("\n")) if test_inputs else None
def uinput():
""" Unit-testable input function wrapper """
if it:
return next(it)
else:
return sys.stdin.readline()
# Getting string inputs. Place all uinput() calls here
num = [int(s) for s in uinput().split()]
gaps = []
prevli = [int(s) for s in uinput().split()]
for i in range(num[0] - 1):
li = [int(s) for s in uinput().split()]
min = li[0] - prevli[1]
max = li[1] - prevli[0]
gaps.append((max, min, i))
prevli = li
alist = [(int(s), i) for i, s in enumerate(uinput().split())]
# Decoding inputs into a list
inputs = [sorted(gaps), sorted(alist), num[0]-1]
return inputs
def calculate(test_inputs=None):
""" Base class calculate method wrapper """
return Fug(get_inputs(test_inputs)).calculate()
###############################################################################
# Unit Tests
###############################################################################
class unitTests(unittest.TestCase):
def test_sample_tests(self):
""" Quiz sample tests. Add \n to separate lines """
# Sample test 1
test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8"
self.assertEqual(calculate(test), "Yes\n2 3 1")
self.assertEqual(
get_inputs(test),
[[(3, 1, 1), (5, 2, 2), (7, 3, 0)],
[(3, 2), (4, 0), (5, 1), (8, 3)], 3])
# My tests
test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2"
self.assertEqual(calculate(test), "Yes\n1 2 5 4")
# Other tests
test = "2 2\n11 14\n17 18\n2 9"
self.assertEqual(calculate(test), "No")
# Other tests
test = (
"2 1\n1 1\n1000000000000000000 1000000000000000000" +
"\n999999999999999999")
self.assertEqual(calculate(test), "Yes\n1")
test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5")
self.assertEqual(calculate(test), "Yes\n1 6 3 2")
size = 200000
test = str(size) + " " + str(size) + "\n"
x = size*1000
for i in range(size):
test += str(x) + " " + str(x + i + 1) + "\n"
x += 2 * (i + 1)
for i in reversed(range(size)):
test += str(i) + " "
self.assertEqual(calculate(test)[0], "Y")
def test_Fug_class__basic_functions(self):
""" Fug class basic functions testing """
# Constructor test
d = Fug([[(1, 3, 1), (2, 5, 2), (3, 7, 0)],
[(3, 2), (4, 0), (5, 1), (8, 3)], 3])
# Sort bridges
self.assertEqual(d.asrt[0], (3, 2))
# Sort Gaps
self.assertEqual(d.gsrt[0], (1, 3, 1))
if __name__ == "__main__":
# Avoiding recursion limitaions
sys.setrecursionlimit(100000)
if sys.argv[-1] == "-ut":
unittest.main(argv=[" "])
# Print the result string
sys.stdout.write(calculate())
| {
"input": [
"4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8\n",
"2 2\n11 14\n17 18\n2 9\n",
"2 1\n1 1\n1000000000000000000 1000000000000000000\n999999999999999999\n",
"2 1\n1 1\n100 100\n5\n",
"3 2\n1000000000000000 1000000000000000\n3000000000000000 4000000000000000\n6000000000000000 7000000000000000\n2000000000000000 4000000000000000\n",
"6 9\n1 2\n8 16\n21 27\n31 46\n49 57\n59 78\n26 27 28 13 2 4 2 2 24\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 36\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 100\n4 7 6 1 5 4 3 1 5 2\n",
"6 9\n1 4\n10 18\n23 29\n33 43\n46 57\n59 77\n11 32 32 19 20 17 32 24 32\n",
"3 2\n1 5\n6 12\n14 100000000000\n10000000000 4\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 20\n9 10 2 9 10 4 9 9 9 10\n",
"2 1\n1 2\n5 6\n1\n",
"5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5\n",
"3 2\n1000000000000000 1000000000000000\n3000000000000000 4000000000000000\n6000000000000000 7000000000000000\n3052752506693368 4000000000000000\n",
"6 9\n1 4\n10 18\n23 29\n33 43\n46 57\n59 77\n14 32 32 19 20 17 32 24 32\n",
"3 2\n1000000000000000 1000000000000001\n3000000000000000 4000000000000000\n6000000000000000 7000000000000000\n2000000000000000 4000000000000000\n",
"5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 20 6 2 6 9 5\n",
"2 2\n11 14\n15 18\n2 9\n",
"6 9\n1 2\n8 16\n21 27\n31 46\n49 57\n59 78\n26 27 28 26 2 4 2 2 24\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 36\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 5 2\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 29\n9 10 2 9 10 4 9 9 9 10\n",
"5 9\n1 2\n3 2\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 5 2\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 29\n9 10 2 9 10 4 9 9 13 10\n",
"5 9\n1 2\n3 2\n5 7\n16 13\n14 20\n2 3 4 10 6 2 6 9 5\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 8 2\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 29\n9 11 2 9 10 4 9 9 13 10\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 8 2\n",
"5 10\n1 2\n3 1\n5 7\n11 13\n14 29\n9 11 2 9 10 4 9 9 13 10\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 8 2\n",
"5 10\n1 2\n3 1\n5 7\n11 13\n14 29\n9 14 2 9 10 4 9 9 13 10\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 001\n4 7 6 1 5 4 3 1 8 2\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 50\n79 80\n81 82\n84 87\n88 91\n98 001\n4 7 6 1 5 4 3 1 8 2\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 50\n79 80\n89 82\n84 87\n88 91\n98 001\n4 7 6 1 5 4 3 1 8 2\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n11 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 50\n79 80\n89 82\n84 87\n88 91\n98 001\n4 7 6 1 5 4 3 1 8 2\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n11 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 111\n130 68\n69 70\n74 50\n79 80\n89 82\n84 87\n88 91\n98 001\n4 7 6 1 5 4 3 1 8 2\n",
"6 9\n1 2\n8 16\n21 27\n31 46\n49 57\n59 151\n26 27 28 13 2 4 2 2 24\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 36\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 100\n4 7 6 1 5 4 3 2 5 2\n",
"2 1\n1 1\n1000000000000000000 1000000000100000000\n999999999999999999\n",
"3 2\n1000000000000000 1000000000000000\n3000000000000000 4000000000000000\n6000000000000000 7000000000000000\n3052752506693368 973599012707272\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 36\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n118 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 5 2\n",
"6 9\n1 4\n10 18\n23 29\n33 43\n46 57\n67 77\n14 32 32 19 20 17 32 24 32\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 22\n9 10 2 9 10 4 9 9 9 10\n",
"5 9\n1 2\n3 2\n5 7\n16 19\n14 20\n2 3 4 10 6 2 6 9 5\n",
"20 10\n4 9\n10 15\n21 18\n20 21\n25 27\n29 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 5 2\n",
"5 10\n1 2\n3 3\n5 7\n11 13\n14 29\n9 10 2 9 10 7 9 9 13 10\n",
"20 10\n4 9\n10 15\n17 18\n20 21\n25 27\n29 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 25\n65 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 8 2\n",
"20 10\n4 9\n10 15\n17 29\n20 21\n25 27\n13 32\n35 40\n46 48\n49 51\n53 56\n59 60\n63 64\n130 68\n69 70\n74 75\n79 80\n81 82\n84 87\n88 91\n98 000\n4 7 6 1 5 4 3 1 8 2\n",
"5 10\n1 2\n3 1\n5 7\n11 13\n14 29\n9 14 2 9 2 4 9 9 13 10\n"
],
"output": [
"Yes\n2 3 1 ",
"No",
"Yes\n1 ",
"No",
"Yes\n1 2 ",
"No",
"No",
"Yes\n1 6 4 5 8 ",
"Yes\n2 1 ",
"No",
"No",
"Yes\n1 6 3 2 ",
"No\n",
"Yes\n1 6 4 5 8\n",
"Yes\n1 2\n",
"Yes\n1 6 3 2\n",
"Yes\n1\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n1\n",
"No\n",
"No\n",
"Yes\n1 6 4 5 8\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.
The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [li, ri], besides, ri < li + 1 for 1 ≤ i ≤ n - 1.
To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that li ≤ x ≤ ri, li + 1 ≤ y ≤ ri + 1 and y - x = a.
The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.
Input
The first line contains integers n (2 ≤ n ≤ 2·105) and m (1 ≤ m ≤ 2·105) — the number of islands and bridges.
Next n lines each contain two integers li and ri (1 ≤ li ≤ ri ≤ 1018) — the coordinates of the island endpoints.
The last line contains m integer numbers a1, a2, ..., am (1 ≤ ai ≤ 1018) — the lengths of the bridges that Andrewid got.
Output
If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b1, b2, ..., bn - 1, which mean that between islands i and i + 1 there must be used a bridge number bi.
If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case.
Examples
Input
4 4
1 4
7 8
9 10
12 14
4 5 3 8
Output
Yes
2 3 1
Input
2 2
11 14
17 18
2 9
Output
No
Input
2 1
1 1
1000000000000000000 1000000000000000000
999999999999999999
Output
Yes
1
Note
In the first sample test you can, for example, place the second bridge between points 3 and 8, place the third bridge between points 7 and 10 and place the first bridge between points 10 and 14.
In the second sample test the first bridge is too short and the second bridge is too long, so the solution doesn't exist.
### Input:
4 4
1 4
7 8
9 10
12 14
4 5 3 8
### Output:
Yes
2 3 1
### Input:
2 2
11 14
17 18
2 9
### Output:
No
### Code:
#!/usr/bin/env python
# 556D_fug.py - Codeforces.com 556D Fug quiz
#
# Copyright (C) 2015 Sergey
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Input
The first line contains integers n and m - the number of islands and bridges.
Next n lines each contain two integers li and ri - the coordinates of the
island endpoints.
The last line contains m integer numbers a1..am - the lengths of the bridges
that Andrewid got.
Output
If it is impossible to place a bridge between each pair of adjacent islands
in the required manner, print on a single line "No" (without the quotes)
, otherwise print in the first line "Yes" (without the quotes), and in the
second line print n-1 numbers b1, bn-1, which mean that between islands
i and i+1 there must be used a bridge number bi.
If there are multiple correct answers, print any of them. Note that in this
problem it is necessary to print "Yes" and "No" in correct case
"""
# Standard modules
import unittest
import sys
import re
# Additional modules
import bisect
###############################################################################
# Fastlist Class
###############################################################################
class Fastlist(object):
""" Fastlist representation """
def __init__(self, l=[], load=5000, sorted=0):
self._load = load
self._sorted = sorted
self._lists = []
self._starts = []
self._mins = []
self._insert_list()
self._irev = 0
self.extend(l)
def _index_location(self, index):
if len(self._lists[0]) == 0:
raise IndexError("List index out of range")
if index == 0:
return (0, 0)
if index == -1:
return (len(self._lists) - 1, len(self._lists[-1]) - 1)
if self._sorted:
raise RuntimeError("No index access to the sorted list, exc 0, -1")
length = len(self)
if index < 0:
index = length + index
if index >= length:
raise IndexError("List index out of range")
il = bisect.bisect_right(self._starts, index) - 1
return (il, index - self._starts[il])
def _insert_list(self, il=None):
if il is None:
il = len(self._lists)
self._lists.insert(il, [])
if self._sorted:
if il == 0:
self._mins.insert(il, None)
else:
self._mins.insert(il, self._lists[il-1][-1])
else:
if il == 0:
self._starts.insert(il, 0)
else:
start = self._starts[il-1] + len(self._lists[il-1])
self._starts.insert(il, start)
def _del_list(self, il):
del self._lists[il]
if self._sorted:
del self._mins[il]
else:
del self._starts[il]
def _rebalance(self, il):
illen = len(self._lists[il])
if illen >= self._load * 2:
self._insert_list(il)
self._even_lists(il)
if illen <= self._load * 0.2:
if il != 0:
self._even_lists(il-1)
elif len(self._lists) > 1:
self._even_lists(il)
def _even_lists(self, il):
tot = len(self._lists[il]) + len(self._lists[il+1])
if tot < self._load * 1:
self._lists[il] += self._lists[il+1]
self._del_list(il+1)
if self._sorted:
self._mins[il] = self._lists[il][0]
else:
half = tot//2
ltot = self._lists[il] + self._lists[il+1]
self._lists[il] = ltot[:half]
self._lists[il+1] = ltot[half:]
if self._sorted:
self._mins[il] = self._lists[il][0]
self._mins[il+1] = self._lists[il+1][0]
else:
self._starts[il+1] = self._starts[il] + len(self._lists[il])
def _obj_location(self, obj, l=0):
if not self._sorted:
raise RuntimeError("No by value access to an unserted list")
il = 0
if len(self._mins) > 1 and obj > self._mins[0]:
if l:
il = bisect.bisect_left(self._mins, obj) - 1
else:
il = bisect.bisect_right(self._mins, obj) - 1
if l:
ii = bisect.bisect_left(self._lists[il], obj)
else:
ii = bisect.bisect_right(self._lists[il], obj)
if ii == len(self._lists[il]) and il != len(self._lists) - 1:
ii = 0
il += 1
return (il, ii)
def insert(self, index, obj):
(il, ii) = self._index_location(index)
self._lists[il].insert(ii, obj)
for j in range(il + 1, len(self._starts)):
self._starts[j] += 1
self._rebalance(il)
def append(self, obj):
if len(self._lists[-1]) >= self._load:
self._insert_list()
self._lists[-1].append(obj)
if self._sorted and self._mins[0] is None:
self._mins[0] = self._lists[0][0]
def extend(self, iter):
for n in iter:
self.append(n)
def pop(self, index=None):
if index is None:
index = -1
(il, ii) = self._index_location(index)
item = self._lists[il].pop(ii)
if self._sorted:
if ii == 0 and len(self._lists[il]) > 0:
self._mins[il] = self._lists[il][0]
else:
for j in range(il + 1, len(self._starts)):
self._starts[j] -= 1
self._rebalance(il)
return item
def clear(self):
self._lists.clear()
self._starts.clear()
self._mins.clear()
self._insert_list()
def as_list(self):
return sum(self._lists, [])
def insort(self, obj, l=0):
(il, ii) = self._obj_location(obj, l)
self._lists[il].insert(ii, obj)
if ii == 0:
self._mins[il] = obj
self._rebalance(il)
def add(self, obj):
if self._sorted:
self.insort(obj)
else:
self.append(obj)
def insort_left(self, obj):
self.insort(obj, l=1)
def lower_bound(self, obj):
(self._il, self._ii) = self._obj_location(obj, l=1)
return self
def upper_bound(self, obj):
(self._il, self._ii) = self._obj_location(obj)
return self
def __str__(self):
return str(self.as_list())
def __setitem__(self, index, obj):
if isinstance(index, int):
(il, ii) = self._index_location(index)
self._lists[il][ii] = obj
elif isinstance(index, slice):
raise RuntimeError("Slice assignment is not supported")
def __getitem__(self, index):
if isinstance(index, int):
(il, ii) = self._index_location(index)
return self._lists[il][ii]
elif isinstance(index, slice):
rg = index.indices(len(self))
if rg[0] == 0 and rg[1] == len(self) and rg[2] == 1:
return self.as_list()
return [self.__getitem__(index) for index in range(*rg)]
def __iadd__(self, obj):
if self._sorted:
[self.insort(n) for n in obj]
else:
[self.append(n) for n in obj]
return self
def __delitem__(self, index):
if isinstance(index, int):
self.pop(index)
elif isinstance(index, slice):
rg = index.indices(len(self))
[self.__delitem__(rg[0]) for i in range(*rg)]
def __len__(self):
if self._sorted:
return sum([len(l) for l in self._lists])
return self._starts[-1] + len(self._lists[-1])
def __contains__(self, obj):
if self._sorted:
it = self.lower_bound(obj)
return not it.iter_end() and obj == it.iter_getitem()
else:
for n in self:
if obj == n:
return True
return False
def __bool__(self):
return len(self._lists[0]) != 0
def __iter__(self):
self._il = self._ii = self._irev = 0
return self
def __reversed__(self):
self._il = len(self._lists) - 1
self._ii = len(self._lists[self._il]) - 1
self._irev = 1
return self
def __next__(self):
if self._il in (-1, len(self._lists)) or len(self._lists[0]) == 0:
raise StopIteration("Iteration stopped")
item = self._lists[self._il][self._ii]
if not self._irev:
self._ii += 1
if self._ii == len(self._lists[self._il]):
self._il += 1
self._ii = 0
else:
self._ii -= 1
if self._ii == 0:
self._il -= 1
self._ii = len(self._lists[self._il])
return item
def iter_getitem(self):
return self._lists[self._il][self._ii]
def iter_end(self):
return (self._il == len(self._lists) - 1 and
self._ii == len(self._lists[self._il]))
def iter_del(self):
self.iter_pop()
def iter_pop(self):
item = self._lists[self._il].pop(self._ii)
if self._sorted:
if self._ii == 0 and len(self._lists[self._il]) > 0:
self._mins[self._il] = self._lists[self._il][0]
else:
for j in range(self._il + 1, len(self._starts)):
self._starts[j] -= 1
self._rebalance(self._il)
return item
###############################################################################
# Fug Class
###############################################################################
class Fug:
""" Fug representation """
def __init__(self, args):
""" Default constructor """
self.gsrt = args[0]
self.asrt = args[1]
self.gn = args[2]
self.result = [0]*self.gn
self.a = Fastlist(self.asrt, load=500, sorted=1)
def calculate(self):
""" Main calcualtion function of the class """
for i in range(self.gn):
g = self.gsrt[i]
it = self.a.lower_bound((g[1], 0))
if not it.iter_end():
alb = it.iter_getitem()
if alb[0] > g[0]:
return "No"
self.result[g[2]] = alb[1]+1
it.iter_del()
else:
return "No"
answer = "Yes\n" + " ".join(str(n) for n in self.result)
return answer
###############################################################################
# Executable code
###############################################################################
def get_inputs(test_inputs=None):
it = iter(test_inputs.split("\n")) if test_inputs else None
def uinput():
""" Unit-testable input function wrapper """
if it:
return next(it)
else:
return sys.stdin.readline()
# Getting string inputs. Place all uinput() calls here
num = [int(s) for s in uinput().split()]
gaps = []
prevli = [int(s) for s in uinput().split()]
for i in range(num[0] - 1):
li = [int(s) for s in uinput().split()]
min = li[0] - prevli[1]
max = li[1] - prevli[0]
gaps.append((max, min, i))
prevli = li
alist = [(int(s), i) for i, s in enumerate(uinput().split())]
# Decoding inputs into a list
inputs = [sorted(gaps), sorted(alist), num[0]-1]
return inputs
def calculate(test_inputs=None):
""" Base class calculate method wrapper """
return Fug(get_inputs(test_inputs)).calculate()
###############################################################################
# Unit Tests
###############################################################################
class unitTests(unittest.TestCase):
def test_sample_tests(self):
""" Quiz sample tests. Add \n to separate lines """
# Sample test 1
test = "4 4\n1 4\n7 8\n9 10\n12 14\n4 5 3 8"
self.assertEqual(calculate(test), "Yes\n2 3 1")
self.assertEqual(
get_inputs(test),
[[(3, 1, 1), (5, 2, 2), (7, 3, 0)],
[(3, 2), (4, 0), (5, 1), (8, 3)], 3])
# My tests
test = "5 5\n1 1\n2 7\n8 8\n10 10\n16 16\n1 1 5 6 2"
self.assertEqual(calculate(test), "Yes\n1 2 5 4")
# Other tests
test = "2 2\n11 14\n17 18\n2 9"
self.assertEqual(calculate(test), "No")
# Other tests
test = (
"2 1\n1 1\n1000000000000000000 1000000000000000000" +
"\n999999999999999999")
self.assertEqual(calculate(test), "Yes\n1")
test = ("5 9\n1 2\n3 3\n5 7\n11 13\n14 20\n2 3 4 10 6 2 6 9 5")
self.assertEqual(calculate(test), "Yes\n1 6 3 2")
size = 200000
test = str(size) + " " + str(size) + "\n"
x = size*1000
for i in range(size):
test += str(x) + " " + str(x + i + 1) + "\n"
x += 2 * (i + 1)
for i in reversed(range(size)):
test += str(i) + " "
self.assertEqual(calculate(test)[0], "Y")
def test_Fug_class__basic_functions(self):
""" Fug class basic functions testing """
# Constructor test
d = Fug([[(1, 3, 1), (2, 5, 2), (3, 7, 0)],
[(3, 2), (4, 0), (5, 1), (8, 3)], 3])
# Sort bridges
self.assertEqual(d.asrt[0], (3, 2))
# Sort Gaps
self.assertEqual(d.gsrt[0], (1, 3, 1))
if __name__ == "__main__":
# Avoiding recursion limitaions
sys.setrecursionlimit(100000)
if sys.argv[-1] == "-ut":
unittest.main(argv=[" "])
# Print the result string
sys.stdout.write(calculate())
|
582_B. Once Again..._3156 | You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.
Input
The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).
Output
Print a single number — the length of a sought sequence.
Examples
Input
4 3
3 1 4 2
Output
5
Note
The array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. | f = lambda: map(int, input().split())
n, m = f()
t = list(f())
s = [0] * 301
d = s[:]
for i in t: d[i] += 1
for i in t * min(m, 2 * n): s[i] = max(s[:i + 1]) + 1
print(max(s) + max((m - n * 2) * max(d), 0)) | {
"input": [
"4 3\n3 1 4 2\n",
"100 10000000\n1 2 2 1 2 2 1 1 2 2 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1\n",
"99 10000000\n96 97 98 93 94 95 90 91 92 87 88 89 84 85 86 81 82 83 78 79 80 75 76 77 72 73 74 69 70 71 66 67 68 63 64 65 60 61 62 57 58 59 54 55 56 51 52 53 48 49 50 45 46 47 42 43 44 39 40 41 36 37 38 33 34 35 30 31 32 27 28 29 24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 11 6 7 8 3 4 5 2 1 99\n",
"98 10000000\n1 2 95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"99 10000000\n1 2 3 95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"31 3767\n16 192 152 78 224 202 186 52 118 19 13 38 199 196 35 295 100 64 205 37 166 124 169 214 66 243 134 192 253 270 92\n",
"2 8698\n71 225\n",
"100 10000000\n285 219 288 277 266 249 297 286 290 266 210 201 275 280 200 272 297 253 246 292 272 285 226 250 297 270 214 251 263 285 237 292 245 225 247 221 263 250 253 280 235 288 278 297 283 294 208 279 227 290 246 208 274 238 282 240 214 277 239 282 255 278 214 292 277 267 290 257 239 234 252 246 217 274 254 249 229 275 210 297 254 215 222 228 262 287 290 292 277 227 292 282 248 278 207 249 236 240 252 216\n",
"1 10000000\n1\n",
"99 84\n62 4 145 285 106 132 30 96 211 28 144 190 95 184 227 177 128 60 143 19 19 81 38 83 108 172 241 228 48 39 171 282 233 294 74 271 178 87 24 180 212 190 223 153 230 198 261 232 150 18 190 91 265 61 280 13 207 70 182 117 270 77 242 163 138 212 165 273 247 23 52 88 243 85 293 12 135 284 162 91 174 109 42 19 218 289 9 59 9 117 61 122 78 287 144 176 281 123 243\n",
"2 766\n147 282\n",
"39 1057\n1 120 247 206 260 117 152 24 162 266 202 152 278 199 63 188 271 62 62 177 213 77 229 197 263 178 211 102 255 257 163 134 14 66 11 113 216 288 225\n",
"98 10000000\n1 2 195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104\n",
"99 9\n218 254 64 32 130 52 242 40 29 188 196 300 258 165 110 151 265 142 295 166 141 260 158 218 184 251 180 16 177 125 192 279 201 189 170 37 7 150 117 79 97 13 69 156 254 287 17 214 95 300 150 197 133 161 46 26 82 119 174 6 252 42 264 136 273 127 42 274 113 278 165 173 231 209 159 56 248 39 46 41 222 278 114 84 150 13 63 106 179 279 44 15 13 74 50 168 38 181 127\n",
"46 13793\n1 239 20 83 33 183 122 208 46 141 11 264 196 266 104 130 116 117 31 213 235 207 219 206 206 46 89 112 260 191 245 234 87 255 186 4 251 177 130 59 81 54 227 116 105 284\n",
"81 10683\n3 52 265 294 213 242 185 151 27 165 128 237 124 14 43 147 104 162 124 103 233 156 288 57 289 195 129 77 97 138 153 289 203 126 34 5 97 35 224 120 200 203 222 94 171 294 293 108 145 193 227 206 34 295 1 233 258 7 246 34 60 232 58 169 77 150 272 279 171 228 168 84 114 229 149 97 66 246 212 236 151\n",
"1 1\n5\n",
"100 100\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 199\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 10000000\n31 150 132 17 273 18 292 260 226 217 165 68 36 176 89 75 227 246 137 151 87 215 267 242 21 156 27 27 202 73 218 290 57 2 85 159 96 39 191 268 67 64 55 266 29 209 215 85 149 267 161 153 118 293 104 197 91 252 275 56 288 76 82 239 215 105 283 88 76 294 138 166 9 273 14 119 67 101 250 13 63 215 80 5 221 234 258 195 129 67 152 56 277 129 111 98 213 22 209 299\n",
"2 2\n1 2\n",
"68 2450\n107 297 185 215 224 128 8 65 101 202 19 145 255 233 138 223 144 132 32 122 153 85 31 160 219 125 167 220 138 255 219 119 165 249 47 124 20 37 160 24 156 154 163 226 270 88 74 192 204 300 194 184 235 93 267 160 12 216 91 191 267 241 152 9 111 76 201 295\n",
"99 10000000\n97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2 99\n",
"1 1000\n42\n",
"98 10000000\n95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 97 98\n",
"99 105\n16 118 246 3 44 149 156 290 44 267 221 123 57 175 233 24 23 120 298 228 119 62 23 183 169 294 195 115 131 157 223 298 77 106 283 117 255 41 17 298 22 176 164 187 214 101 10 181 117 70 271 291 59 156 44 204 140 205 253 176 270 43 188 287 40 250 271 100 244 297 133 228 98 218 290 69 171 66 195 283 63 154 191 66 238 104 32 122 79 190 55 110 276 2 188 26 44 276 230\n",
"98 10000000\n1 1 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\n",
"99 10000000\n300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300\n",
"100 10000000\n300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300\n",
"2 1\n1 2\n",
"2 13101\n180 199\n",
"98 10000000\n195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"95 10000000\n192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"100 10000000\n2 4 2 5 2 1 1 3 2 4 3 5 3 4 2 4 2 4 1 2 3 3 1 1 3 3 1 3 5 1 2 1 5 2 3 4 5 2 1 2 1 3 4 4 4 3 5 5 3 1 5 2 1 4 4 3 2 3 2 3 2 4 2 1 3 3 3 2 3 5 1 5 4 3 1 4 5 3 2 4 5 4 1 3 4 1 1 3 4 2 2 5 4 2 2 3 3 2 3 1\n",
"2 1000\n1 2\n",
"100 10000000\n98 99 96 97 94 95 92 93 90 91 88 89 86 87 84 85 82 83 80 81 78 79 76 77 74 75 72 73 70 71 68 69 66 67 64 65 62 63 60 61 58 59 56 57 54 55 52 53 50 51 48 49 46 47 44 45 42 43 40 41 38 39 36 37 34 35 32 33 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 14 15 12 13 10 11 8 9 6 7 4 5 2 3 1 100\n",
"98 10000000\n1 2 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\n",
"99 116\n102 257 115 247 279 111 118 255 198 168 183 184 32 3 36 204 178 186 88 67 205 91 21 40 116 93 2 148 226 65 37 69 69 7 82 205 152 25 34 272 26 283 78 142 17 110 101 250 120 128 145 276 182 57 19 104 228 221 94 220 279 216 220 294 3 289 185 272 73 180 246 107 246 260 219 268 218 41 166 50 230 143 166 158 194 153 256 209 28 255 77 33 143 296 38 81 133 57 263\n",
"15 12226\n18 125 213 221 124 147 154 182 134 184 51 49 267 88 251\n",
"100 82\n151 81 114 37 17 178 92 164 215 108 286 89 108 87 77 166 110 215 212 300 125 92 247 221 78 120 163 113 249 141 36 241 179 116 187 287 69 103 76 80 160 200 249 170 159 72 8 138 171 45 97 271 114 176 54 181 4 259 246 39 29 292 203 49 122 253 99 259 252 74 231 92 43 142 23 144 109 282 47 207 140 212 9 3 255 137 285 146 22 84 52 98 41 21 177 63 217 62 291 64\n",
"99 10000000\n299 299 300 300 299 299 300 299 299 299 299 299 299 299 299 300 300 300 299 300 300 300 299 299 299 299 299 299 300 299 299 300 299 299 300 300 300 299 300 300 299 299 300 299 300 300 299 300 299 300 299 300 300 299 299 299 299 299 299 300 299 299 300 300 300 299 300 299 300 300 299 299 299 299 299 299 299 299 300 299 300 300 299 300 300 299 299 300 300 299 300 300 299 300 299 299 300 299 299\n",
"95 10000000\n92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 94 95\n",
"29 1918\n8 81 38 146 195 199 31 153 267 139 48 202 38 259 139 71 253 3 289 44 210 81 78 259 236 189 219 102 133\n",
"100 200\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"99 125\n85 108 102 3 173 193 27 38 288 272 14 270 98 42 34 206 275 54 20 164 207 255 3 196 183 3 61 37 98 223 208 231 144 76 114 19 138 156 157 198 124 39 120 283 34 139 240 240 247 132 211 81 225 12 101 108 63 20 30 158 266 201 101 101 113 157 132 108 41 215 54 27 154 102 175 276 103 35 52 130 10 266 229 202 85 210 116 149 214 14 121 263 217 152 240 275 113 253 53\n",
"29 7954\n1 257 8 47 4 26 49 228 120 53 138 101 101 35 293 232 299 195 219 45 195 174 96 157 168 138 288 114 291\n",
"100 10000000\n97 98 99 94 95 96 91 92 93 88 89 90 85 86 87 82 83 84 79 80 81 76 77 78 73 74 75 70 71 72 67 68 69 64 65 66 61 62 63 58 59 60 55 56 57 52 53 54 49 50 51 46 47 48 43 44 45 40 41 42 37 38 39 34 35 36 31 32 33 28 29 30 25 26 27 22 23 24 19 20 21 16 17 18 13 14 15 10 11 12 7 8 9 4 5 6 1 2 3 100\n",
"100 201\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 10000000\n1 2 2 1 2 2 1 1 2 2 2 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1\n",
"99 10000000\n96 97 98 93 94 95 90 91 92 87 88 89 84 85 86 81 82 83 78 79 80 75 76 77 72 73 74 69 70 71 66 67 68 63 64 65 60 51 62 57 58 59 54 55 56 51 52 53 48 49 50 45 46 47 42 43 44 39 40 41 36 37 38 33 34 35 30 31 32 27 28 29 24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 11 6 7 8 3 4 5 2 1 99\n",
"99 10000000\n1 2 3 95 96 97 92 93 65 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"2 15293\n71 225\n",
"99 84\n62 4 145 285 106 132 30 96 211 28 96 190 95 184 227 177 128 60 143 19 19 81 38 83 108 172 241 228 48 39 171 282 233 294 74 271 178 87 24 180 212 190 223 153 230 198 261 232 150 18 190 91 265 61 280 13 207 70 182 117 270 77 242 163 138 212 165 273 247 23 52 88 243 85 293 12 135 284 162 91 174 109 42 19 218 289 9 59 9 117 61 122 78 287 144 176 281 123 243\n",
"2 1127\n147 282\n",
"39 1057\n1 4 247 206 260 117 152 24 162 266 202 152 278 199 63 188 271 62 62 177 213 77 229 197 263 178 211 102 255 257 163 134 14 66 11 113 216 288 225\n",
"99 9\n218 254 64 32 130 52 242 40 29 188 196 300 258 165 110 151 265 142 295 166 141 260 158 218 184 251 180 16 177 125 192 279 201 189 170 37 7 150 117 79 97 13 69 156 254 287 17 214 95 300 150 197 133 161 46 26 82 119 174 6 252 42 264 136 273 253 42 274 113 278 165 173 231 209 159 56 248 39 46 41 222 278 114 84 150 13 63 106 179 279 44 15 13 74 50 168 38 181 127\n",
"81 10683\n3 52 265 294 213 242 185 151 27 165 128 237 124 14 43 147 104 162 124 103 233 156 46 57 289 195 129 77 97 138 153 289 203 126 34 5 97 35 224 120 200 203 222 94 171 294 293 108 145 193 227 206 34 295 1 233 258 7 246 34 60 232 58 169 77 150 272 279 171 228 168 84 114 229 149 97 66 246 212 236 151\n",
"1 1\n10\n",
"100 100\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 19 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 199\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 76 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 10000000\n31 150 132 17 273 18 292 260 226 217 293 68 36 176 89 75 227 246 137 151 87 215 267 242 21 156 27 27 202 73 218 290 57 2 85 159 96 39 191 268 67 64 55 266 29 209 215 85 149 267 161 153 118 293 104 197 91 252 275 56 288 76 82 239 215 105 283 88 76 294 138 166 9 273 14 119 67 101 250 13 63 215 80 5 221 234 258 195 129 67 152 56 277 129 111 98 213 22 209 299\n",
"68 2450\n107 297 185 215 224 128 8 65 101 202 19 145 255 233 138 223 144 132 32 122 153 85 31 160 219 125 167 220 138 255 219 119 165 249 47 124 20 15 160 24 156 154 163 226 270 88 74 192 204 300 194 184 235 93 267 160 12 216 91 191 267 241 152 9 111 76 201 295\n",
"99 10000000\n97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 6 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2 99\n",
"1 1100\n42\n",
"99 105\n16 118 246 3 44 149 156 290 44 267 221 123 57 175 233 15 23 120 298 228 119 62 23 183 169 294 195 115 131 157 223 298 77 106 283 117 255 41 17 298 22 176 164 187 214 101 10 181 117 70 271 291 59 156 44 204 140 205 253 176 270 43 188 287 40 250 271 100 244 297 133 228 98 218 290 69 171 66 195 283 63 154 191 66 238 104 32 122 79 190 55 110 276 2 188 26 44 276 230\n",
"98 10000000\n1 1 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 18 23 22 21 26 25 24 29 28 27 32 31 2 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\n",
"2 20926\n180 199\n",
"98 10000000\n195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 211 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"95 10000000\n192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 256 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"100 10000000\n3 4 2 5 2 1 1 3 2 4 3 5 3 4 2 4 2 4 1 2 3 3 1 1 3 3 1 3 5 1 2 1 5 2 3 4 5 2 1 2 1 3 4 4 4 3 5 5 3 1 5 2 1 4 4 3 2 3 2 3 2 4 2 1 3 3 3 2 3 5 1 5 4 3 1 4 5 3 2 4 5 4 1 3 4 1 1 3 4 2 2 5 4 2 2 3 3 2 3 1\n",
"15 12226\n18 125 213 221 124 147 154 182 134 184 51 91 267 88 251\n",
"100 82\n151 81 114 37 17 178 92 164 215 108 286 89 108 87 77 166 110 215 212 300 125 92 247 221 78 120 163 113 249 141 36 241 179 116 187 287 69 103 76 80 160 200 249 170 159 72 8 138 171 45 97 271 114 176 54 181 4 259 246 39 29 292 203 49 122 253 99 259 252 74 231 92 43 142 23 144 194 282 47 207 140 212 9 3 255 137 285 146 22 84 52 98 41 21 177 63 217 62 291 64\n",
"99 10000000\n299 299 300 300 299 299 300 299 299 299 299 299 299 299 299 300 300 300 299 300 300 300 299 299 299 299 299 299 300 299 299 300 299 299 300 300 300 299 300 300 299 299 300 299 300 300 299 300 299 300 299 300 300 299 299 299 299 299 299 300 299 299 300 300 300 299 300 299 300 300 299 299 299 299 299 299 299 299 300 299 300 300 299 300 300 104 299 300 300 299 300 300 299 300 299 299 300 299 299\n",
"29 1918\n8 81 38 146 195 199 31 153 267 139 48 202 38 259 139 61 253 3 289 44 210 81 78 259 236 189 219 102 133\n",
"100 200\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 14 12 9 10 7 8 5 6 3 4 1 2\n",
"99 125\n85 108 102 3 173 193 27 38 288 272 14 270 98 42 34 206 275 54 20 164 207 255 3 196 183 3 61 37 98 223 94 231 144 76 114 19 138 156 157 198 124 39 120 283 34 139 240 240 247 132 211 81 225 12 101 108 63 20 30 158 266 201 101 101 113 157 132 108 41 215 54 27 154 102 175 276 103 35 52 130 10 266 229 202 85 210 116 149 214 14 121 263 217 152 240 275 113 253 53\n",
"100 201\n99 100 97 98 67 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"4 3\n3 1 8 2\n",
"2 1222\n71 225\n",
"99 84\n62 4 145 285 106 132 30 96 211 28 96 190 95 184 227 177 8 60 143 19 19 81 38 83 108 172 241 228 48 39 171 282 233 294 74 271 178 87 24 180 212 190 223 153 230 198 261 232 150 18 190 91 265 61 280 13 207 70 182 117 270 77 242 163 138 212 165 273 247 23 52 88 243 85 293 12 135 284 162 91 174 109 42 19 218 289 9 59 9 117 61 122 78 287 144 176 281 123 243\n",
"100 100\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 19 35 36 33 34 31 49 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"100 199\n99 100 97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 82 79 80 77 132 75 76 73 74 71 72 69 70 76 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 52 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2\n",
"68 1307\n107 297 185 215 224 128 8 65 101 202 19 145 255 233 138 223 144 132 32 122 153 85 31 160 219 125 167 220 138 255 219 119 165 249 47 124 20 15 160 24 156 154 163 226 270 88 74 192 204 300 194 184 235 93 267 160 12 216 91 191 267 241 152 9 111 76 201 295\n",
"98 10000000\n195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 211 162 163 164 159 160 161 156 157 158 153 154 155 200 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"100 10000000\n3 4 2 5 2 1 1 3 2 4 3 5 3 4 2 4 2 4 2 2 3 3 1 1 3 3 1 3 5 1 2 1 5 2 3 4 5 2 1 2 1 3 4 4 4 3 5 5 3 1 5 2 1 4 4 3 2 3 2 3 2 4 2 1 3 3 3 2 3 5 1 5 4 3 1 4 5 3 2 4 5 4 1 3 4 1 1 3 4 2 2 5 4 2 2 3 3 2 3 1\n",
"98 10000000\n1 2 95 96 97 92 93 84 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"98 10000000\n1 2 195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 117 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104\n",
"98 10000000\n95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 69 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 97 98\n",
"100 10000000\n98 99 96 97 94 95 92 93 90 91 88 89 86 87 84 85 82 83 80 81 78 79 76 77 74 75 72 73 70 71 68 69 66 67 64 65 62 63 60 61 58 59 56 57 54 55 52 53 34 51 48 49 46 47 44 45 42 43 40 41 38 39 36 37 34 35 32 33 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 14 15 12 13 10 11 8 9 6 7 4 5 2 3 1 100\n",
"98 10000000\n1 2 5 4 3 8 7 6 11 10 9 14 13 12 17 16 19 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\n",
"95 10000000\n92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 40 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 94 95\n",
"100 10000000\n97 98 99 94 95 96 91 92 93 88 89 90 85 86 87 82 83 84 79 80 81 76 77 78 73 74 75 70 71 72 67 68 69 64 65 66 61 62 63 58 59 60 55 56 57 52 53 54 49 50 51 46 47 48 43 44 45 40 41 42 37 38 39 34 35 36 31 32 33 28 29 30 25 26 27 22 23 24 19 20 21 16 17 18 13 14 15 10 6 12 7 8 9 4 5 6 1 2 3 100\n",
"99 10000000\n96 97 98 93 94 95 90 91 92 87 88 89 84 85 86 81 82 83 78 79 80 75 76 77 72 73 74 69 70 71 66 67 68 63 64 65 60 51 62 57 58 59 54 55 56 51 52 53 48 49 50 45 46 47 42 43 44 39 40 41 36 37 38 33 34 35 30 31 32 27 28 29 24 25 26 21 22 23 18 19 20 15 16 17 12 13 14 9 10 1 6 7 8 3 4 5 2 1 99\n",
"98 10000000\n1 2 95 96 97 92 93 84 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 96 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"99 10000000\n1 2 3 95 44 97 92 93 65 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 35 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 21 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4\n",
"2 1127\n142 282\n",
"39 1057\n1 4 247 206 260 117 152 24 162 266 202 152 278 199 63 188 271 62 62 92 213 77 229 197 263 178 211 102 255 257 163 134 14 66 11 113 216 288 225\n",
"98 10000000\n1 2 195 196 197 192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 177 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 61 148 149 144 145 146 141 142 143 138 117 140 135 136 137 132 133 134 129 130 131 126 127 128 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104\n",
"99 9\n218 254 64 32 130 52 242 40 29 188 196 300 258 165 110 151 265 142 295 166 141 260 158 218 184 251 180 10 177 125 192 279 201 189 170 37 7 150 117 79 97 13 69 156 254 287 17 214 95 300 150 197 133 161 46 26 82 119 174 6 252 42 264 136 273 253 42 274 113 278 165 173 231 209 159 56 248 39 46 41 222 278 114 84 150 13 63 106 179 279 44 15 13 74 50 168 38 181 127\n",
"81 10683\n3 52 265 294 213 242 185 151 27 165 128 237 124 14 43 147 104 162 124 103 233 156 46 57 289 195 129 77 97 138 153 289 203 126 34 5 97 35 224 120 200 203 222 94 171 294 293 108 145 193 227 206 34 295 1 233 258 7 246 34 60 232 25 169 77 150 272 279 171 228 168 84 114 229 149 97 66 246 212 236 151\n",
"1 1\n12\n",
"100 10000000\n31 150 132 17 273 18 292 260 226 217 293 68 36 176 89 75 227 246 137 151 87 215 267 242 21 156 27 27 202 73 218 290 57 2 85 159 96 39 191 268 67 64 55 266 29 209 215 85 149 267 161 153 118 293 104 197 91 252 275 56 288 76 82 239 215 105 283 88 76 294 138 166 9 273 14 119 67 101 250 13 63 215 80 5 221 234 258 195 129 67 152 56 277 129 111 138 213 22 209 299\n",
"99 10000000\n97 98 95 96 93 94 91 92 89 90 87 88 85 86 83 84 81 122 79 80 77 78 75 76 73 74 71 72 69 70 67 68 65 66 63 64 61 62 59 60 57 58 55 56 53 54 51 6 49 50 47 48 45 46 43 44 41 42 39 40 37 38 35 36 33 34 31 32 29 30 27 28 25 26 23 24 21 22 19 20 17 18 15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2 99\n",
"98 10000000\n95 96 97 92 93 94 89 90 91 86 87 88 83 84 85 80 81 82 77 78 79 74 75 76 71 72 73 68 69 70 65 66 67 62 63 64 59 60 61 56 57 58 53 54 55 50 51 52 47 48 49 44 45 46 41 42 43 38 39 40 69 36 37 32 33 34 29 30 31 26 27 28 23 24 25 20 17 22 17 18 19 14 15 16 11 12 13 8 9 10 5 6 7 2 3 4 97 98\n",
"99 105\n16 118 246 3 44 149 156 290 44 267 221 123 57 175 233 15 23 120 298 228 119 62 23 183 169 294 21 115 131 157 223 298 77 106 283 117 255 41 17 298 22 176 164 187 214 101 10 181 117 70 271 291 59 156 44 204 140 205 253 176 270 43 188 287 40 250 271 100 244 297 133 228 98 218 290 69 171 66 195 283 63 154 191 66 238 104 32 122 79 190 55 110 276 2 188 26 44 276 230\n",
"98 10000000\n1 1 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 18 23 22 21 26 25 24 29 28 27 32 31 2 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 51 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 63 90 95 94 93 98 97 96\n",
"95 10000000\n192 193 194 189 190 191 186 187 188 183 184 185 180 181 182 15 178 179 174 175 176 171 172 173 168 169 170 165 166 167 162 163 164 159 160 161 156 157 158 153 154 155 150 151 152 147 148 149 144 145 146 141 142 143 138 139 140 135 136 137 132 133 134 129 130 131 126 127 256 123 124 125 120 121 122 117 118 119 114 115 116 111 112 113 108 109 110 105 106 107 102 103 104 1 2\n",
"100 10000000\n98 99 96 97 94 95 92 93 90 91 88 89 86 87 84 85 82 164 80 81 78 79 76 77 74 75 72 73 70 71 68 69 66 67 64 65 62 63 60 61 58 59 56 57 54 55 52 53 34 51 48 49 46 47 44 45 42 43 40 41 38 39 36 37 34 35 32 33 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 14 15 12 13 10 11 8 9 6 7 4 5 2 3 1 100\n",
"98 10000000\n1 2 5 4 3 8 7 6 11 10 9 14 13 12 17 16 19 20 19 18 23 22 21 26 25 24 29 28 27 32 31 30 35 34 33 38 37 36 41 40 39 44 43 42 47 46 45 50 49 48 53 52 89 56 55 54 59 58 57 62 61 60 65 64 63 68 67 66 71 70 69 74 73 72 77 76 75 80 79 78 83 82 81 86 85 84 89 88 87 92 91 90 95 94 93 98 97 96\n"
],
"output": [
"5\n",
"560000000\n",
"10000065\n",
"20000034\n",
"20000034\n",
"7546\n",
"8699\n",
"50000016\n",
"10000000\n",
"280\n",
"767\n",
"2128\n",
"10000066\n",
"51\n",
"27600\n",
"32070\n",
"1\n",
"150\n",
"249\n",
"40000023\n",
"3\n",
"7366\n",
"10000050\n",
"1000\n",
"20000034\n",
"435\n",
"20000032\n",
"990000000\n",
"1000000000\n",
"2\n",
"13102\n",
"10000065\n",
"10000063\n",
"260000004\n",
"1001\n",
"10000050\n",
"10000033\n",
"268\n",
"12234\n",
"274\n",
"580000001\n",
"20000033\n",
"3845\n",
"250\n",
"404\n",
"15919\n",
"10000067\n",
"251\n",
"550000000\n",
"20000033\n",
"20000034\n",
"15294\n",
"280\n",
"1128\n",
"2129\n",
"50\n",
"32069\n",
"1\n",
"201\n",
"399\n",
"40000023\n",
"7366\n",
"20000002\n",
"1100\n",
"436\n",
"20000032\n",
"20927\n",
"10000065\n",
"10000063\n",
"270000002\n",
"12234\n",
"274\n",
"570000002\n",
"3845\n",
"401\n",
"404\n",
"403\n",
"5\n",
"1223\n",
"281\n",
"202\n",
"400\n",
"3937\n",
"10000064\n",
"270000003\n",
"20000033\n",
"20000034\n",
"20000033\n",
"20000002\n",
"20000033\n",
"20000033\n",
"20000034\n",
"20000033\n",
"20000032\n",
"20000034\n",
"1128\n",
"2129\n",
"20000034\n",
"50\n",
"32069\n",
"1\n",
"40000023\n",
"20000002\n",
"20000033\n",
"436\n",
"20000032\n",
"10000063\n",
"20000002\n",
"20000033\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.
Input
The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).
Output
Print a single number — the length of a sought sequence.
Examples
Input
4 3
3 1 4 2
Output
5
Note
The array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence.
### Input:
4 3
3 1 4 2
### Output:
5
### Input:
100 10000000
1 2 2 1 2 2 1 1 2 2 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 2 1 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1
### Output:
560000000
### Code:
f = lambda: map(int, input().split())
n, m = f()
t = list(f())
s = [0] * 301
d = s[:]
for i in t: d[i] += 1
for i in t * min(m, 2 * n): s[i] = max(s[:i + 1]) + 1
print(max(s) + max((m - n * 2) * max(d), 0)) |
604_B. More Cowbell_3160 | Kevin Sun wants to move his precious collection of n cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into k boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection.
Kevin is a meticulous cowbell collector and knows that the size of his i-th (1 ≤ i ≤ n) cowbell is an integer si. In fact, he keeps his cowbells sorted by size, so si - 1 ≤ si for any i > 1. Also an expert packer, Kevin can fit one or two cowbells into a box of size s if and only if the sum of their sizes does not exceed s. Given this information, help Kevin determine the smallest s for which it is possible to put all of his cowbells into k boxes of size s.
Input
The first line of the input contains two space-separated integers n and k (1 ≤ n ≤ 2·k ≤ 100 000), denoting the number of cowbells and the number of boxes, respectively.
The next line contains n space-separated integers s1, s2, ..., sn (1 ≤ s1 ≤ s2 ≤ ... ≤ sn ≤ 1 000 000), the sizes of Kevin's cowbells. It is guaranteed that the sizes si are given in non-decreasing order.
Output
Print a single integer, the smallest s for which it is possible for Kevin to put all of his cowbells into k boxes of size s.
Examples
Input
2 1
2 5
Output
7
Input
4 3
2 3 5 9
Output
9
Input
3 2
3 5 7
Output
8
Note
In the first sample, Kevin must pack his two cowbells into the same box.
In the second sample, Kevin can pack together the following sets of cowbells: {2, 3}, {5} and {9}.
In the third sample, the optimal solution is {3, 5} and {7}. | n, k = map(int, input().split())
a = [int(s) for s in input().split()]
p = n - k
q = 2*k - n
if n < k:
q = n
p = 0
ma = 0
for i in range ((n - q) // 2):
ma = max((a[i] + a[n - q - i - 1]), ma)
ma2 = 0
for i in range(n - q, n):
ma2 = max(a[i], ma2)
print(max(ma,ma2))
| {
"input": [
"4 3\n2 3 5 9\n",
"2 1\n2 5\n",
"3 2\n3 5 7\n",
"10 5\n15 15 20 28 38 44 46 52 69 94\n",
"100 89\n474 532 759 772 803 965 1043 1325 1342 1401 1411 1452 1531 1707 1906 1928 2034 2222 2335 2606 2757 2968 2978 3211 3513 3734 3772 3778 3842 3948 3976 4038 4055 4113 4182 4267 4390 4408 4478 4595 4668 4792 4919 5133 5184 5255 5312 5341 5476 5628 5683 5738 5767 5806 5973 6051 6134 6254 6266 6279 6314 6342 6599 6676 6747 6777 6827 6842 7057 7097 7259 7340 7378 7405 7510 7520 7698 7796 8148 8351 8507 8601 8805 8814 8826 8978 9116 9140 9174 9338 9394 9403 9407 9423 9429 9519 9764 9784 9838 9946\n",
"10 9\n7 29 35 38 41 47 54 56 73 74\n",
"100 50\n156 182 208 409 496 515 659 761 772 794 827 912 1003 1236 1305 1388 1412 1422 1428 1465 1613 2160 2411 2440 2495 2684 2724 2925 3033 3035 3155 3260 3378 3442 3483 3921 4031 4037 4091 4113 4119 4254 4257 4442 4559 4614 4687 4839 4896 5054 5246 5316 5346 5859 5928 5981 6148 6250 6422 6433 6448 6471 6473 6485 6503 6779 6812 7050 7064 7074 7141 7378 7424 7511 7574 7651 7808 7858 8286 8291 8446 8536 8599 8628 8636 8768 8900 8981 9042 9055 9114 9146 9186 9411 9480 9590 9681 9749 9757 9983\n",
"1 40000\n23456\n",
"100 74\n10 211 323 458 490 592 979 981 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 5257 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 7611 7646 7887 7887 8065 8075 8160 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986\n",
"1 1\n1\n",
"4 2\n1 2 8 9\n",
"10 10\n4 19 22 24 25 43 49 56 78 88\n",
"100 50\n145 195 228 411 577 606 629 775 1040 1040 1058 1187 1307 1514 1784 1867 1891 2042 2042 2236 2549 2555 2560 2617 2766 2807 2829 2917 3070 3072 3078 3095 3138 3147 3149 3196 3285 3287 3309 3435 3531 3560 3563 3769 3830 3967 4081 4158 4315 4387 4590 4632 4897 4914 5128 5190 5224 5302 5402 5416 5420 5467 5517 5653 5820 5862 5941 6053 6082 6275 6292 6316 6490 6530 6619 6632 6895 7071 7234 7323 7334 7412 7626 7743 8098 8098 8136 8158 8264 8616 8701 8718 8770 8803 8809 8983 9422 9530 9811 9866\n",
"100 50\n56 298 387 456 518 532 589 792 870 1041 1055 1122 1141 1166 1310 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 6228 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 9087 9323 9477 9489 9518 9621 9699 9804\n",
"100 97\n340 402 415 466 559 565 649 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1599 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 3615 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 8534 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 4095 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 5511 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"1 2\n10\n",
"20 11\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 61\n82 167 233 425 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"1 2342\n12345\n",
"1 50000\n2\n",
"100 50\n130 248 312 312 334 589 702 916 921 1034 1047 1346 1445 1500 1585 1744 1951 2123 2273 2362 2400 2455 2496 2530 2532 2944 3074 3093 3094 3134 3698 3967 4047 4102 4109 4260 4355 4466 4617 4701 4852 4892 4915 4917 4936 4981 4999 5106 5152 5203 5214 5282 5412 5486 5525 5648 5897 5933 5969 6251 6400 6421 6422 6558 6805 6832 6908 6924 6943 6980 7092 7206 7374 7417 7479 7546 7672 7756 7973 8020 8028 8079 8084 8085 8137 8153 8178 8239 8639 8667 8829 9263 9333 9370 9420 9579 9723 9784 9841 9993\n",
"10 9\n6 10 10 32 36 38 69 80 82 93\n",
"2 2\n2 3\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2454 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"10 10\n3 15 31 61 63 63 68 94 98 100\n",
"100 89\n474 532 211 772 803 965 1043 1325 1342 1401 1411 1452 1531 1707 1906 1928 2034 2222 2335 2606 2757 2968 2978 3211 3513 3734 3772 3778 3842 3948 3976 4038 4055 4113 4182 4267 4390 4408 4478 4595 4668 4792 4919 5133 5184 5255 5312 5341 5476 5628 5683 5738 5767 5806 5973 6051 6134 6254 6266 6279 6314 6342 6599 6676 6747 6777 6827 6842 7057 7097 7259 7340 7378 7405 7510 7520 7698 7796 8148 8351 8507 8601 8805 8814 8826 8978 9116 9140 9174 9338 9394 9403 9407 9423 9429 9519 9764 9784 9838 9946\n",
"1 40000\n675\n",
"100 74\n10 211 323 458 490 592 979 768 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 5257 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 7611 7646 7887 7887 8065 8075 8160 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986\n",
"4 2\n0 2 8 9\n",
"10 10\n4 19 22 24 25 43 49 56 78 176\n",
"100 50\n145 195 228 411 577 606 629 775 1040 1040 1058 1187 1307 1514 1784 1867 1891 2042 2042 2236 2549 2555 2560 2617 2766 2807 2829 2917 3070 3072 3078 3095 3138 3147 3149 3196 3285 3287 3309 3435 3531 3560 3563 3769 3830 3967 4081 4158 4315 4387 4590 4632 4897 4914 5128 5190 5224 5302 5402 5416 5420 5467 5517 5653 5820 5862 5941 6053 6082 6275 6292 6316 6490 6530 6619 6632 6895 7071 7234 2360 7334 7412 7626 7743 8098 8098 8136 8158 8264 8616 8701 8718 8770 8803 8809 8983 9422 9530 9811 9866\n",
"100 50\n56 298 387 456 518 532 589 792 870 1041 1055 1122 1141 1166 1310 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 3295 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 9087 9323 9477 9489 9518 9621 9699 9804\n",
"100 97\n340 402 415 466 559 565 649 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 3615 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 8534 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 4095 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"20 11\n1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"1 50000\n4\n",
"10 9\n12 10 10 32 36 38 69 80 82 93\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2093 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"10 10\n3 15 31 1 63 63 68 94 98 100\n",
"2 1\n0 5\n",
"3 2\n3 5 6\n",
"1 7770\n258\n",
"10 10\n5 19 22 24 25 63 49 56 78 334\n",
"1 7770\n277\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 3749 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 3070 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6180 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 12792\n",
"2 2\n1 6\n",
"1 10297\n453\n",
"1 9704\n333\n",
"10 9\n7 29 35 38 41 47 54 56 73 137\n",
"10 10\n4 19 22 24 25 43 49 32 78 88\n",
"1 2342\n22263\n",
"1 50000\n3\n",
"3 4\n3 5 7\n",
"1 40000\n780\n",
"4 2\n0 3 8 9\n",
"10 9\n12 10 10 32 36 25 69 80 82 95\n",
"1 10664\n675\n",
"100 74\n10 211 323 458 490 592 979 768 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 1601 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 7611 7646 7887 7887 8065 8075 8160 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986\n",
"10 10\n4 19 22 24 25 63 49 56 78 176\n",
"100 50\n145 195 228 411 577 606 629 775 1040 1040 1058 1187 1307 393 1784 1867 1891 2042 2042 2236 2549 2555 2560 2617 2766 2807 2829 2917 3070 3072 3078 3095 3138 3147 3149 3196 3285 3287 3309 3435 3531 3560 3563 3769 3830 3967 4081 4158 4315 4387 4590 4632 4897 4914 5128 5190 5224 5302 5402 5416 5420 5467 5517 5653 5820 5862 5941 6053 6082 6275 6292 6316 6490 6530 6619 6632 6895 7071 7234 2360 7334 7412 7626 7743 8098 8098 8136 8158 8264 8616 8701 8718 8770 8803 8809 8983 9422 9530 9811 9866\n",
"100 50\n56 298 387 456 518 532 589 792 870 1041 1055 1122 1141 1166 1512 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 3295 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 9087 9323 9477 9489 9518 9621 9699 9804\n",
"100 97\n340 402 415 466 559 565 649 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 3615 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 3070 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"10 9\n12 10 10 32 36 25 69 80 82 93\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2524 2298 2360 2441 2093 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"2 2\n0 5\n",
"1 7770\n675\n",
"10 10\n5 19 22 24 25 63 49 56 78 176\n",
"100 97\n340 402 415 466 559 565 649 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 3070 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6180 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 3864 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"10 9\n12 3 10 32 36 25 69 80 82 93\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2524 2298 223 2441 2093 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"2 2\n1 5\n",
"100 97\n340 402 415 466 559 565 649 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 3749 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 3070 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6180 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 846 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 3864 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"10 9\n12 3 10 32 36 25 42 80 82 93\n",
"2 2\n1 4\n",
"10 10\n5 19 22 9 25 63 49 56 78 334\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 2324 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 846 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 3864 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"1 6505\n277\n",
"10 10\n5 19 22 9 25 63 49 9 78 334\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 1748 1826 2067 3749 2324 2368 2389 2607 2633 4008 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 3070 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6180 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 12792\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 2324 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 846 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 3825 6853 6854 3864 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"1 10297\n277\n",
"10 10\n5 19 22 9 25 117 49 9 78 334\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"100 61\n82 167 233 636 432 456 154 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 2324 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 846 4648 4651 4784 926 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 3825 6853 6854 3864 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"10 10\n5 6 22 9 25 117 49 9 78 334\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 2656 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"1 9704\n453\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 2656 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 3875 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n340 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 3875 5635 5732 5584 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n240 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 3875 5635 5732 5584 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n240 402 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 3875 5635 5732 5584 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 4414 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 97\n240 176 415 466 559 565 164 689 734 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1217 1929 3370 2278 2529 1043 2677 2839 2894 2951 3079 3237 3201 3556 3568 3569 3578 740 3641 3673 3892 4142 4418 4515 4766 4846 6097 5225 5269 5352 5460 3875 5635 5732 5584 5941 5976 5984 6104 6113 6402 6409 6460 5393 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 4414 8101 8154 8376 8379 8432 1981 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 1440 9983\n",
"100 89\n474 532 759 772 803 965 1043 1325 1342 1401 1411 1452 1531 1707 1906 1928 2034 2222 2335 2606 2757 2968 2978 3211 3513 3734 3772 3778 3842 3948 3976 4038 4055 4113 4182 4267 4390 4408 4478 4595 4668 4792 4919 5133 5184 5255 5312 5341 5476 5628 5683 5738 5767 5806 5973 6051 6134 2248 6266 6279 6314 6342 6599 6676 6747 6777 6827 6842 7057 7097 7259 7340 7378 7405 7510 7520 7698 7796 8148 8351 8507 8601 8805 8814 8826 8978 9116 9140 9174 9338 9394 9403 9407 9423 9429 9519 9764 9784 9838 9946\n",
"100 74\n10 211 323 458 490 592 979 981 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 5257 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 7611 7646 7887 7887 8065 8075 2185 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986\n",
"100 97\n340 402 415 466 559 565 72 689 727 771 774 776 789 795 973 1088 1212 1293 1429 1514 1587 1599 1929 1997 2278 2529 2656 2677 2839 2894 2951 3079 3237 3250 3556 3568 3569 3578 3615 3641 3673 3892 4142 4418 4515 4766 4846 4916 5225 5269 5352 5460 5472 5635 5732 5886 5941 5976 5984 6104 6113 6402 6409 6460 6550 6563 6925 7006 7289 7401 7441 7451 7709 7731 7742 7750 7752 7827 8101 8154 8376 8379 8432 8534 8578 8630 8706 8814 8882 8972 9041 9053 9109 9173 9473 9524 9547 9775 9791 9983\n",
"1 1\n10\n",
"20 11\n1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 61\n82 167 233 425 432 122 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 5361 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2454 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3390 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 6998 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"4 3\n2 3 5 6\n",
"2 1\n1 5\n",
"100 89\n474 532 211 772 803 965 1043 1325 1342 1401 1411 1452 1531 1707 1906 1928 2034 2222 2335 2606 2757 2968 2978 3211 3513 3734 3772 3778 3842 3948 3976 4038 4055 4113 4182 4267 4390 4408 4478 4595 4668 4792 4919 5133 5184 5255 5312 5341 5476 5628 5683 5738 5767 5806 5973 6051 6134 6254 6266 6279 6314 6342 6599 6676 6747 6777 6827 6842 4012 7097 7259 7340 7378 7405 7510 7520 7698 7796 8148 8351 8507 8601 8805 8814 8826 8978 9116 9140 9174 9338 9394 9403 9407 9423 9429 9519 9764 9784 9838 9946\n",
"100 74\n10 211 323 458 490 592 979 768 1143 1376 1443 1499 1539 1612 1657 1874 2001 2064 2123 2274 2346 2471 2522 2589 2879 2918 2933 2952 3160 3164 3167 3270 3382 3404 3501 3522 3616 3802 3868 3985 4007 4036 4101 4580 4687 4713 4714 4817 4955 5257 5280 5343 5428 5461 5566 5633 5727 5874 5925 6233 6309 6389 6500 6701 6731 6847 6916 7088 7088 7278 7296 7328 7564 9461 7646 7887 7887 8065 8075 8160 8300 8304 8316 8355 8404 8587 8758 8794 8890 9038 9163 9235 9243 9339 9410 9587 9868 9916 9923 9986\n",
"10 10\n4 19 22 24 25 38 49 56 78 176\n",
"100 50\n145 195 228 411 577 606 629 775 1040 1040 1058 1187 1307 1514 1784 1867 1891 2042 2042 2236 2549 2555 2560 2617 2766 2807 2829 2917 3070 3072 3078 3095 3138 3147 3149 3196 3285 3287 3309 3435 3531 3560 3563 3769 3830 3967 4081 4158 4315 4387 4590 4632 4897 4914 5128 5190 5224 5302 5402 5416 5420 5467 5517 5653 5820 5862 5941 6053 6082 6275 6292 6316 6490 6530 6619 6632 1696 7071 7234 2360 7334 7412 7626 7743 8098 8098 8136 8158 8264 8616 8701 8718 8770 8803 8809 8983 9422 9530 9811 9866\n",
"100 50\n56 298 387 456 518 532 589 792 870 1041 1055 1122 1141 1166 1310 1329 1523 1548 1626 1730 1780 1833 1850 1911 2006 2157 2303 2377 2403 2442 2450 2522 2573 2822 2994 3200 3238 3252 3280 3311 3345 3422 3429 3506 3526 3617 3686 3791 4134 4467 4525 4614 4633 4792 5017 5220 5243 5338 5445 5536 5639 5675 5763 5875 6129 6220 3295 6287 6385 6616 6789 6822 6940 6959 6985 7297 7304 7391 7443 7580 7824 7884 7981 8055 8063 8223 8280 8322 8346 8473 8688 8986 1903 9323 9477 9489 9518 9621 9699 9804\n",
"100 84\n53 139 150 233 423 570 786 861 995 1017 1072 1196 1276 1331 1680 1692 1739 892 1826 2067 2280 2324 2368 2389 2607 2633 2760 2782 2855 2996 3030 3093 3513 3536 3557 3594 3692 3707 3823 3832 4009 4047 4088 4095 4408 4537 4565 4601 4784 4878 4935 5029 5252 5322 5389 5407 6765 5567 5857 6182 6186 6198 6280 6290 6353 6454 6458 6567 6843 7166 7216 7257 7261 7375 7378 7539 7542 7762 7771 7797 7980 8363 8606 8612 8663 8801 8808 8823 8918 8975 8997 9240 9245 9259 9356 9755 9759 9760 9927 9970\n",
"20 11\n1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1\n",
"100 61\n82 167 233 636 432 456 494 507 562 681 683 921 1218 1323 1395 1531 1586 1591 1675 1766 1802 1842 2116 2625 2697 2735 2739 3337 3349 3395 3406 3596 3610 3721 4059 4078 4305 4330 4357 4379 4558 4648 4651 4784 4819 4920 5049 5312 4653 5418 5440 5463 5547 5594 5821 5951 5972 6141 6193 6230 6797 6842 6853 6854 7017 7026 7145 7322 7391 7460 7599 7697 7756 7768 7872 7889 8094 8215 8408 8440 8462 8714 8756 8760 8881 9063 9111 9184 9281 9373 9406 9417 9430 9511 9563 9634 9660 9788 9883 9927\n",
"1 31139\n4\n",
"10 9\n12 10 10 32 36 38 69 80 48 93\n",
"100 49990\n221 257 543 613 818 855 884 1195 1233 1293 1327 1474 1567 1568 1728 1789 1809 1957 1994 2198 2217 2289 2298 2360 2441 2093 2517 2519 2597 2652 2909 2958 2970 3271 3310 3409 3450 3646 3950 3965 4016 4116 4134 4159 4462 4624 4631 4783 4804 5031 5276 5538 5729 5845 5880 5894 5959 5961 6028 6105 6184 6335 6370 6523 6532 6677 6762 6868 7786 7066 7245 7360 7490 7492 7645 7677 7786 7804 8038 8131 8207 8400 8507 8556 8575 8599 8673 8676 8712 8816 9123 9158 9216 9369 9628 9707 9768 9800 9876 9934\n",
"3 2\n5 5 6\n"
],
"output": [
"9\n",
"7\n",
"8\n",
"109\n",
"9946\n",
"74\n",
"10676\n",
"23456\n",
"9986\n",
"1\n",
"10\n",
"88\n",
"10011\n",
"10009\n",
"9983\n",
"9970\n",
"10\n",
"2\n",
"9927\n",
"12345\n",
"2\n",
"11103\n",
"93\n",
"3\n",
"9934\n",
"100\n",
"9946\n",
"675\n",
"9986\n",
"10\n",
"176\n",
"10011\n",
"10009\n",
"9983\n",
"9970\n",
"2\n",
"9927\n",
"4\n",
"93\n",
"9934\n",
"100\n",
"5\n",
"8\n",
"258\n",
"334\n",
"277\n",
"12792\n",
"6\n",
"453\n",
"333\n",
"137\n",
"88\n",
"22263\n",
"3\n",
"7\n",
"780\n",
"11\n",
"95\n",
"675\n",
"9986\n",
"176\n",
"10011\n",
"10009\n",
"9983\n",
"9970\n",
"9927\n",
"93\n",
"9934\n",
"5\n",
"675\n",
"176\n",
"9983\n",
"9970\n",
"9927\n",
"93\n",
"9934\n",
"5\n",
"9983\n",
"9970\n",
"9927\n",
"93\n",
"4\n",
"334\n",
"9983\n",
"9927\n",
"277\n",
"334\n",
"9983\n",
"12792\n",
"9927\n",
"277\n",
"334\n",
"9983\n",
"9927\n",
"334\n",
"9983\n",
"453\n",
"9983\n",
"9983\n",
"9983\n",
"9983\n",
"9983\n",
"9983\n",
"9983\n",
"9983\n",
"9946\n",
"9986\n",
"9983\n",
"10\n",
"2\n",
"9927\n",
"9934\n",
"6\n",
"6\n",
"9946\n",
"9986\n",
"176\n",
"10011\n",
"10009\n",
"9970\n",
"2\n",
"9927\n",
"4\n",
"93\n",
"9934\n",
"10\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kevin Sun wants to move his precious collection of n cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into k boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection.
Kevin is a meticulous cowbell collector and knows that the size of his i-th (1 ≤ i ≤ n) cowbell is an integer si. In fact, he keeps his cowbells sorted by size, so si - 1 ≤ si for any i > 1. Also an expert packer, Kevin can fit one or two cowbells into a box of size s if and only if the sum of their sizes does not exceed s. Given this information, help Kevin determine the smallest s for which it is possible to put all of his cowbells into k boxes of size s.
Input
The first line of the input contains two space-separated integers n and k (1 ≤ n ≤ 2·k ≤ 100 000), denoting the number of cowbells and the number of boxes, respectively.
The next line contains n space-separated integers s1, s2, ..., sn (1 ≤ s1 ≤ s2 ≤ ... ≤ sn ≤ 1 000 000), the sizes of Kevin's cowbells. It is guaranteed that the sizes si are given in non-decreasing order.
Output
Print a single integer, the smallest s for which it is possible for Kevin to put all of his cowbells into k boxes of size s.
Examples
Input
2 1
2 5
Output
7
Input
4 3
2 3 5 9
Output
9
Input
3 2
3 5 7
Output
8
Note
In the first sample, Kevin must pack his two cowbells into the same box.
In the second sample, Kevin can pack together the following sets of cowbells: {2, 3}, {5} and {9}.
In the third sample, the optimal solution is {3, 5} and {7}.
### Input:
4 3
2 3 5 9
### Output:
9
### Input:
2 1
2 5
### Output:
7
### Code:
n, k = map(int, input().split())
a = [int(s) for s in input().split()]
p = n - k
q = 2*k - n
if n < k:
q = n
p = 0
ma = 0
for i in range ((n - q) // 2):
ma = max((a[i] + a[n - q - i - 1]), ma)
ma2 = 0
for i in range(n - q, n):
ma2 = max(a[i], ma2)
print(max(ma,ma2))
|
626_E. Simple Skewness_3163 | Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of n (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.
The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of elements in the list.
The second line contains n integers xi (0 ≤ xi ≤ 1 000 000) — the ith element of the list.
Output
In the first line, print a single integer k — the size of the subset.
In the second line, print k integers — the elements of the subset in any order.
If there are multiple optimal subsets, print any.
Examples
Input
4
1 2 3 12
Output
3
1 2 12
Input
4
1 1 2 2
Output
3
1 1 2
Input
2
1 2
Output
2
1 2
Note
In the first case, the optimal subset is <image>, which has mean 5, median 2, and simple skewness of 5 - 2 = 3.
In the second case, the optimal subset is <image>. Note that repetition is allowed.
In the last case, any subset has the same median and mean, so all have simple skewness of 0. | from itertools import accumulate
from fractions import Fraction
n = int(input())
A = [int(x) for x in input().split()]
A.sort()
B = list(accumulate([0] + A))
def condition(i, z):
return (2*z - 1)*(A[i-z] + A[-z]) > 2*(B[i+1] - B[i-z+1] + B[-1] - B[-z])
def average(i, z):
return Fraction((B[i+1] - B[i-z] + B[-1] - B[-z-1]) , 2*z + 1)
maxans = 0
argmax = (0, 0)
for i in range(1, n-1):
x, y = 0, min(i, n-1-i)
while y - x > 1:
z = (x + y)//2
if condition(i, z):
x = z
else:
y = z
if condition(i, y): x = y
if maxans < average(i, x) - A[i]:
maxans = average(i, x) - A[i]
argmax = (i, x)
print(argmax[1]*2 + 1)
for i in range(argmax[0] - argmax[1], argmax[0] + 1):
print(A[i], end = ' ')
for i in range(-argmax[1], 0):
print(A[i], end = ' ')
| {
"input": [
"2\n1 2\n",
"4\n1 1 2 2\n",
"4\n1 2 3 12\n",
"21\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 1000000\n",
"1\n412237\n",
"3\n76427 184396 963319\n",
"5\n741304 281944 258539 54430 284591\n",
"2\n725491 635622\n",
"40\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 999872 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 934464 868928 868928 737856 737856 475712 0\n",
"1\n935454\n",
"2\n847420 569122\n",
"4\n950582 784676 190241 964614\n",
"4\n109509 792173 120296 495368\n",
"1\n1000000\n",
"1\n534166\n",
"4\n231438 762672 125033 26806\n",
"3\n599645 198217 986791\n",
"2\n566563 590441\n",
"2\n248707 649443\n",
"5\n460447 303948 286063 992238 738282\n",
"20\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712\n",
"5\n301519 370449 319010 460799 983970\n",
"5\n900232 289442 225592 622868 113587\n",
"3\n758573 206400 991528\n",
"1\n253309\n",
"3\n198356 154895 894059\n",
"5\n582376 311446 253801 560676 530279\n",
"4\n549294 703669 96824 126683\n",
"3\n880502 176898 958582\n",
"2\n407635 619942\n",
"1\n94381\n",
"21\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 999998\n",
"4\n390366 733171 92086 595244\n",
"1\n486777\n",
"3\n76427 184396 1437965\n",
"5\n741304 281944 258539 54430 419816\n",
"2\n51907 635622\n",
"40\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 999872 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 1364934 868928 868928 737856 737856 475712 0\n",
"1\n1696575\n",
"2\n847420 966923\n",
"4\n950582 649987 190241 964614\n",
"4\n109509 792173 88452 495368\n",
"1\n1000001\n",
"1\n410450\n",
"4\n231438 1402360 125033 26806\n",
"3\n88771 198217 986791\n",
"2\n566563 792523\n",
"2\n248707 1199711\n",
"5\n460447 167993 286063 992238 738282\n",
"20\n999999 999998 999996 999992 999984 999968 999936 999872 999744 999488 998976 997952 995904 991808 983616 758345 934464 868928 737856 475712\n",
"5\n301519 370449 36656 460799 983970\n",
"5\n900232 570744 225592 622868 113587\n",
"3\n688616 206400 991528\n",
"1\n208702\n",
"3\n198356 154895 1445756\n",
"5\n582376 311446 46457 560676 530279\n",
"4\n549294 703669 185327 126683\n",
"3\n880502 120259 958582\n",
"2\n407635 880302\n",
"1\n173299\n",
"21\n999999 999998 999996 999992 999984 174767 999936 999872 999744 999488 998976 997952 995904 991808 983616 967232 934464 868928 737856 475712 999998\n",
"4\n390366 1291931 92086 595244\n",
"2\n1 3\n",
"4\n1 0 2 2\n",
"4\n1 2 1 12\n",
"1\n449273\n",
"3\n76427 184396 1187133\n",
"5\n741304 281944 258539 54430 15172\n",
"2\n16179 635622\n",
"40\n999999 999999 999998 999998 999996 999996 999992 999992 999984 999984 999968 999968 999936 999936 470707 999872 999744 999744 999488 999488 998976 998976 997952 997952 995904 995904 991808 991808 983616 983616 967232 967232 934464 1364934 868928 868928 737856 737856 475712 0\n",
"1\n2267645\n",
"2\n847420 448499\n",
"4\n950582 649987 214953 964614\n",
"4\n109509 409442 88452 495368\n",
"1\n1010001\n",
"1\n701708\n",
"4\n231438 1402360 125033 14616\n",
"3\n88771 158611 986791\n",
"2\n1127897 792523\n",
"2\n255532 1199711\n",
"5\n460447 167993 286063 347037 738282\n",
"20\n999999 999998 999996 999992 999984 999968 999936 1444212 999744 999488 998976 997952 995904 991808 983616 758345 934464 868928 737856 475712\n",
"5\n301519 370449 36656 174158 983970\n",
"5\n1532321 570744 225592 622868 113587\n",
"3\n688616 310389 991528\n",
"1\n52345\n",
"3\n198356 156571 1445756\n",
"5\n582376 311446 52784 560676 530279\n",
"4\n549294 703669 311387 126683\n"
],
"output": [
"1\n 1 \n",
"3\n 1 1 2 \n",
"3\n 1 2 12 \n",
"1\n 475712 \n",
"1\n 412237 \n",
"3\n 76427 184396 963319 \n",
"3\n 281944 284591 741304 \n",
"1\n 635622 \n",
"3\n 737856 737856 999999 \n",
"1\n 935454 \n",
"1\n 569122 \n",
"1\n 190241 \n",
"3\n 109509 120296 792173 \n",
"1\n 1000000 \n",
"1\n 534166 \n",
"3\n 26806 125033 762672 \n",
"1\n 198217 \n",
"1\n 566563 \n",
"1\n 248707 \n",
"3\n 286063 303948 992238 \n",
"1\n 475712 \n",
"3\n 301519 319010 983970 \n",
"3\n 113587 225592 900232 \n",
"1\n 206400 \n",
"1\n 253309 \n",
"3\n 154895 198356 894059 \n",
"3\n 253801 311446 582376 \n",
"3\n 96824 126683 703669 \n",
"1\n 176898 \n",
"1\n 407635 \n",
"1\n 94381 \n",
"3\n 999998 999998 999999 \n",
"3\n 92086 390366 733171 \n",
"1\n486777 ",
"3\n76427 184396 1437965 ",
"3\n258539 281944 741304 ",
"1\n51907 ",
"3\n737856 737856 1364934 ",
"1\n1696575 ",
"1\n847420 ",
"1\n190241 ",
"3\n88452 109509 792173 ",
"1\n1000001 ",
"1\n410450 ",
"3\n26806 125033 1402360 ",
"3\n88771 198217 986791 ",
"1\n566563 ",
"1\n248707 ",
"3\n167993 286063 992238 ",
"3\n737856 758345 999999 ",
"3\n301519 370449 983970 ",
"3\n113587 225592 900232 ",
"1\n206400 ",
"1\n208702 ",
"3\n154895 198356 1445756 ",
"3\n46457 311446 582376 ",
"3\n126683 185327 703669 ",
"1\n120259 ",
"1\n407635 ",
"1\n173299 ",
"3\n174767 475712 999999 ",
"3\n92086 390366 1291931 ",
"1\n1 ",
"1\n0 ",
"3\n1 1 12 ",
"1\n449273 ",
"3\n76427 184396 1187133 ",
"3\n15172 54430 741304 ",
"1\n16179 ",
"3\n470707 475712 1364934 ",
"1\n2267645 ",
"1\n448499 ",
"1\n214953 ",
"3\n88452 109509 495368 ",
"1\n1010001 ",
"1\n701708 ",
"3\n14616 125033 1402360 ",
"3\n88771 158611 986791 ",
"1\n792523 ",
"1\n255532 ",
"3\n167993 286063 738282 ",
"3\n737856 758345 1444212 ",
"3\n36656 174158 983970 ",
"3\n113587 225592 1532321 ",
"1\n310389 ",
"1\n52345 ",
"3\n156571 198356 1445756 ",
"3\n52784 311446 582376 ",
"3\n126683 311387 703669 "
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Define the simple skewness of a collection of numbers to be the collection's mean minus its median. You are given a list of n (not necessarily distinct) integers. Find the non-empty subset (with repetition) with the maximum simple skewness.
The mean of a collection is the average of its elements. The median of a collection is its middle element when all of its elements are sorted, or the average of its two middle elements if it has even size.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of elements in the list.
The second line contains n integers xi (0 ≤ xi ≤ 1 000 000) — the ith element of the list.
Output
In the first line, print a single integer k — the size of the subset.
In the second line, print k integers — the elements of the subset in any order.
If there are multiple optimal subsets, print any.
Examples
Input
4
1 2 3 12
Output
3
1 2 12
Input
4
1 1 2 2
Output
3
1 1 2
Input
2
1 2
Output
2
1 2
Note
In the first case, the optimal subset is <image>, which has mean 5, median 2, and simple skewness of 5 - 2 = 3.
In the second case, the optimal subset is <image>. Note that repetition is allowed.
In the last case, any subset has the same median and mean, so all have simple skewness of 0.
### Input:
2
1 2
### Output:
1
1
### Input:
4
1 1 2 2
### Output:
3
1 1 2
### Code:
from itertools import accumulate
from fractions import Fraction
n = int(input())
A = [int(x) for x in input().split()]
A.sort()
B = list(accumulate([0] + A))
def condition(i, z):
return (2*z - 1)*(A[i-z] + A[-z]) > 2*(B[i+1] - B[i-z+1] + B[-1] - B[-z])
def average(i, z):
return Fraction((B[i+1] - B[i-z] + B[-1] - B[-z-1]) , 2*z + 1)
maxans = 0
argmax = (0, 0)
for i in range(1, n-1):
x, y = 0, min(i, n-1-i)
while y - x > 1:
z = (x + y)//2
if condition(i, z):
x = z
else:
y = z
if condition(i, y): x = y
if maxans < average(i, x) - A[i]:
maxans = average(i, x) - A[i]
argmax = (i, x)
print(argmax[1]*2 + 1)
for i in range(argmax[0] - argmax[1], argmax[0] + 1):
print(A[i], end = ' ')
for i in range(-argmax[1], 0):
print(A[i], end = ' ')
|
676_A. Nicholas and Permutation_3169 | Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.
Nicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation.
The second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.
Output
Print a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.
Examples
Input
5
4 5 1 3 2
Output
3
Input
7
1 6 5 3 4 7 2
Output
6
Input
6
6 5 4 3 2 1
Output
5
Note
In the first sample, one may obtain the optimal answer by swapping elements 1 and 2.
In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.
In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2. | n = int(input())
a = list(map(int, input().split()))
maxLocate = a.index(n)
minLocate = a.index(1)
distanceMax = len(a) - 1 - a.index(n)
distanceMin = len(a) - 1 - a.index(1)
print(max(maxLocate, minLocate, distanceMax, distanceMin))
| {
"input": [
"6\n6 5 4 3 2 1\n",
"7\n1 6 5 3 4 7 2\n",
"5\n4 5 1 3 2\n",
"76\n1 47 54 17 38 37 12 32 14 48 43 71 60 56 4 13 64 41 52 57 62 24 23 49 20 10 63 3 25 66 59 40 58 33 53 46 70 7 35 61 72 74 73 19 30 5 29 6 15 28 21 27 51 55 50 9 65 8 67 39 76 42 31 34 16 2 36 11 26 44 22 45 75 18 69 68\n",
"12\n3 6 7 8 9 10 12 5 4 2 11 1\n",
"81\n63 22 4 41 43 74 64 39 10 35 20 81 11 28 70 67 53 79 16 61 68 52 27 37 58 9 50 49 18 30 72 47 7 60 78 51 23 48 73 66 44 13 15 57 56 38 1 76 25 45 36 34 42 8 75 26 59 14 71 21 6 77 5 17 2 32 40 54 46 24 29 3 31 19 65 62 33 69 12 80 55\n",
"98\n85 94 69 86 22 52 27 79 53 91 35 55 33 88 8 75 76 95 64 54 67 30 70 49 6 16 2 48 80 32 25 90 98 46 9 96 36 81 10 92 28 11 37 97 15 41 38 40 83 44 29 47 23 3 31 61 87 39 78 20 68 12 17 73 59 18 77 72 43 51 84 24 89 65 26 7 74 93 21 19 5 14 50 42 82 71 60 56 34 62 58 57 45 66 13 63 4 1\n",
"22\n8 3 17 4 16 21 14 11 10 15 6 18 13 12 22 20 5 2 9 7 19 1\n",
"14\n6 10 13 9 7 1 12 14 3 2 5 4 11 8\n",
"100\n76 70 67 54 40 1 48 63 64 36 42 90 99 27 47 17 93 7 13 84 16 57 74 5 83 61 19 56 52 92 38 91 82 79 34 66 71 28 37 98 35 94 77 53 73 10 26 80 15 32 8 81 3 95 44 46 72 6 33 11 21 85 4 30 24 51 49 96 87 55 14 31 12 60 45 9 29 22 58 18 88 2 50 59 20 86 23 41 100 39 62 68 69 97 78 43 25 89 65 75\n",
"4\n1 2 4 3\n",
"70\n19 12 15 18 36 16 61 69 24 7 11 13 3 48 55 21 37 17 43 31 41 22 28 32 27 63 38 49 59 56 30 25 67 51 52 45 50 44 66 57 26 60 5 46 33 6 23 34 8 40 2 68 14 39 65 64 62 42 47 54 10 53 9 1 70 58 20 4 29 35\n",
"11\n5 4 6 9 10 11 7 3 1 2 8\n",
"6\n5 4 2 6 1 3\n",
"82\n50 24 17 41 49 18 80 11 79 72 57 31 21 35 2 51 36 66 20 65 38 3 45 32 59 81 28 30 70 55 29 76 73 6 33 39 8 7 19 48 63 1 77 43 4 13 78 54 69 9 40 46 74 82 60 71 16 64 12 14 47 26 44 5 10 75 53 25 27 15 56 42 58 34 23 61 67 62 68 22 37 52\n",
"6\n2 1 3 4 5 6\n",
"99\n33 48 19 41 59 64 16 12 17 13 7 1 9 6 4 92 61 49 60 25 74 65 22 97 30 32 10 62 14 55 80 66 82 78 31 23 87 93 27 98 20 29 88 84 77 34 83 96 79 90 56 89 58 72 52 47 21 76 24 70 44 94 5 39 8 18 57 36 40 68 43 75 3 2 35 99 63 26 67 73 15 11 53 28 42 46 69 50 51 95 38 37 54 85 81 91 45 86 71\n",
"67\n66 16 2 53 35 38 49 28 18 6 36 58 21 47 27 5 50 62 44 12 52 37 11 56 15 31 25 65 17 29 59 41 7 42 4 43 39 10 1 40 24 13 20 54 19 67 46 60 51 45 64 30 8 33 26 9 3 22 34 23 57 48 55 14 63 61 32\n",
"19\n12 19 3 11 15 6 18 14 5 10 2 13 9 7 4 8 17 16 1\n",
"13\n8 4 3 7 5 11 9 1 10 2 13 12 6\n",
"32\n15 32 11 3 18 23 19 14 5 8 6 21 13 24 25 4 16 9 27 20 17 31 2 22 7 12 30 1 26 10 29 28\n",
"31\n29 13 26 27 9 28 2 16 30 21 12 11 3 31 23 6 22 20 1 5 14 24 19 18 8 4 10 17 15 25 7\n",
"7\n1 5 3 6 2 4 7\n",
"4\n3 1 4 2\n",
"84\n75 8 66 21 61 63 72 51 52 13 59 25 28 58 64 53 79 41 34 7 67 11 39 56 44 24 50 9 49 55 1 80 26 6 73 74 27 69 65 37 18 43 36 17 30 3 47 29 76 78 32 22 12 68 46 5 42 81 57 31 33 83 54 48 14 62 10 16 4 20 71 70 35 15 45 19 60 77 2 23 84 40 82 38\n",
"100\n22 47 34 65 69 5 68 78 53 54 41 23 80 51 11 8 2 85 81 75 25 58 29 73 30 49 10 71 17 96 76 89 79 20 12 15 55 7 46 32 19 3 82 35 74 44 38 40 92 14 6 50 97 63 45 93 37 18 62 77 87 36 83 9 90 61 57 28 39 43 52 42 24 56 21 84 26 99 88 59 33 70 4 60 98 95 94 100 13 48 66 72 16 31 64 91 1 86 27 67\n",
"9\n6 8 5 3 4 7 9 2 1\n",
"44\n4 38 6 40 29 3 44 2 30 35 25 36 34 10 11 31 21 7 14 23 37 19 27 18 5 22 1 16 17 9 39 13 15 32 43 8 41 26 42 12 24 33 20 28\n",
"6\n5 2 3 1 6 4\n",
"52\n16 45 23 7 15 19 43 20 4 32 35 36 9 50 5 26 38 46 13 33 12 2 48 37 41 31 10 28 8 42 3 21 11 1 17 27 34 30 44 40 6 51 49 47 25 22 18 24 52 29 14 39\n",
"100\n100 97 92 12 62 17 19 58 37 26 30 95 31 35 87 10 13 43 98 61 28 89 76 1 23 21 11 22 50 56 91 74 3 24 96 55 64 67 14 4 71 16 18 9 77 68 51 81 32 82 46 88 86 60 29 66 72 85 70 7 53 63 33 45 83 2 25 94 52 93 5 69 20 47 49 54 57 39 34 27 90 80 78 59 40 42 79 6 38 8 48 15 65 73 99 44 41 84 36 75\n",
"2\n1 2\n",
"4\n2 4 1 3\n",
"50\n31 45 3 34 13 43 32 4 42 9 7 8 24 14 35 6 19 46 44 17 18 1 25 20 27 41 2 16 12 10 11 47 38 21 28 49 30 15 50 36 29 26 22 39 48 5 23 37 33 40\n",
"6\n3 2 1 4 6 5\n",
"51\n47 29 2 11 43 44 27 1 39 14 25 30 33 21 38 45 34 51 16 50 42 31 41 46 15 48 13 19 6 37 35 7 22 28 20 4 17 10 5 8 24 40 9 36 18 49 12 26 23 3 32\n",
"5\n2 3 1 5 4\n",
"94\n29 85 82 78 61 83 80 63 11 38 50 43 9 24 4 87 79 45 3 17 90 7 34 27 1 76 26 39 84 47 22 41 81 19 44 23 56 92 35 31 72 62 70 53 40 88 13 14 73 2 59 86 46 94 15 12 77 57 89 42 75 48 18 51 32 55 71 30 49 91 20 60 5 93 33 64 21 36 10 28 8 65 66 69 74 58 6 52 25 67 16 37 54 68\n",
"3\n1 3 2\n",
"34\n34 30 7 16 6 1 10 23 29 13 15 25 32 26 18 11 28 3 14 21 19 5 31 33 4 17 8 9 24 20 27 22 2 12\n",
"42\n42 15 24 26 4 34 19 29 38 32 31 33 14 41 21 3 11 39 25 6 5 20 23 10 16 36 18 28 27 1 7 40 22 30 9 2 37 17 8 12 13 35\n",
"4\n1 4 2 3\n",
"37\n24 1 12 23 11 6 30 15 4 21 13 20 25 17 5 8 36 19 32 26 14 9 7 18 10 29 37 35 16 2 22 34 3 27 31 33 28\n",
"97\n40 63 44 64 84 92 38 41 28 91 3 70 76 67 94 96 35 79 29 22 78 88 85 8 21 1 93 54 71 80 37 17 13 26 62 59 75 87 69 33 89 49 77 61 12 39 6 36 58 18 73 50 82 45 74 52 11 34 95 7 23 30 15 32 31 16 55 19 20 83 60 72 10 53 51 14 27 9 68 47 5 2 81 46 57 86 56 43 48 66 24 25 4 42 65 97 90\n",
"10\n2 9 3 4 1 10 5 6 7 8\n",
"89\n68 40 14 58 56 25 8 44 49 55 9 76 66 54 33 81 42 15 59 17 21 30 75 60 4 48 64 6 52 63 61 27 12 57 72 67 23 86 77 80 22 13 43 73 26 78 50 51 18 62 1 29 82 16 74 2 87 24 3 41 11 46 47 69 10 84 65 39 35 79 70 32 34 31 20 19 53 71 36 28 83 88 38 85 7 5 37 45 89\n",
"4\n4 2 1 3\n",
"48\n29 26 14 18 34 33 13 39 32 1 37 20 35 19 28 48 30 23 46 27 5 22 24 38 12 15 8 36 43 45 16 47 6 9 31 40 44 17 2 41 11 42 25 4 21 3 10 7\n",
"8\n2 3 4 5 1 6 8 7\n",
"10\n8 7 10 1 2 3 4 6 5 9\n",
"4\n1 4 3 2\n",
"15\n3 14 13 12 7 2 4 11 15 1 8 6 5 10 9\n",
"29\n21 11 10 25 2 5 9 16 29 8 17 4 15 13 6 22 7 24 19 12 18 20 1 3 23 28 27 14 26\n",
"25\n12 13 22 17 1 18 14 5 21 2 10 4 3 23 11 6 20 8 24 16 15 19 9 7 25\n",
"88\n1 83 73 46 61 31 39 86 57 43 16 29 26 80 82 7 36 42 13 20 6 64 19 40 24 12 47 87 8 34 75 9 69 3 11 52 14 25 84 59 27 10 54 51 81 74 65 77 70 17 60 35 23 44 49 2 4 88 5 21 41 32 68 66 15 55 48 58 78 53 22 38 45 33 30 50 85 76 37 79 63 18 28 62 72 56 71 67\n",
"100\n66 100 53 88 7 73 54 41 31 42 8 46 65 90 78 14 94 30 79 39 89 5 83 50 38 61 37 86 22 95 60 98 34 57 91 10 75 25 15 43 23 17 96 35 93 48 87 47 56 13 19 9 82 62 67 80 11 55 99 70 18 26 58 85 12 44 16 45 4 49 20 71 92 24 81 2 76 32 6 21 84 36 52 97 59 63 40 51 27 64 68 3 77 72 28 33 29 1 74 69\n",
"18\n8 6 14 17 9 11 15 13 5 3 18 1 2 7 12 16 4 10\n",
"6\n5 4 2 1 6 3\n",
"8\n2 5 6 4 8 3 1 7\n",
"3\n2 3 1\n",
"6\n4 6 3 5 2 1\n",
"4\n4 3 1 2\n",
"61\n61 11 26 29 31 40 32 30 35 3 18 52 9 53 42 4 50 54 20 58 28 49 22 12 2 19 16 15 57 34 51 43 7 17 25 41 56 47 55 60 46 14 44 45 24 27 33 1 48 13 59 23 38 39 6 5 36 10 8 37 21\n",
"4\n4 3 2 1\n",
"65\n10 11 55 43 53 25 35 26 16 37 41 38 59 21 48 2 65 49 17 23 18 30 62 36 3 4 47 15 28 63 57 54 31 46 44 12 51 7 29 13 56 52 14 22 39 19 8 27 45 5 6 34 32 61 20 50 9 24 33 58 60 40 1 42 64\n",
"3\n1 2 3\n",
"92\n67 57 76 78 25 89 6 82 11 16 26 17 59 48 73 10 21 31 27 80 4 5 22 13 92 55 45 85 63 28 75 60 54 88 91 47 29 35 7 87 1 39 43 51 71 84 83 81 46 9 38 56 90 24 37 41 19 86 50 61 79 20 18 14 69 23 62 65 49 52 58 53 36 2 68 64 15 42 30 34 66 32 44 40 8 33 3 77 74 12 70 72\n",
"23\n1 23 11 20 9 3 12 4 7 17 5 15 2 10 18 16 8 22 14 13 19 21 6\n",
"4\n3 1 2 4\n",
"54\n6 39 17 3 45 52 16 21 23 48 42 36 13 37 46 10 43 27 49 7 38 32 31 30 15 25 2 29 8 51 54 19 41 44 24 34 22 5 20 14 12 1 33 40 4 26 9 35 18 28 47 50 11 53\n",
"69\n29 49 25 51 21 35 11 61 39 54 40 37 60 42 27 33 59 53 34 10 46 2 23 69 8 47 58 36 1 38 19 12 7 48 13 3 6 22 18 5 65 24 50 41 66 44 67 57 4 56 62 43 9 30 14 15 28 31 64 26 16 55 68 17 32 20 45 52 63\n",
"60\n60 27 34 32 54 55 33 12 40 3 47 44 50 39 38 59 11 25 17 15 16 30 21 31 10 52 5 23 4 48 6 26 36 57 14 22 8 56 58 9 24 7 37 53 42 43 20 49 51 19 2 46 28 18 35 13 29 45 41 1\n",
"4\n2 1 4 3\n",
"57\n39 28 53 36 3 6 12 56 55 20 50 19 43 42 18 40 24 52 38 17 33 23 22 41 14 7 26 44 45 16 35 1 8 47 31 5 30 51 32 4 37 25 13 34 54 21 46 10 15 11 2 27 29 48 49 9 57\n",
"4\n3 4 1 2\n",
"3\n2 1 3\n",
"4\n1 2 3 4\n",
"86\n64 56 41 10 31 69 47 39 37 36 27 19 9 42 15 6 78 59 52 17 71 45 72 14 2 54 38 79 4 18 16 8 46 75 50 82 44 24 20 55 58 86 61 43 35 32 33 40 63 30 28 60 13 53 12 57 77 81 76 66 73 84 85 62 68 22 51 5 49 7 1 70 80 65 34 48 23 21 83 11 74 26 29 67 25 3\n",
"100\n22 59 25 77 68 79 32 45 20 28 61 60 38 86 33 10 100 15 53 75 78 39 67 13 66 34 96 4 63 23 73 29 31 35 71 55 16 14 72 56 94 97 17 93 47 84 57 8 21 51 54 85 26 76 49 81 2 92 62 44 91 87 11 24 95 69 5 7 99 6 65 48 70 12 41 18 74 27 42 3 80 30 50 98 58 37 82 89 83 36 40 52 19 9 88 46 43 1 90 64\n",
"83\n64 8 58 17 67 46 3 82 23 70 72 16 53 45 13 20 12 48 40 4 6 47 76 60 19 44 30 78 28 22 75 15 25 29 63 74 55 32 14 51 35 31 62 77 27 42 65 71 56 61 66 41 68 49 7 34 2 83 36 5 33 26 37 80 59 50 1 9 54 21 18 24 38 73 81 52 10 39 43 79 57 11 69\n",
"53\n53 30 50 22 51 31 32 38 12 7 39 43 1 23 6 8 24 52 2 21 34 13 3 35 5 15 19 11 47 18 9 20 29 4 36 45 27 41 25 48 16 46 44 17 10 14 42 26 40 28 33 37 49\n",
"87\n14 20 82 47 39 75 71 45 3 37 63 19 32 68 7 41 48 76 27 46 84 49 4 44 26 69 17 64 1 18 58 33 11 23 21 86 67 52 70 16 77 78 6 74 15 87 10 59 13 34 22 2 65 38 66 61 51 57 35 60 81 40 36 80 31 43 83 56 79 55 29 5 12 8 50 30 53 72 54 9 24 25 42 62 73 28 85\n",
"55\n26 15 31 21 32 43 34 51 7 12 5 44 17 54 18 25 48 47 20 3 41 24 45 2 11 22 29 39 37 53 35 28 36 9 50 10 30 38 19 13 4 8 27 1 42 6 49 23 55 40 33 16 46 14 52\n",
"75\n75 28 60 19 59 17 65 26 32 23 18 64 8 62 4 11 42 16 47 5 72 46 9 1 25 21 2 50 33 6 36 68 30 12 20 40 53 45 34 7 37 39 38 44 63 61 67 3 66 51 29 73 24 57 70 27 10 56 22 55 13 49 35 15 54 41 14 74 69 48 52 31 71 43 58\n",
"56\n6 20 38 46 10 11 40 19 5 1 47 33 4 18 32 36 37 45 56 49 48 52 12 26 31 14 2 9 24 3 16 51 41 43 23 17 34 7 29 50 55 25 39 44 22 27 54 8 28 35 30 42 13 53 21 15\n",
"77\n10 20 57 65 53 69 59 45 58 32 28 72 4 14 1 33 40 47 7 5 51 76 37 16 41 61 42 2 21 26 38 74 35 64 43 77 71 50 39 48 27 63 73 44 52 66 9 18 23 54 25 6 8 56 13 67 36 22 15 46 62 75 55 11 31 17 24 29 60 68 12 30 3 70 49 19 34\n",
"47\n7 3 8 12 24 16 29 10 28 38 1 20 37 40 21 5 15 6 45 23 36 44 25 43 41 4 11 42 18 35 32 31 39 33 27 30 22 34 14 13 17 47 19 9 46 26 2\n",
"2\n2 1\n",
"79\n75 79 43 66 72 52 29 65 74 38 24 1 5 51 13 7 71 33 4 61 2 36 63 47 64 44 34 27 3 21 17 37 54 53 49 20 28 60 39 10 16 76 6 77 73 22 50 48 78 30 67 56 31 26 40 59 41 11 18 45 69 62 15 23 32 70 19 55 68 57 35 25 12 46 14 42 9 8 58\n",
"4\n2 1 3 4\n",
"8\n4 5 3 8 6 7 1 2\n",
"68\n13 6 27 21 65 23 59 14 62 43 33 31 38 41 67 20 16 25 42 4 28 40 29 9 64 17 2 26 32 58 60 53 46 48 47 54 44 50 39 19 30 57 61 1 11 18 37 24 55 15 63 34 8 52 56 7 10 12 35 66 5 36 45 49 68 22 51 3\n",
"100\n41 67 94 18 14 83 59 12 19 54 13 68 75 26 15 65 80 40 23 30 34 78 47 21 63 79 4 70 3 31 86 69 92 10 61 74 97 100 9 99 32 27 91 55 85 52 16 17 28 1 64 29 58 76 98 25 84 7 2 96 20 72 36 46 49 82 93 44 45 6 38 87 57 50 53 35 60 33 8 89 39 42 37 48 62 81 73 43 95 11 66 88 90 22 24 77 71 51 5 56\n",
"100\n5 6 88 37 97 51 25 81 54 17 57 98 99 44 67 24 30 93 100 36 8 38 84 42 21 4 75 31 85 48 70 77 43 50 65 94 29 32 68 86 56 39 69 47 20 60 52 53 10 34 79 2 95 40 89 64 71 26 22 46 1 62 91 76 83 41 9 78 16 63 13 3 28 92 27 49 7 12 96 72 80 23 14 19 18 66 59 87 90 45 73 82 33 74 35 61 55 15 58 11\n",
"95\n36 73 18 77 15 71 50 57 79 65 94 88 9 69 52 70 26 66 78 89 55 20 72 83 75 68 32 28 45 74 19 22 54 23 84 90 86 12 42 58 11 81 39 31 85 47 60 44 59 43 21 7 30 41 64 76 93 46 87 48 10 40 3 14 38 49 29 35 2 67 5 34 13 37 27 56 91 17 62 80 8 61 53 95 24 92 6 82 63 33 51 25 4 16 1\n",
"66\n66 39 3 2 55 53 60 54 12 49 10 30 59 26 32 46 50 56 7 13 43 36 24 28 11 8 6 21 35 25 42 57 23 45 64 5 34 61 27 51 52 9 15 1 38 17 63 48 37 20 58 14 47 19 22 41 31 44 33 65 4 62 40 18 16 29\n",
"9\n7 2 3 4 5 6 1 9 8\n",
"4\n4 2 3 1\n",
"28\n28 13 16 6 1 12 4 27 22 7 18 3 21 26 25 11 5 10 20 24 19 15 14 8 23 17 9 2\n",
"38\n9 35 37 28 36 21 10 25 19 4 26 5 22 7 27 18 6 14 15 24 1 17 11 34 20 8 2 16 3 23 32 31 13 12 38 33 30 29\n",
"43\n43 24 20 13 22 29 28 4 30 3 32 40 31 8 7 9 35 27 18 5 42 6 17 19 23 12 41 21 16 37 33 34 2 14 36 38 25 10 15 39 26 11 1\n",
"3\n3 1 2\n",
"30\n6 19 14 22 26 17 27 8 25 3 24 30 4 18 23 16 9 13 29 20 15 2 5 11 28 12 1 10 21 7\n",
"4\n3 2 4 1\n",
"100\n12 1 76 78 97 82 59 80 48 8 91 51 54 74 16 10 89 99 83 63 93 90 55 25 30 33 29 6 9 65 92 79 44 39 15 58 37 46 32 19 27 3 75 49 62 71 98 42 69 50 26 81 96 5 7 61 60 21 20 36 18 34 40 4 47 85 64 38 22 84 2 68 11 56 31 66 17 14 95 43 53 35 23 52 70 13 72 45 41 77 73 87 88 94 28 86 24 67 100 57\n",
"16\n11 6 9 8 7 14 12 13 10 15 2 5 3 1 4 16\n",
"4\n3 2 1 4\n",
"59\n1 27 10 37 53 9 14 49 46 26 50 42 59 11 47 15 24 56 43 45 44 38 5 8 58 30 52 12 23 32 22 3 31 41 2 25 29 6 54 16 35 33 18 55 4 51 57 28 40 19 13 21 7 39 36 48 34 17 20\n",
"4\n4 1 2 3\n",
"96\n64 3 47 83 19 10 72 61 73 95 16 40 54 84 8 86 28 4 37 42 92 48 63 76 67 1 59 66 20 35 93 2 43 7 45 70 34 33 26 91 85 89 13 29 58 68 44 25 87 75 49 71 41 17 55 36 32 31 74 22 52 79 30 88 50 78 38 39 65 27 69 77 81 94 82 53 21 80 57 60 24 46 51 9 18 15 96 62 6 23 11 12 90 5 14 56\n",
"100\n28 30 77 4 81 67 31 25 66 56 88 73 83 51 57 34 21 90 38 76 22 99 53 70 91 3 64 54 6 94 8 5 97 80 50 45 61 40 16 95 36 98 9 2 17 44 72 55 18 58 47 12 87 24 7 32 14 23 65 41 63 48 62 39 92 27 43 19 46 13 42 52 96 84 26 69 100 79 93 49 35 60 71 59 68 15 10 29 20 1 78 33 75 86 11 85 74 82 89 37\n",
"4\n4 1 3 2\n",
"6\n2 3 4 1 6 5\n",
"10\n5 2 3 4 1 6 7 8 10 9\n",
"85\n1 18 58 8 22 76 3 61 12 33 54 41 6 24 82 15 10 17 38 64 26 4 62 28 47 14 66 9 84 75 2 71 67 43 37 32 85 21 69 52 55 63 81 51 74 59 65 34 29 36 30 45 27 53 13 79 39 57 5 70 19 40 7 42 68 48 16 80 83 23 46 35 72 31 11 44 73 77 50 56 49 25 60 20 78\n",
"4\n3 4 2 1\n",
"74\n19 51 59 34 8 40 42 55 65 16 74 26 49 63 64 70 35 72 7 12 43 18 61 27 47 31 13 32 71 22 25 67 9 1 48 50 33 10 21 46 11 45 17 37 28 60 69 66 38 2 30 3 39 15 53 68 57 41 6 36 24 73 4 23 5 62 44 14 20 29 52 54 56 58\n",
"100\n1 88 38 56 62 99 39 80 12 33 57 24 28 84 37 42 10 95 83 58 8 40 20 2 30 78 60 79 36 71 51 31 27 65 22 47 6 19 61 94 75 4 74 35 15 23 92 9 70 13 11 59 90 18 66 81 64 72 16 32 34 67 46 91 21 87 77 97 82 41 7 86 26 43 45 3 93 17 52 96 50 63 48 5 53 44 29 25 98 54 49 14 73 69 89 55 76 85 68 100\n",
"41\n24 18 7 23 3 15 1 17 25 5 30 10 34 36 2 14 9 21 41 40 20 28 33 35 12 22 11 8 19 16 31 27 26 32 29 4 13 38 37 39 6\n",
"10\n2 3 4 5 6 7 1 8 10 9\n",
"78\n7 61 69 47 68 42 65 78 70 3 32 59 49 51 23 71 11 63 22 18 43 34 24 13 27 16 19 40 21 46 48 77 28 66 54 67 60 15 75 62 9 26 52 58 4 25 8 37 41 76 1 6 30 50 44 36 5 14 29 53 17 12 2 57 73 35 64 39 56 10 33 20 45 74 31 55 38 72\n",
"33\n22 13 10 33 8 25 15 14 21 28 27 19 26 24 1 12 5 11 32 20 30 31 18 4 6 23 7 29 16 2 17 9 3\n",
"80\n51 20 37 12 68 11 28 52 76 21 7 5 3 16 64 34 25 2 6 40 60 62 75 13 45 17 56 29 32 47 79 73 49 72 15 46 30 54 80 27 43 24 74 18 42 71 14 4 44 63 65 33 1 77 55 57 41 59 58 70 69 35 19 67 10 36 26 23 48 50 39 61 9 66 38 8 31 22 53 78\n",
"36\n1 32 27 35 22 7 34 15 18 36 31 28 13 2 10 21 20 17 16 4 3 24 19 29 11 12 25 5 33 26 14 6 9 23 30 8\n",
"27\n20 14 18 10 5 3 9 4 24 22 21 27 17 15 26 2 23 7 12 11 6 8 19 25 16 13 1\n",
"93\n76 35 5 87 7 21 59 71 24 37 2 73 31 74 4 52 28 20 56 27 65 86 16 45 85 67 68 70 47 72 91 88 14 32 62 69 78 41 15 22 57 18 50 13 39 58 17 83 64 51 25 11 38 77 82 90 8 26 29 61 10 43 79 53 48 6 23 55 63 49 81 92 80 44 89 60 66 30 1 9 36 33 19 46 75 93 3 12 42 84 40 54 34\n",
"4\n1 3 4 2\n",
"40\n35 39 28 11 9 31 36 8 5 32 26 19 38 33 2 22 23 25 6 37 12 7 3 10 17 24 20 16 27 4 34 15 40 14 18 13 29 21 30 1\n",
"17\n13 12 5 3 9 16 8 14 2 4 10 1 6 11 7 15 17\n",
"58\n1 26 28 14 22 33 57 40 9 42 44 37 24 19 58 12 48 3 34 31 49 4 16 47 55 52 27 23 46 18 20 32 56 6 39 36 41 38 13 43 45 21 53 54 29 17 5 10 25 30 2 35 11 7 15 51 8 50\n",
"6\n2 5 3 6 4 1\n",
"46\n29 3 12 33 45 40 19 17 25 27 28 1 16 23 24 46 31 8 44 15 5 32 22 11 4 36 34 10 35 26 21 7 14 2 18 9 20 41 6 43 42 37 38 13 39 30\n",
"90\n2 67 26 58 9 49 76 22 60 30 77 20 13 7 37 81 47 16 19 12 14 45 41 68 85 54 28 24 46 1 27 43 32 89 53 35 59 75 18 51 17 64 66 80 31 88 87 90 38 72 55 71 42 11 73 69 62 78 23 74 65 79 84 4 86 52 10 6 3 82 56 5 48 33 21 57 40 29 61 63 34 36 83 8 15 44 50 70 39 25\n",
"24\n2 10 23 22 20 19 18 16 11 12 15 17 21 8 24 13 1 5 6 7 14 3 9 4\n",
"3\n3 2 1\n",
"100\n56 64 1 95 72 39 9 49 87 29 94 7 32 6 30 48 50 25 31 78 90 45 60 44 80 68 17 20 73 15 75 98 83 13 71 22 36 26 96 88 35 3 85 54 16 41 92 99 69 86 93 33 43 62 77 46 47 37 12 10 18 40 27 4 63 55 28 59 23 34 61 53 76 42 51 91 21 70 8 58 38 19 5 66 84 11 52 24 81 82 79 67 97 65 57 74 2 89 100 14\n",
"71\n40 6 62 3 41 52 31 66 27 16 35 5 17 60 2 15 51 22 67 61 71 53 1 64 8 45 28 18 50 30 12 69 20 26 10 37 36 49 70 32 33 11 57 14 9 55 4 58 29 25 44 65 39 48 24 47 19 46 56 38 34 42 59 63 54 23 7 68 43 13 21\n",
"35\n24 33 20 8 34 11 31 25 2 4 18 13 9 35 16 30 23 32 17 1 14 22 19 21 28 26 3 15 5 12 27 29 10 6 7\n",
"100\n83 96 73 70 30 25 7 77 58 89 76 85 49 82 45 51 14 62 50 9 31 32 16 15 97 64 4 37 20 93 24 10 80 71 100 39 75 72 78 74 8 29 53 86 79 48 3 68 90 99 56 87 63 94 36 1 40 65 6 44 43 84 17 52 34 95 38 47 60 57 98 59 33 41 46 81 23 27 19 2 54 91 55 35 26 12 92 18 28 66 69 21 5 67 13 11 22 88 61 42\n",
"64\n23 5 51 40 12 46 44 8 64 31 58 55 45 24 54 39 21 19 52 61 30 42 16 18 15 32 53 22 28 26 11 25 48 56 27 9 29 41 35 49 59 38 62 7 34 1 20 33 60 17 2 3 43 37 57 14 6 36 13 10 50 4 63 47\n",
"4\n2 4 3 1\n",
"45\n45 29 24 2 31 5 34 41 26 44 33 43 15 3 4 11 21 37 27 12 14 39 23 42 16 6 13 19 8 38 20 9 25 22 40 17 32 35 18 10 28 7 30 36 1\n",
"39\n16 28 4 33 26 36 25 23 22 30 27 7 12 34 17 6 3 38 10 24 13 31 29 39 14 32 9 20 35 11 18 21 8 2 15 37 5 19 1\n",
"62\n21 23 34 38 11 61 55 30 37 48 54 51 46 47 6 56 36 49 1 35 12 28 29 20 43 42 5 8 22 57 44 4 53 10 58 33 27 25 16 45 50 40 18 15 3 41 39 2 7 60 59 13 32 24 52 31 14 9 19 26 17 62\n",
"26\n6 21 20 16 26 17 11 2 24 4 1 12 14 8 25 7 15 10 22 5 13 18 9 23 19 3\n",
"6\n4 2 3 1 6 5\n",
"21\n1 9 14 18 13 12 11 20 16 2 4 19 15 7 6 17 8 5 3 10 21\n",
"91\n91 69 56 16 73 55 14 82 80 46 57 81 22 71 63 76 43 37 77 75 70 3 26 2 28 17 51 38 30 67 41 47 54 62 34 25 84 11 87 39 32 52 31 36 50 19 21 53 29 24 79 8 74 64 44 7 6 18 10 42 13 9 83 58 4 88 65 60 20 90 66 49 86 89 78 48 5 27 23 59 61 15 72 45 40 33 68 85 35 12 1\n",
"100\n100 97 35 55 45 3 46 98 77 64 94 85 73 43 49 79 72 9 70 62 80 88 29 58 61 20 89 83 66 86 82 15 6 87 42 96 90 75 63 38 81 40 5 23 4 18 41 19 99 60 8 12 76 51 39 93 53 26 21 50 47 28 13 30 68 59 34 54 24 56 31 27 65 16 32 10 36 52 44 91 22 14 33 25 7 78 67 17 57 37 92 11 2 69 84 95 74 71 48 1\n",
"4\n1 3 2 4\n",
"5\n1 4 5 2 3\n",
"49\n16 7 42 32 11 35 15 8 23 41 6 20 47 24 9 45 49 2 37 48 25 28 5 18 3 19 12 4 22 33 13 14 10 36 44 17 40 38 30 26 1 43 29 46 21 34 27 39 31\n",
"73\n58 38 47 34 39 64 69 66 72 57 9 4 67 22 35 13 61 14 28 52 56 20 31 70 27 24 36 1 62 17 10 5 12 33 16 73 18 49 63 71 44 65 23 30 40 8 50 46 60 25 11 26 37 55 29 68 42 2 3 32 59 7 15 43 41 48 51 53 6 45 54 19 21\n",
"100\n96 80 47 60 56 9 78 20 37 72 68 15 100 94 51 26 65 38 50 19 4 70 25 63 22 30 13 58 43 69 18 33 5 66 39 73 12 55 95 92 97 1 14 83 10 28 64 31 46 91 32 86 74 54 29 52 89 53 90 44 62 40 16 24 67 81 36 34 7 23 79 87 75 98 84 3 41 77 76 42 71 35 49 61 2 27 59 82 99 85 21 11 45 6 88 48 17 57 8 93\n",
"63\n2 5 29 48 31 26 21 16 47 24 43 22 61 28 6 39 60 27 14 52 37 7 53 8 62 56 63 10 50 18 44 13 4 9 25 11 23 42 45 41 59 12 32 36 40 51 1 35 49 54 57 20 19 34 38 46 33 3 55 15 30 58 17\n",
"20\n15 17 10 20 7 2 16 9 13 6 18 5 19 8 11 14 4 12 3 1\n",
"72\n52 64 71 40 32 10 62 21 11 37 38 13 22 70 1 66 41 50 27 20 42 47 25 68 49 12 15 72 44 60 53 5 23 14 43 29 65 36 51 54 35 67 7 19 55 48 58 46 39 24 33 30 61 45 57 2 31 3 18 59 6 9 4 63 8 16 26 34 28 69 17 56\n",
"76\n1 47 54 17 38 37 12 32 14 48 43 71 60 56 4 13 64 41 52 57 62 6 23 49 20 10 63 3 25 66 59 40 58 33 53 46 70 7 35 61 72 74 73 19 30 5 29 6 15 28 21 27 51 55 50 9 65 8 67 39 76 42 31 34 16 2 36 11 26 44 22 45 75 18 69 68\n",
"12\n3 6 7 8 13 10 12 5 4 2 11 1\n",
"81\n63 22 4 41 43 74 64 39 10 35 20 81 11 28 70 67 53 79 16 61 68 52 27 37 58 9 50 49 24 30 72 47 7 60 78 51 23 48 73 66 44 13 15 57 56 38 1 76 25 45 36 34 42 8 75 26 59 14 71 21 6 77 5 17 2 32 40 54 46 24 29 3 31 19 65 62 33 69 12 80 55\n",
"98\n85 94 69 86 22 52 27 79 53 91 35 55 53 88 8 75 76 95 64 54 67 30 70 49 6 16 2 48 80 32 25 90 98 46 9 96 36 81 10 92 28 11 37 97 15 41 38 40 83 44 29 47 23 3 31 61 87 39 78 20 68 12 17 73 59 18 77 72 43 51 84 24 89 65 26 7 74 93 21 19 5 14 50 42 82 71 60 56 34 62 58 57 45 66 13 63 4 1\n",
"22\n8 3 17 4 16 21 14 11 10 15 6 18 13 12 22 37 5 2 9 7 19 1\n",
"100\n76 70 67 54 40 1 48 63 64 36 42 90 99 27 47 17 93 7 13 84 16 57 74 5 83 61 19 56 52 92 38 91 82 79 34 66 71 28 37 98 35 94 77 53 73 10 26 80 15 32 8 81 3 95 44 46 72 6 33 11 21 85 4 48 24 51 49 96 87 55 14 31 12 60 45 9 29 22 58 18 88 2 50 59 20 86 23 41 100 39 62 68 69 97 78 43 25 89 65 75\n",
"70\n19 12 15 18 36 16 61 69 24 0 11 13 3 48 55 21 37 17 43 31 41 22 28 32 27 63 38 49 59 56 30 25 67 51 52 45 50 44 66 57 26 60 5 46 33 6 23 34 8 40 2 68 14 39 65 64 62 42 47 54 10 53 9 1 70 58 20 4 29 35\n",
"6\n5 7 2 6 1 3\n",
"99\n33 48 19 41 59 64 16 12 17 13 7 1 9 6 4 92 61 49 60 25 74 65 22 97 30 32 10 62 14 55 80 66 82 78 31 23 87 93 27 98 20 29 88 84 77 34 83 96 79 90 56 89 58 72 52 47 21 76 24 70 44 94 5 39 8 18 57 36 40 68 43 75 3 2 35 99 63 26 67 73 15 11 53 28 42 46 69 50 51 95 38 37 2 85 81 91 45 86 71\n",
"67\n66 16 2 53 35 38 49 28 18 6 36 58 21 47 42 5 50 62 44 12 52 37 11 56 15 31 25 65 17 29 59 41 7 42 4 43 39 10 1 40 24 13 20 54 19 67 46 60 51 45 64 30 8 33 26 9 3 22 34 23 57 48 55 14 63 61 32\n",
"19\n12 19 3 11 15 6 18 14 5 10 4 13 9 7 4 8 17 16 1\n",
"13\n8 4 3 7 2 11 9 1 10 2 13 12 6\n",
"32\n15 32 11 3 18 23 19 14 7 8 6 21 13 24 25 4 16 9 27 20 17 31 2 22 7 12 30 1 26 10 29 28\n",
"7\n1 4 3 6 2 4 7\n",
"84\n75 8 66 21 61 63 72 51 52 13 59 25 28 58 64 53 79 41 34 7 67 11 39 56 44 24 50 9 49 55 1 80 26 6 73 74 27 69 65 37 18 43 36 17 30 3 47 29 76 78 32 22 12 68 46 5 42 81 57 31 33 83 54 48 14 62 10 16 4 20 71 70 35 15 45 19 60 77 2 23 84 40 82 70\n",
"100\n22 47 34 65 69 5 68 78 53 54 41 23 80 51 11 7 2 85 81 75 25 58 29 73 30 49 10 71 17 96 76 89 79 20 12 15 55 7 46 32 19 3 82 35 74 44 38 40 92 14 6 50 97 63 45 93 37 18 62 77 87 36 83 9 90 61 57 28 39 43 52 42 24 56 21 84 26 99 88 59 33 70 4 60 98 95 94 100 13 48 66 72 16 31 64 91 1 86 27 67\n",
"9\n6 11 5 3 4 7 9 2 1\n",
"44\n4 38 6 40 29 3 44 2 30 35 25 22 34 10 11 31 21 7 14 23 37 19 27 18 5 22 1 16 17 9 39 13 15 32 43 8 41 26 42 12 24 33 20 28\n",
"100\n100 97 92 12 12 17 19 58 37 26 30 95 31 35 87 10 13 43 98 61 28 89 76 1 23 21 11 22 50 56 91 74 3 24 96 55 64 67 14 4 71 16 18 9 77 68 51 81 32 82 46 88 86 60 29 66 72 85 70 7 53 63 33 45 83 2 25 94 52 93 5 69 20 47 49 54 57 39 34 27 90 80 78 59 40 42 79 6 38 8 48 15 65 73 99 44 41 84 36 75\n",
"50\n31 45 3 34 13 43 32 4 42 9 7 8 24 14 35 6 19 46 44 10 18 1 25 20 27 41 2 16 12 10 11 47 38 21 28 49 30 15 50 36 29 26 22 39 48 5 23 37 33 40\n",
"51\n47 29 2 11 43 44 27 1 39 13 25 30 33 21 38 45 34 51 16 50 42 31 41 46 15 48 13 19 6 37 35 7 22 28 20 4 17 10 5 8 24 40 9 36 18 49 12 26 23 3 32\n",
"5\n2 3 1 5 2\n",
"34\n34 30 7 16 6 1 10 29 29 13 15 25 32 26 18 11 28 3 14 21 19 5 31 33 4 17 8 9 24 20 27 22 2 12\n",
"42\n42 15 24 26 4 34 19 29 38 32 31 33 14 41 21 3 11 39 25 6 5 20 23 10 16 36 18 28 27 1 7 40 22 30 9 2 37 17 8 12 2 35\n",
"97\n40 63 44 64 84 92 38 72 28 91 3 70 76 67 94 96 35 79 29 22 78 88 85 8 21 1 93 54 71 80 37 17 13 26 62 59 75 87 69 33 89 49 77 61 12 39 6 36 58 18 73 50 82 45 74 52 11 34 95 7 23 30 15 32 31 16 55 19 20 83 60 72 10 53 51 14 27 9 68 47 5 2 81 46 57 86 56 43 48 66 24 25 4 42 65 97 90\n",
"10\n2 9 3 4 1 10 5 6 3 8\n",
"89\n68 40 14 58 56 25 8 44 49 55 9 76 66 54 33 81 42 15 59 17 21 30 75 60 4 48 64 6 52 63 61 27 12 57 72 67 23 86 77 80 22 13 43 73 26 78 50 51 18 62 1 29 82 16 74 2 87 24 3 41 11 46 47 69 10 84 65 39 35 79 70 32 34 31 20 19 53 71 36 35 83 88 38 85 7 5 37 45 89\n",
"15\n6 14 13 12 7 2 4 11 15 1 8 6 5 10 9\n",
"29\n21 11 10 25 2 5 9 16 29 8 17 4 27 13 6 22 7 24 19 12 18 20 1 3 23 28 27 14 26\n",
"100\n66 100 53 88 7 73 54 41 31 42 8 46 65 90 78 14 94 30 79 39 89 5 83 50 38 61 37 86 22 95 60 98 34 46 91 10 75 25 15 43 23 17 96 35 93 48 87 47 56 13 19 9 82 62 67 80 11 55 99 70 18 26 58 85 12 44 16 45 4 49 20 71 92 24 81 2 76 32 6 21 84 36 52 97 59 63 40 51 27 64 68 3 77 72 28 33 29 1 74 69\n",
"61\n61 11 26 29 31 40 32 30 35 3 18 52 9 53 42 4 50 54 20 58 28 49 22 12 2 19 16 15 57 34 51 43 7 17 25 41 56 47 38 60 46 14 44 45 24 27 33 1 48 13 59 23 38 39 6 5 36 10 8 37 21\n",
"65\n10 11 55 43 53 25 35 26 16 37 41 38 59 21 48 2 65 49 17 23 18 30 62 36 3 4 47 15 28 63 57 54 31 46 45 12 51 7 29 13 56 52 14 22 39 19 8 27 45 5 6 34 32 61 20 50 9 24 33 58 60 40 1 42 64\n",
"60\n60 27 34 32 54 55 33 12 40 3 47 44 50 39 38 59 11 25 17 15 16 30 21 31 10 52 5 23 4 48 6 26 36 57 14 22 8 56 58 9 24 7 37 53 42 43 20 49 51 19 2 46 28 18 46 13 29 45 41 1\n",
"57\n39 28 53 36 3 6 12 56 55 20 50 19 43 42 18 40 24 52 38 17 33 23 22 41 14 7 26 44 45 16 35 1 8 47 31 5 30 51 32 4 37 25 13 34 54 21 34 10 15 11 2 27 29 48 49 9 57\n",
"86\n64 56 41 10 31 69 47 39 37 36 27 19 9 42 15 6 78 59 52 17 71 45 72 14 2 54 38 79 4 18 16 8 46 75 50 82 44 24 20 55 58 86 61 43 35 32 33 40 63 30 28 60 13 53 12 57 77 81 76 66 73 84 85 62 68 22 51 6 49 7 1 70 80 65 34 48 23 21 83 11 74 26 29 67 25 3\n",
"83\n64 8 58 17 67 46 3 82 23 70 72 16 53 45 13 20 12 48 40 4 6 47 76 60 19 44 30 78 28 22 75 15 25 29 63 74 55 32 14 51 35 31 62 77 27 42 65 71 56 61 66 41 68 49 7 34 2 83 36 5 33 26 37 80 59 50 1 9 54 21 18 17 38 73 81 52 10 39 43 79 57 11 69\n",
"53\n53 30 28 22 51 31 32 38 12 7 39 43 1 23 6 8 24 52 2 21 34 13 3 35 5 15 19 11 47 18 9 20 29 4 36 45 27 41 25 48 16 46 44 17 10 14 42 26 40 28 33 37 49\n",
"87\n14 4 82 47 39 75 71 45 3 37 63 19 32 68 7 41 48 76 27 46 84 49 4 44 26 69 17 64 1 18 58 33 11 23 21 86 67 52 70 16 77 78 6 74 15 87 10 59 13 34 22 2 65 38 66 61 51 57 35 60 81 40 36 80 31 43 83 56 79 55 29 5 12 8 50 30 53 72 54 9 24 25 42 62 73 28 85\n",
"55\n26 15 31 21 32 43 43 51 7 12 5 44 17 54 18 25 48 47 20 3 41 24 45 2 11 22 29 39 37 53 35 28 36 9 50 10 30 38 19 13 4 8 27 1 42 6 49 23 55 40 33 16 46 14 52\n",
"75\n75 28 60 19 59 17 65 26 32 23 18 64 8 62 4 11 42 16 47 5 72 46 9 1 25 21 2 50 33 6 36 68 30 12 20 40 53 45 34 7 37 39 38 44 63 61 67 3 66 51 57 73 24 57 70 27 10 56 22 55 13 49 35 15 54 41 14 74 69 48 52 31 71 43 58\n",
"79\n75 79 43 66 72 52 29 65 74 38 24 1 5 51 13 7 71 33 4 61 2 36 63 47 64 44 34 27 3 21 17 37 54 53 49 20 28 60 39 10 16 9 6 77 73 22 50 48 78 30 67 56 31 26 40 59 41 11 18 45 69 62 15 23 32 70 19 55 68 57 35 25 12 46 14 42 9 8 58\n",
"100\n5 6 88 37 97 51 25 81 54 17 57 98 99 44 67 24 30 93 100 36 8 38 84 42 21 4 75 31 85 48 70 77 43 50 65 94 29 32 68 86 56 39 69 47 20 60 52 53 10 34 79 2 95 40 89 64 71 26 22 46 1 62 91 76 39 41 9 78 16 63 13 3 28 92 27 49 7 12 96 72 80 23 14 19 18 66 59 87 90 45 73 82 33 74 35 61 55 15 58 11\n",
"66\n66 39 3 2 55 53 60 54 12 49 10 30 59 26 32 46 50 56 7 13 43 36 24 28 11 8 6 21 35 25 42 57 23 45 64 5 34 61 27 51 52 9 15 1 38 17 63 48 37 20 58 14 47 19 22 41 31 44 33 5 4 62 40 18 16 29\n",
"9\n7 2 3 5 5 6 1 9 8\n",
"28\n28 18 16 6 1 12 4 27 22 7 18 3 21 26 25 11 5 10 20 24 19 15 14 8 23 17 9 2\n",
"38\n9 35 37 28 36 21 10 25 19 7 26 5 22 7 27 18 6 14 15 24 1 17 11 34 20 8 2 16 3 23 32 31 13 12 38 33 30 29\n",
"43\n43 24 20 13 22 29 28 4 30 3 32 32 31 8 7 9 35 27 18 5 42 6 17 19 23 12 41 21 16 37 33 34 2 14 36 38 25 10 15 39 26 11 1\n",
"30\n12 19 14 22 26 17 27 8 25 3 24 30 4 18 23 16 9 13 29 20 15 2 5 11 28 12 1 10 21 7\n",
"16\n11 6 9 8 10 14 12 13 10 15 2 5 3 1 4 16\n",
"96\n64 3 47 83 19 10 72 61 73 95 16 40 54 84 8 86 28 4 37 42 92 48 63 76 67 1 59 66 20 35 93 2 43 7 45 70 34 33 26 91 85 89 13 29 58 68 44 25 87 75 49 71 41 17 55 36 32 31 36 22 52 79 30 88 50 78 38 39 65 27 69 77 81 94 82 53 21 80 57 60 24 46 51 9 18 15 96 62 6 23 11 12 90 5 14 56\n",
"100\n28 30 77 4 81 67 31 25 66 56 88 73 83 51 57 34 21 90 38 76 22 99 53 70 91 3 64 54 6 94 8 5 97 80 50 45 61 40 16 95 36 98 9 2 31 44 72 55 18 58 47 12 87 24 7 32 14 23 65 41 63 48 62 39 92 27 43 19 46 13 42 52 96 84 26 69 100 79 93 49 35 60 71 59 68 15 10 29 20 1 78 33 75 86 11 85 74 82 89 37\n",
"85\n1 18 58 8 22 76 3 61 12 33 54 41 6 24 82 15 10 17 17 64 26 4 62 28 47 14 66 9 84 75 2 71 67 43 37 32 85 21 69 52 55 63 81 51 74 59 65 34 29 36 30 45 27 53 13 79 39 57 5 70 19 40 7 42 68 48 16 80 83 23 46 35 72 31 11 44 73 77 50 56 49 25 60 20 78\n",
"36\n1 32 27 35 22 7 34 15 18 36 31 4 13 2 10 21 20 17 16 4 3 24 19 29 11 12 25 5 33 26 14 6 9 23 30 8\n",
"93\n76 35 5 87 7 21 59 71 24 37 2 73 31 42 4 52 28 20 56 27 65 86 16 45 85 67 68 70 47 72 91 88 14 32 62 69 78 41 15 22 57 18 50 13 39 58 17 83 64 51 25 11 38 77 82 90 8 26 29 61 10 43 79 53 48 6 23 55 63 49 81 92 80 44 89 60 66 30 1 9 36 33 19 46 75 93 3 12 42 84 40 54 34\n",
"40\n35 39 28 11 9 31 36 8 5 32 26 19 38 33 2 22 23 25 7 37 12 7 3 10 17 24 20 16 27 4 34 15 40 14 18 13 29 21 30 1\n",
"58\n1 26 28 14 22 10 57 40 9 42 44 37 24 19 58 12 48 3 34 31 49 4 16 47 55 52 27 23 46 18 20 32 56 6 39 36 41 38 13 43 45 21 53 54 29 17 5 10 25 30 2 35 11 7 15 51 8 50\n",
"24\n2 10 23 21 20 19 18 16 11 12 15 17 21 8 24 13 1 5 6 7 14 3 9 4\n",
"71\n40 6 62 3 41 52 31 66 27 16 35 5 17 60 2 15 51 22 67 61 71 53 1 64 8 45 28 18 50 30 6 69 20 26 10 37 36 49 70 32 33 11 57 14 9 55 4 58 29 25 44 65 39 48 24 47 19 46 56 38 34 42 59 63 54 23 7 68 43 13 21\n",
"45\n45 29 24 2 31 5 34 41 26 44 33 43 15 3 4 11 21 37 27 12 14 39 23 42 16 6 13 16 8 38 20 9 25 22 40 17 32 35 18 10 28 7 30 36 1\n",
"62\n21 23 34 38 11 61 55 30 37 48 54 51 46 47 6 56 36 49 1 35 12 28 29 20 43 42 5 8 22 57 44 4 53 10 58 33 27 25 16 45 50 40 18 0 3 41 39 2 7 60 59 13 32 24 52 31 14 9 19 26 17 62\n",
"91\n91 69 56 16 73 55 14 82 80 46 57 81 22 71 63 76 43 37 77 75 70 3 26 2 28 17 51 38 30 67 41 47 54 62 34 25 84 11 87 39 32 52 31 36 50 27 21 53 29 24 79 8 74 64 44 7 6 18 10 42 13 9 83 58 4 88 65 60 20 90 66 49 86 89 78 48 5 27 23 59 61 15 72 45 40 33 68 85 35 12 1\n",
"49\n16 7 42 32 3 35 15 8 23 41 6 20 47 24 9 45 49 2 37 48 25 28 5 18 3 19 12 4 22 33 13 14 10 36 44 17 40 38 30 26 1 43 29 46 21 34 27 39 31\n",
"63\n2 5 29 48 31 26 21 16 47 24 43 22 61 28 6 39 60 27 14 52 37 7 53 8 62 56 63 10 50 18 31 13 4 9 25 11 23 42 45 41 59 12 32 36 40 51 1 35 49 54 57 20 19 34 38 46 33 3 55 15 30 58 17\n",
"20\n15 17 10 20 7 2 23 9 13 6 18 5 19 8 11 14 4 12 3 1\n",
"31\n29 13 26 27 9 28 2 16 30 21 12 11 3 31 23 6 22 20 1 5 14 24 19 18 8 4 10 17 15 25 14\n",
"94\n29 85 82 78 61 83 80 63 11 38 50 43 9 24 4 87 79 45 3 17 90 7 34 27 1 76 26 39 84 47 4 41 81 19 44 23 56 92 35 31 72 62 70 53 40 88 13 14 73 2 59 86 46 94 15 12 77 57 89 42 75 48 18 51 32 55 71 30 49 91 20 60 5 93 33 64 21 36 10 28 8 65 66 69 74 58 6 52 25 67 16 37 54 68\n",
"8\n2 3 0 5 1 6 8 7\n",
"4\n1 4 3 1\n",
"88\n1 83 73 46 61 31 39 86 57 43 16 29 26 80 82 7 36 42 13 20 6 64 19 40 24 12 47 87 8 34 75 9 69 3 11 52 14 25 84 59 27 10 54 51 81 74 65 77 70 17 60 35 23 44 49 2 7 88 5 21 41 32 68 66 15 55 48 58 78 53 22 38 45 33 30 50 85 76 37 79 63 18 28 62 72 56 71 67\n",
"6\n5 4 4 1 6 3\n",
"8\n2 10 6 4 8 3 1 7\n",
"4\n4 3 3 1\n",
"54\n6 39 14 3 45 52 16 21 23 48 42 36 13 37 46 10 43 27 49 7 38 32 31 30 15 25 2 29 8 51 54 19 41 44 24 34 22 5 20 14 12 1 33 40 4 26 9 35 18 28 47 50 11 53\n",
"69\n29 49 25 51 21 35 11 61 39 54 40 37 60 42 27 33 59 53 34 10 46 2 23 69 8 47 58 36 1 38 19 12 7 48 13 3 6 22 18 5 65 24 50 41 66 44 35 57 4 56 62 43 9 30 14 15 28 31 64 26 16 55 68 17 32 20 45 52 63\n",
"4\n1 0 3 4\n",
"100\n22 59 25 77 68 79 32 45 20 28 61 60 38 86 33 10 100 15 63 75 78 39 67 13 66 34 96 4 63 23 73 29 31 35 71 55 16 14 72 56 94 97 17 93 47 84 57 8 21 51 54 85 26 76 49 81 2 92 62 44 91 87 11 24 95 69 5 7 99 6 65 48 70 12 41 18 74 27 42 3 80 30 50 98 58 37 82 89 83 36 40 52 19 9 88 46 43 1 90 64\n",
"77\n10 20 57 65 53 69 59 45 58 32 28 72 4 14 1 33 40 47 7 5 51 76 37 16 41 61 42 2 21 26 38 74 35 64 43 77 71 41 39 48 27 63 73 44 52 66 9 18 23 54 25 6 8 56 13 67 36 22 15 46 62 75 55 11 31 17 24 29 60 68 12 30 3 70 49 19 34\n",
"47\n7 3 8 12 24 16 29 10 28 38 1 20 37 40 21 5 15 6 45 23 36 44 25 43 41 4 11 42 18 35 32 31 39 33 27 30 22 34 14 13 17 47 23 9 46 26 2\n",
"4\n2 1 0 4\n",
"100\n41 67 94 18 14 83 59 12 19 54 13 68 75 26 15 65 80 40 23 30 34 78 47 21 63 79 4 70 3 31 86 69 92 10 61 74 97 100 9 99 32 27 91 55 85 52 16 17 28 1 64 29 58 76 98 25 84 7 2 96 20 72 36 46 49 82 93 44 45 6 38 87 57 50 53 35 60 33 8 89 39 42 37 48 62 81 73 43 95 11 66 88 90 22 36 77 71 51 5 56\n",
"95\n36 73 18 77 15 71 50 57 79 65 94 88 9 69 72 70 26 66 78 89 55 20 72 83 75 68 32 28 45 74 19 22 54 23 84 90 86 12 42 58 11 81 39 31 85 47 60 44 59 43 21 7 30 41 64 76 93 46 87 48 10 40 3 14 38 49 29 35 2 67 5 34 13 37 27 56 91 17 62 80 8 61 53 95 24 92 6 82 63 33 51 25 4 16 1\n",
"59\n1 27 10 37 53 9 14 49 46 26 50 42 59 11 47 15 24 56 43 45 44 38 5 10 58 30 52 12 23 32 22 3 31 41 2 25 29 6 54 16 35 33 18 55 4 51 57 28 40 19 13 21 7 39 36 48 34 17 20\n",
"6\n4 3 4 1 6 5\n",
"10\n5 2 3 3 1 6 7 8 10 9\n",
"100\n1 88 38 56 62 99 39 80 12 33 57 24 28 84 37 42 10 95 83 58 8 40 20 2 30 78 60 79 36 71 51 31 27 65 22 47 6 19 61 94 75 4 74 35 15 23 92 9 70 13 11 59 90 18 66 81 64 72 16 32 34 67 46 91 21 87 77 97 82 41 7 86 26 43 45 3 93 17 88 96 50 63 48 5 53 44 29 25 98 54 49 14 73 69 89 55 76 85 68 100\n",
"41\n24 18 7 23 3 15 1 17 25 5 2 10 34 36 2 14 9 21 41 40 20 28 33 35 12 22 11 8 19 16 31 27 26 32 29 4 13 38 37 39 6\n",
"78\n7 61 69 47 68 42 65 78 70 3 32 59 49 51 23 71 11 63 22 18 64 34 24 13 27 16 19 40 21 46 48 77 28 66 54 67 60 15 75 62 9 26 52 58 4 25 8 37 41 76 1 6 30 50 44 36 5 14 29 53 17 12 2 57 73 35 64 39 56 10 33 20 45 74 31 55 38 72\n",
"80\n51 20 37 12 68 11 28 52 76 21 7 5 3 16 64 34 25 2 6 40 60 62 75 13 45 17 56 29 32 47 79 73 49 72 15 46 30 54 80 27 43 24 74 18 42 71 14 4 44 63 65 33 1 77 55 57 41 59 58 70 69 35 19 67 10 36 26 23 48 50 39 61 9 66 38 8 31 39 53 78\n",
"27\n20 14 18 10 5 3 9 4 24 22 21 27 17 15 26 2 23 4 12 11 6 8 19 25 16 13 1\n",
"6\n2 3 3 6 4 1\n",
"90\n2 67 26 58 9 49 76 22 60 30 77 20 13 7 37 81 47 16 19 12 14 13 41 68 85 54 28 24 46 1 27 43 32 89 53 35 59 75 18 51 17 64 66 80 31 88 87 90 38 72 55 71 42 11 73 69 62 78 23 74 65 79 84 4 86 52 10 6 3 82 56 5 48 33 21 57 40 29 61 63 34 36 83 8 15 44 50 70 39 25\n",
"100\n56 64 1 95 72 39 9 49 87 29 94 7 32 6 30 48 50 25 31 78 90 45 60 44 80 68 17 20 73 15 75 98 83 13 71 22 36 26 96 88 35 3 85 54 16 41 92 99 69 86 93 33 43 62 77 46 47 37 12 10 18 40 27 6 63 55 28 59 23 34 61 53 76 42 51 91 21 70 8 58 38 19 5 66 84 11 52 24 81 82 79 67 97 65 57 74 2 89 100 14\n",
"100\n83 96 73 70 30 25 7 77 58 89 76 85 49 82 45 51 14 62 50 9 31 32 16 15 97 64 4 37 20 93 24 10 80 71 100 39 75 72 78 74 8 29 53 86 79 48 3 68 90 99 56 87 63 94 53 1 40 65 6 44 43 84 17 52 34 95 38 47 60 57 98 59 33 41 46 81 23 27 19 2 54 91 55 35 26 12 92 18 28 66 69 21 5 67 13 11 22 88 61 42\n",
"4\n3 4 3 1\n",
"39\n16 28 4 33 26 36 25 10 22 30 27 7 12 34 17 6 3 38 10 24 13 31 29 39 14 32 9 20 35 11 18 21 8 2 15 37 5 19 1\n",
"26\n6 21 20 16 26 17 11 0 24 4 1 12 14 8 25 7 15 10 22 5 13 18 9 23 19 3\n",
"6\n4 2 3 1 6 4\n",
"100\n100 97 35 55 45 3 46 98 77 64 94 85 73 43 49 79 72 9 70 62 80 88 29 58 61 20 89 83 66 86 82 15 6 87 42 96 90 75 63 38 81 40 5 23 4 18 41 19 99 60 8 12 76 51 39 93 53 26 21 50 47 28 13 30 68 59 34 54 24 56 31 27 65 16 32 10 36 52 44 91 22 14 50 25 7 78 67 17 57 37 92 11 2 69 84 95 74 71 48 1\n",
"73\n58 38 47 34 39 64 69 66 72 57 9 4 67 22 35 13 61 14 28 52 56 20 31 70 27 24 36 1 62 17 10 5 12 33 16 73 18 29 63 71 44 65 23 30 40 8 50 46 60 25 11 26 37 55 29 68 42 2 3 32 59 7 15 43 41 48 51 53 6 45 54 19 21\n"
],
"output": [
"5\n",
"6\n",
"3\n",
"75\n",
"11\n",
"69\n",
"97\n",
"21\n",
"8\n",
"94\n",
"3\n",
"64\n",
"8\n",
"4\n",
"53\n",
"5\n",
"87\n",
"45\n",
"18\n",
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"99\n",
"1\n",
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"3\n",
"38\n",
"21\n",
"4\n",
"99\n",
"45\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.
Nicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation.
The second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.
Output
Print a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.
Examples
Input
5
4 5 1 3 2
Output
3
Input
7
1 6 5 3 4 7 2
Output
6
Input
6
6 5 4 3 2 1
Output
5
Note
In the first sample, one may obtain the optimal answer by swapping elements 1 and 2.
In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.
In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2.
### Input:
6
6 5 4 3 2 1
### Output:
5
### Input:
7
1 6 5 3 4 7 2
### Output:
6
### Code:
n = int(input())
a = list(map(int, input().split()))
maxLocate = a.index(n)
minLocate = a.index(1)
distanceMax = len(a) - 1 - a.index(n)
distanceMin = len(a) - 1 - a.index(1)
print(max(maxLocate, minLocate, distanceMax, distanceMin))
|
69_A. Young Physicist_3173 | A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.
Input
The first line contains a positive integer n (1 ≤ n ≤ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≤ xi, yi, zi ≤ 100).
Output
Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not.
Examples
Input
3
4 1 7
-2 4 -1
1 -5 -3
Output
NO
Input
3
3 -1 7
-5 2 -4
2 -1 -3
Output
YES | sum1,sum2,sum3 = 0,0,0
n = int(input())
while n:
n-=1
l = list(map(int, input().split()))
sum1 += l[0]
sum2 += l[1]
sum3 += l[2]
if sum1==0 and sum2 ==0 and sum3 ==0:
print("YES")
else:
print("NO") | {
"input": [
"3\n3 -1 7\n-5 2 -4\n2 -1 -3\n",
"3\n4 1 7\n-2 4 -1\n1 -5 -3\n",
"14\n43 23 17\n4 17 44\n5 -5 -16\n-43 -7 -6\n47 -48 12\n50 47 -45\n2 14 43\n37 -30 15\n4 -17 -11\n17 9 -45\n-50 -3 -8\n-50 0 0\n-50 0 0\n-16 0 0\n",
"3\n1 2 3\n3 2 1\n0 0 0\n",
"44\n52 -54 -29\n-82 -5 -94\n-54 43 43\n91 16 71\n7 80 -91\n3 15 29\n-99 -6 -77\n-3 -77 -64\n73 67 34\n25 -10 -18\n-29 91 63\n-72 86 -16\n-68 85 -81\n-3 36 44\n-74 -14 -80\n34 -96 -97\n-76 -78 -33\n-24 44 -58\n98 12 77\n95 -63 -6\n-51 3 -90\n-92 -10 72\n7 3 -68\n57 -53 71\n29 57 -48\n35 -60 10\n79 -70 -61\n-20 77 55\n-86 -15 -35\n84 -88 -18\n100 -42 77\n-20 46 8\n-41 -43 -65\n38 -98 -23\n-100 65 45\n-7 -91 -63\n46 88 -85\n48 59 100\n0 0 100\n0 0 100\n0 0 100\n0 0 100\n0 0 100\n0 0 1\n",
"3\n96 49 -12\n2 -66 28\n-98 17 -16\n",
"4\n68 3 100\n68 21 -100\n-100 -24 0\n-36 0 0\n",
"18\n-86 -28 70\n-31 -89 42\n31 -48 -55\n95 -17 -43\n24 -95 -85\n-21 -14 31\n68 -18 81\n13 31 60\n-15 28 99\n-42 15 9\n28 -61 -62\n-16 71 29\n-28 75 -48\n-77 -67 36\n-100 83 89\n100 100 -100\n57 34 -100\n0 0 -53\n",
"26\n86 7 20\n-57 -64 39\n-45 6 -93\n-44 -21 100\n-11 -49 21\n73 -71 -80\n-2 -89 56\n-65 -2 7\n5 14 84\n57 41 13\n-12 69 54\n40 -25 27\n-17 -59 0\n64 -91 -30\n-53 9 42\n-54 -8 14\n-35 82 27\n-48 -59 -80\n88 70 79\n94 57 97\n44 63 25\n84 -90 -40\n-100 100 -100\n-92 100 -100\n0 10 -100\n0 0 -82\n",
"10\n47 -2 -27\n0 26 -14\n5 -12 33\n2 18 3\n45 -30 -49\n4 -18 8\n-46 -44 -41\n-22 -10 -40\n-35 -21 26\n33 20 38\n",
"13\n-3 -36 -46\n-11 -50 37\n42 -11 -15\n9 42 44\n-29 -12 24\n3 9 -40\n-35 13 50\n14 43 18\n-13 8 24\n-48 -15 10\n50 9 -50\n21 0 -50\n0 0 -6\n",
"18\n-14 -64 -91\n-8 -66 -86\n-23 92 -40\n6 -3 -53\n57 41 78\n-79 42 -22\n-88 -17 45\n4 -45 44\n83 -18 -25\n34 86 -92\n75 -30 12\n44 99 11\n-67 -13 72\n22 83 -56\n-37 71 72\n-9 -100 100\n0 -100 31\n0 -58 0\n",
"1\n1 -2 0\n",
"2\n5 -23 12\n0 0 0\n",
"1\n0 0 0\n",
"37\n-64 -79 26\n-22 59 93\n-5 39 -12\n77 -9 76\n55 -86 57\n83 100 -97\n-70 94 84\n-14 46 -94\n26 72 35\n14 78 -62\n17 82 92\n-57 11 91\n23 15 92\n-80 -1 1\n12 39 18\n-23 -99 -75\n-34 50 19\n-39 84 -7\n45 -30 -39\n-60 49 37\n45 -16 -72\n33 -51 -56\n-48 28 5\n97 91 88\n45 -82 -11\n-21 -15 -90\n-53 73 -26\n-74 85 -90\n-40 23 38\n100 -13 49\n32 -100 -100\n0 -100 -70\n0 -100 0\n0 -100 0\n0 -100 0\n0 -100 0\n0 -37 0\n",
"5\n70 -46 86\n-100 94 24\n-27 63 -63\n57 -100 -47\n0 -11 0\n",
"2\n-23 77 -86\n23 -77 86\n",
"23\n-70 37 78\n42 84 6\n28 -94 -24\n-49 76 95\n-67 18 84\n-53 78 -5\n65 -63 -64\n-66 -64 -69\n81 -93 95\n10 52 -79\n-89 -61 -64\n-64 -47 43\n-81 -35 55\n80 82 73\n-60 -81 -18\n49 -10 -19\n-58 70 12\n-24 -15 -93\n98 -93 -54\n-28 -75 11\n100 100 -63\n100 100 0\n56 34 0\n",
"42\n11 27 92\n-18 -56 -57\n1 71 81\n33 -92 30\n82 83 49\n-87 -61 -1\n-49 45 49\n73 26 15\n-22 22 -77\n29 -93 87\n-68 44 -90\n-4 -84 20\n85 67 -6\n-39 26 77\n-28 -64 20\n65 -97 24\n-72 -39 51\n35 -75 -91\n39 -44 -8\n-25 -27 -57\n91 8 -46\n-98 -94 56\n94 -60 59\n-9 -95 18\n-53 -37 98\n-8 -94 -84\n-52 55 60\n15 -14 37\n65 -43 -25\n94 12 66\n-8 -19 -83\n29 81 -78\n-58 57 33\n24 86 -84\n-53 32 -88\n-14 7 3\n89 97 -53\n-5 -28 -91\n-100 100 -6\n-84 100 0\n0 100 0\n0 70 0\n",
"10\n25 -33 43\n-27 -42 28\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-49 -22 7\n-19 29 41\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -11 41\n-5 8 33\n29 23 32\n30 -33 -11\n39 -49 -36\n28 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -17\n9 -25 -6\n-42 -22 20\n-19 15 38\n-21 38 48\n-1 -37 -28\n-10 -13 -50\n-5 21 29\n34 28 50\n50 11 -49\n34 0 0\n",
"3\n0 2 -2\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -35 21\n42 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -12\n-32 -29 41\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -42 -93\n-22 -45 93\n37 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 68 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 61\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"13\n29 49 -11\n38 -11 -20\n25 1 -40\n-11 28 11\n23 -19 1\n45 -41 -17\n-3 0 -19\n-13 -33 49\n-30 0 28\n34 17 45\n-50 9 -27\n-50 0 0\n-37 0 0\n",
"3\n1 2 3\n3 3 1\n0 0 0\n",
"10\n47 -2 -27\n0 26 -14\n5 -12 33\n2 18 3\n45 -30 -49\n4 -18 8\n-46 -44 -41\n-22 -10 -40\n-35 -21 26\n33 5 38\n",
"2\n5 -23 19\n0 0 0\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-49 -22 7\n-19 29 41\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -11 41\n-5 8 33\n29 23 32\n30 -33 -12\n39 -49 -36\n28 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -17\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 38 48\n-1 -37 -28\n-10 -13 -50\n-5 21 29\n34 28 50\n50 11 -49\n34 0 0\n",
"3\n0 2 0\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -35 26\n42 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -12\n-32 -29 41\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -42 -93\n-22 -45 93\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 68 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 61\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"3\n4 1 7\n-2 4 -1\n1 -3 -3\n",
"3\n1 2 3\n4 2 1\n0 0 0\n",
"10\n47 -2 -27\n0 26 -14\n5 -12 33\n2 18 3\n45 -30 -49\n4 -18 8\n-46 -44 -66\n-22 -10 -40\n-35 -21 26\n33 5 38\n",
"2\n5 -23 19\n0 0 -1\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-49 -22 11\n-19 29 41\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -11 41\n-10 8 33\n29 23 32\n30 -33 -12\n39 -49 -36\n28 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -17\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 38 48\n-1 -37 -28\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -49\n34 0 0\n",
"3\n-1 2 0\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -35 26\n42 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 41\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -42 -93\n-22 -45 93\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 68 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"3\n4 1 7\n-2 4 0\n1 -3 -3\n",
"3\n1 2 4\n4 2 1\n0 0 0\n",
"10\n47 -2 -27\n0 26 -14\n5 -12 33\n2 18 3\n45 -30 -49\n4 -18 8\n-46 -38 -66\n-22 -10 -40\n-35 -21 26\n33 5 38\n",
"2\n5 -23 20\n0 0 -1\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-59 -22 11\n-19 29 41\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -11 41\n-10 8 33\n29 23 32\n30 -6 -12\n39 -49 -36\n28 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 38 48\n-1 -37 -28\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -49\n34 0 0\n",
"3\n-2 2 0\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -35 26\n29 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 41\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -42 -93\n-22 -45 90\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 68 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"3\n4 2 7\n-2 4 0\n1 -3 -3\n",
"3\n1 2 4\n0 2 1\n0 0 0\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 3\n45 -30 -49\n4 -18 8\n-46 -38 -66\n-22 -10 -40\n-35 -21 26\n33 5 38\n",
"2\n5 -23 14\n0 0 -1\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-59 -22 11\n-19 27 41\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n29 23 32\n30 -6 -12\n39 -49 -36\n28 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 71 48\n-1 -37 -28\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -49\n34 0 0\n",
"3\n-2 0 0\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -35 26\n29 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -42 -93\n-22 -45 90\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"3\n4 2 7\n-2 4 1\n1 -3 -3\n",
"3\n1 2 4\n0 1 1\n0 0 0\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 6\n45 -30 -49\n4 -18 8\n-46 -38 -66\n-22 -10 -40\n-35 -21 26\n33 5 38\n",
"2\n5 -23 21\n0 0 -1\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -4\n-59 -22 11\n-19 27 59\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n29 23 32\n30 -6 -12\n39 -49 -36\n56 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 71 48\n-1 -37 -28\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n34 0 0\n",
"3\n-3 0 0\n1 -1 3\n-3 0 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-40 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n0 0 -87\n",
"3\n4 0 7\n-2 4 1\n1 -3 -3\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 6\n45 -30 -49\n4 -18 8\n-46 -38 -66\n-22 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n3 -23 21\n0 0 -1\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -6\n-59 -22 11\n-19 27 59\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -12\n39 -49 -36\n56 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -25 -6\n-40 -22 20\n-19 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n34 0 0\n",
"3\n-3 0 0\n1 -1 3\n-1 0 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -50\n22 40 20\n-27 -9 38\n-4 1 1\n-13 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n66 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n1 0 -87\n",
"3\n4 0 0\n-2 4 1\n1 -3 -3\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 6\n45 -30 -67\n4 -18 8\n-46 -38 -66\n-22 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n3 -23 21\n0 0 0\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -39 -6\n-59 -22 11\n-7 27 59\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -8\n39 -49 -36\n56 34 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -47 -6\n-40 -22 20\n-19 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n34 0 0\n",
"3\n-3 0 0\n1 -1 3\n0 0 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -50\n22 40 20\n-13 -9 38\n-4 1 1\n-13 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n33 96 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n49 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n1 0 -87\n",
"3\n4 0 0\n-2 0 1\n1 -3 -3\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 6\n45 -30 -67\n4 -18 8\n-46 -38 -66\n-40 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n6 -23 21\n0 0 0\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -50 -6\n-59 -22 11\n-7 27 59\n8 -27 -43\n8 34 9\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -8\n39 -49 -36\n56 47 -49\n22 29 -34\n-18 -6 7\n",
"12\n3 28 -35\n-32 -44 -5\n9 -47 -6\n-40 -22 20\n-19 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n37 0 0\n",
"3\n-3 -1 0\n1 -1 3\n0 0 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -40\n22 40 20\n-13 -9 38\n-4 1 1\n-13 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n33 3 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n49 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n1 0 -87\n",
"3\n4 0 0\n-2 0 0\n1 -3 -3\n",
"10\n47 -2 -27\n0 26 -6\n5 -12 33\n2 18 6\n45 -30 -67\n4 -18 8\n-79 -38 -66\n-40 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n6 -33 21\n0 0 0\n",
"10\n25 -33 43\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -50 -6\n-59 -22 11\n-7 27 59\n8 -27 -43\n8 34 3\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -8\n39 -49 -36\n56 47 -49\n22 29 -34\n-18 -6 3\n",
"12\n3 28 -35\n-32 -44 -5\n9 -47 -6\n-40 -22 20\n-34 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n37 0 0\n",
"3\n-3 -1 0\n1 -1 3\n0 1 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -40\n22 40 20\n-13 -9 65\n-4 1 1\n-13 6 -31\n-13 -2 34\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n19 3 85\n-76 26 83\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n49 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n1 0 -87\n",
"3\n4 0 0\n-2 0 0\n1 -1 -3\n",
"10\n47 -2 -27\n0 26 -6\n10 -12 33\n2 18 6\n45 -30 -67\n4 -18 8\n-79 -38 -66\n-40 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n6 -33 11\n0 0 0\n",
"10\n25 -33 81\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -50 -6\n-59 -22 11\n-7 27 59\n8 -27 -43\n8 34 3\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -8\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -8\n39 -49 -36\n56 47 -49\n22 29 -2\n-18 -6 3\n",
"12\n3 28 -35\n-32 -44 -5\n9 -47 -6\n-40 -22 20\n-15 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n37 0 0\n",
"3\n-3 -1 0\n1 -1 6\n0 1 0\n",
"10\n21 32 -46\n43 -8 26\n29 2 -40\n22 40 20\n-13 -9 65\n-4 1 1\n-13 6 -31\n-13 -2 13\n-21 34 -2\n-32 -29 46\n",
"33\n-1 -46 -12\n45 -16 -21\n-11 45 -21\n-60 -61 -93\n-22 -45 90\n19 3 85\n-76 26 53\n-4 9 55\n7 -52 -9\n66 8 -85\n-100 -54 11\n-29 59 74\n-24 12 2\n-56 81 85\n-92 69 -52\n-26 -97 91\n54 59 -51\n58 21 -57\n7 111 56\n-47 -20 -51\n-59 77 -13\n-85 27 91\n79 60 -56\n66 -80 5\n21 -99 42\n-31 -29 98\n49 93 76\n-49 45 21\n100 -100 -100\n100 -100 -100\n66 -75 -100\n0 0 -100\n1 0 -87\n",
"10\n47 -2 -27\n0 26 -6\n10 -12 33\n3 18 6\n45 -30 -67\n4 -18 8\n-79 -38 -66\n-40 -10 -40\n-35 -21 26\n33 5 37\n",
"2\n6 -33 14\n0 0 0\n",
"10\n25 -33 81\n-27 -42 31\n-35 -20 19\n41 -42 -1\n49 -50 -6\n-59 -22 1\n-7 27 59\n8 -27 -43\n8 34 3\n-11 -3 33\n",
"10\n-6 21 18\n20 -11 -3\n37 -18 41\n-10 8 33\n34 23 32\n30 -6 -8\n39 -49 -36\n56 47 -49\n22 29 -2\n-18 -6 3\n",
"12\n3 28 -35\n-56 -44 -5\n9 -47 -6\n-40 -22 20\n-15 15 38\n-21 71 48\n-1 -37 -45\n-10 -13 -50\n-5 21 22\n34 28 50\n50 11 -35\n37 0 0\n",
"3\n-3 -1 0\n1 -1 9\n0 1 0\n"
],
"output": [
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.
Input
The first line contains a positive integer n (1 ≤ n ≤ 100), then follow n lines containing three integers each: the xi coordinate, the yi coordinate and the zi coordinate of the force vector, applied to the body ( - 100 ≤ xi, yi, zi ≤ 100).
Output
Print the word "YES" if the body is in equilibrium, or the word "NO" if it is not.
Examples
Input
3
4 1 7
-2 4 -1
1 -5 -3
Output
NO
Input
3
3 -1 7
-5 2 -4
2 -1 -3
Output
YES
### Input:
3
3 -1 7
-5 2 -4
2 -1 -3
### Output:
YES
### Input:
3
4 1 7
-2 4 -1
1 -5 -3
### Output:
NO
### Code:
sum1,sum2,sum3 = 0,0,0
n = int(input())
while n:
n-=1
l = list(map(int, input().split()))
sum1 += l[0]
sum2 += l[1]
sum3 += l[2]
if sum1==0 and sum2 ==0 and sum3 ==0:
print("YES")
else:
print("NO") |
742_A. Arpa’s hard exam and Mehrdad’s naive cheat_3179 | There exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.
Mehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n.
<image>
Mehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.
Input
The single line of input contains one integer n (0 ≤ n ≤ 109).
Output
Print single integer — the last digit of 1378n.
Examples
Input
1
Output
8
Input
2
Output
4
Note
In the first example, last digit of 13781 = 1378 is 8.
In the second example, last digit of 13782 = 1378·1378 = 1898884 is 4. | n = int(input())
if n == 0:
print(1)
if n % 4 == 0 and n!= 0 :
print(6)
if n % 4 == 1:
print(8)
if n % 4 == 2:
print(4)
if n % 4 == 3:
print(2)
| {
"input": [
"2\n",
"1\n",
"12\n",
"1378\n",
"51202278\n",
"989898989\n",
"4\n",
"7\n",
"9\n",
"6\n",
"8\n",
"12193721\n",
"999999995\n",
"999999999\n",
"11\n",
"999999996\n",
"999999998\n",
"3\n",
"14\n",
"15\n",
"10\n",
"999999994\n",
"1000\n",
"13781378\n",
"5\n",
"999999997\n",
"1000000000\n",
"13\n",
"16\n",
"0\n",
"24\n",
"1983990\n",
"937715\n",
"1902349577\n",
"0000000000\n",
"2584\n",
"394254778\n",
"341779918\n",
"21\n",
"215963833\n",
"1065810635\n",
"28\n",
"17\n",
"1760197508\n",
"1001\n",
"5602440\n",
"17877370\n",
"22\n",
"19\n",
"44\n",
"49\n",
"3952697\n",
"74399095\n",
"185380\n",
"212134273\n",
"45271055\n",
"1603265602\n",
"50\n",
"403279506\n",
"1011\n",
"212217\n",
"6373463\n",
"0001000000\n",
"26\n",
"23\n",
"43\n",
"53\n",
"252331\n",
"59773239\n",
"348367\n",
"274204102\n",
"88997880\n",
"37\n",
"333212833\n",
"1111\n",
"117086\n",
"3544279\n",
"0001000010\n",
"30\n",
"74\n",
"32\n",
"87\n",
"425517\n",
"39722903\n",
"129454\n",
"502575216\n",
"151917914\n",
"39\n",
"284885416\n",
"1010\n",
"184257\n",
"5976311\n",
"0101000010\n",
"48\n",
"18\n",
"38\n",
"160\n",
"769275\n",
"60872248\n",
"54684\n",
"787055094\n",
"251769870\n",
"31\n",
"1395680\n",
"0010\n",
"334614\n",
"2269906\n",
"0101000011\n",
"65\n",
"33\n",
"34\n",
"262\n",
"1263861\n",
"85907381\n",
"59967\n",
"646944545\n",
"213990998\n",
"72\n",
"787056\n",
"0011\n",
"245481\n",
"1079259\n",
"0101000111\n",
"27\n",
"42\n",
"25\n",
"400\n",
"1699298\n",
"127860079\n",
"34050\n"
],
"output": [
"4\n",
"8\n",
"6\n",
"4\n",
"4\n",
"8\n",
"6\n",
"2\n",
"8\n",
"4\n",
"6\n",
"8\n",
"2\n",
"2\n",
"2\n",
"6\n",
"4\n",
"2\n",
"4\n",
"2\n",
"4\n",
"4\n",
"6\n",
"4\n",
"8\n",
"8\n",
"6\n",
"8\n",
"6\n",
"1\n",
"6\n",
"4\n",
"2\n",
"8\n",
"1\n",
"6\n",
"4\n",
"4\n",
"8\n",
"8\n",
"2\n",
"6\n",
"8\n",
"6\n",
"8\n",
"6\n",
"4\n",
"4\n",
"2\n",
"6\n",
"8\n",
"8\n",
"2\n",
"6\n",
"8\n",
"2\n",
"4\n",
"4\n",
"4\n",
"2\n",
"8\n",
"2\n",
"6\n",
"4\n",
"2\n",
"2\n",
"8\n",
"2\n",
"2\n",
"2\n",
"4\n",
"6\n",
"8\n",
"8\n",
"2\n",
"4\n",
"2\n",
"4\n",
"4\n",
"4\n",
"6\n",
"2\n",
"8\n",
"2\n",
"4\n",
"6\n",
"4\n",
"2\n",
"6\n",
"4\n",
"8\n",
"2\n",
"4\n",
"6\n",
"4\n",
"4\n",
"6\n",
"2\n",
"6\n",
"6\n",
"4\n",
"4\n",
"2\n",
"6\n",
"4\n",
"4\n",
"4\n",
"2\n",
"8\n",
"8\n",
"4\n",
"4\n",
"8\n",
"8\n",
"2\n",
"8\n",
"4\n",
"6\n",
"6\n",
"2\n",
"8\n",
"2\n",
"2\n",
"2\n",
"4\n",
"8\n",
"6\n",
"4\n",
"2\n",
"4\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.
Mehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n.
<image>
Mehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.
Input
The single line of input contains one integer n (0 ≤ n ≤ 109).
Output
Print single integer — the last digit of 1378n.
Examples
Input
1
Output
8
Input
2
Output
4
Note
In the first example, last digit of 13781 = 1378 is 8.
In the second example, last digit of 13782 = 1378·1378 = 1898884 is 4.
### Input:
2
### Output:
4
### Input:
1
### Output:
8
### Code:
n = int(input())
if n == 0:
print(1)
if n % 4 == 0 and n!= 0 :
print(6)
if n % 4 == 1:
print(8)
if n % 4 == 2:
print(4)
if n % 4 == 3:
print(2)
|
765_E. Tree Folding_3183 | Vanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 = v, a1, ..., ak, and b0 = v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased:
<image>
Help Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path.
Input
The first line of input contains the number of vertices n (2 ≤ n ≤ 2·105).
Next n - 1 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 ≤ u, v ≤ n, u ≠ v) — indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree.
Output
If it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path.
Examples
Input
6
1 2
2 3
2 4
4 5
1 6
Output
3
Input
7
1 2
1 3
3 4
1 5
5 6
6 7
Output
-1
Note
In the first sample case, a path of three edges is obtained after merging paths 2 - 1 - 6 and 2 - 4 - 5.
It is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 - 3 - 4 and 1 - 5 - 6, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path. | import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time
sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7
def LI(): return list(map(int, input().split()))
def II(): return int(input())
def LS(): return input().split()
def S(): return input()
def main():
n = II()
d = collections.defaultdict(set)
for _ in range(n-1):
a,b = LI()
d[a].add(b)
d[b].add(a)
memo = [-1] * (n+1)
def path(t,s):
ps = set()
dt = list(d[t])
for k in dt:
if memo[k] < 0:
continue
ps.add(memo[k])
if s == -1 and len(ps) == 2:
memo[t] = sum(ps) + 2
return memo[t]
if len(ps) > 1:
return -t
if len(ps) == 0:
memo[t] = 0
return 0
memo[t] = list(ps)[0] + 1
return memo[t]
def _path(tt,ss):
q = [(tt,ss)]
tq = []
qi = 0
while len(q) > qi:
t,s = q[qi]
for k in d[t]:
if k == s:
continue
q.append((k,t))
qi += 1
for t,s in q[::-1]:
r = path(t,s)
if r < 0:
return r
return memo[tt]
def _path2(tt,ss):
q = [(tt,ss)]
tq = []
qi = 0
while len(q) > qi:
t,s = q[qi]
for k in d[t]:
if k == s or memo[k] >= 0:
continue
q.append((k,t))
qi += 1
for t,s in q[::-1]:
r = path(t,s)
if r < 0:
return r
return memo[tt]
t = _path(1,-1)
if t < 0:
t = _path2(-t,-1)
if t > 0:
while t%2 == 0:
t//=2
return t
return -1
print(main())
| {
"input": [
"6\n1 2\n2 3\n2 4\n4 5\n1 6\n",
"7\n1 2\n1 3\n3 4\n1 5\n5 6\n6 7\n",
"10\n4 2\n7 4\n2 6\n2 5\n4 8\n10 3\n2 9\n9 1\n5 10\n",
"10\n5 10\n7 8\n8 3\n2 6\n3 2\n9 7\n4 5\n10 1\n6 4\n",
"4\n4 1\n4 3\n4 2\n",
"3\n3 1\n1 2\n",
"9\n1 2\n1 3\n1 4\n1 5\n1 6\n6 7\n6 8\n8 9\n",
"5\n1 5\n2 3\n2 4\n1 2\n",
"8\n6 1\n4 7\n4 8\n8 5\n7 6\n4 3\n4 2\n",
"7\n5 6\n5 7\n5 1\n7 4\n6 3\n3 2\n",
"3\n1 3\n3 2\n",
"2\n1 2\n",
"5\n5 4\n4 3\n3 1\n5 2\n",
"6\n1 6\n3 1\n6 4\n5 3\n2 5\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n8 6\n5 4\n4 10\n8 3\n",
"11\n11 9\n6 7\n7 1\n8 11\n5 6\n3 5\n9 3\n10 8\n2 4\n4 10\n",
"12\n12 6\n6 7\n8 11\n4 8\n10 4\n12 3\n2 10\n6 2\n12 9\n4 1\n9 5\n",
"3\n1 3\n1 2\n",
"4\n2 1\n4 3\n4 2\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n8 6\n1 4\n4 10\n8 3\n",
"6\n2 6\n3 1\n6 4\n5 3\n2 5\n",
"8\n6 1\n3 7\n4 8\n8 5\n7 6\n4 3\n5 2\n",
"10\n5 10\n9 8\n8 3\n2 6\n3 2\n9 7\n4 5\n10 1\n6 4\n",
"8\n6 1\n4 7\n4 8\n8 5\n4 6\n4 3\n4 2\n",
"6\n1 6\n3 1\n3 4\n5 3\n2 5\n",
"5\n1 5\n4 3\n2 4\n1 2\n",
"8\n6 1\n4 7\n4 8\n8 5\n7 6\n4 3\n5 2\n",
"5\n5 4\n4 1\n3 1\n5 2\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n8 6\n1 4\n4 10\n8 2\n",
"5\n5 4\n4 1\n3 2\n5 2\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n1 6\n1 4\n4 10\n8 2\n",
"4\n4 1\n2 3\n4 2\n",
"3\n1 2\n3 2\n",
"5\n5 4\n4 3\n4 1\n5 2\n",
"6\n1 4\n3 1\n6 4\n5 3\n2 5\n",
"8\n6 1\n4 7\n4 8\n8 5\n5 6\n4 3\n4 2\n",
"8\n6 1\n4 7\n7 8\n8 5\n5 6\n4 3\n4 2\n",
"10\n5 10\n7 8\n8 3\n2 6\n3 2\n9 8\n4 5\n10 1\n6 4\n",
"3\n3 2\n1 2\n",
"7\n1 2\n1 3\n3 4\n2 5\n5 6\n6 7\n",
"6\n1 6\n3 1\n1 4\n5 3\n2 5\n",
"6\n1 4\n3 1\n6 4\n5 4\n2 5\n",
"8\n6 1\n4 5\n7 8\n8 5\n5 6\n4 3\n4 2\n",
"5\n2 5\n2 3\n2 4\n1 2\n",
"12\n12 6\n6 7\n8 11\n7 8\n10 4\n12 3\n2 10\n6 2\n12 9\n4 1\n9 5\n",
"7\n1 2\n1 3\n2 4\n1 5\n5 6\n6 7\n",
"8\n6 1\n8 7\n4 8\n8 5\n4 6\n4 3\n4 2\n",
"6\n1 6\n2 1\n3 4\n5 3\n2 5\n",
"6\n2 6\n6 1\n6 4\n5 3\n2 5\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n9 6\n1 4\n4 10\n8 2\n",
"7\n1 2\n1 4\n3 4\n2 5\n5 6\n6 7\n",
"6\n2 6\n3 1\n1 4\n5 3\n2 5\n",
"5\n2 5\n2 3\n2 4\n1 4\n",
"6\n1 6\n4 1\n3 4\n5 3\n2 5\n",
"11\n8 9\n2 7\n1 11\n3 2\n9 1\n8 5\n9 6\n1 4\n4 10\n9 2\n",
"6\n4 6\n3 1\n1 4\n5 3\n2 5\n",
"2\n2 1\n",
"6\n1 6\n3 1\n6 4\n5 1\n2 5\n",
"8\n6 1\n4 7\n4 8\n8 5\n4 6\n4 3\n7 2\n"
],
"output": [
"3\n",
"-1\n",
"-1\n",
"9\n",
"1\n",
"1\n",
"3\n",
"3\n",
"-1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"5\n",
"1\n",
"5\n",
"-1\n",
"1\n",
"3\n",
"-1\n",
"5\n",
"7\n",
"9\n",
"3\n",
"3\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
"-1\n",
"3\n",
"1\n",
"3\n",
"5\n",
"5\n",
"3\n",
"1\n",
"1\n",
"3\n",
"1\n",
"3\n",
"1\n",
"1\n",
"-1\n",
"-1\n",
"3\n",
"5\n",
"1\n",
"-1\n",
"3\n",
"5\n",
"3\n",
"5\n",
"-1\n",
"5\n",
"1\n",
"3\n",
"3\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 = v, a1, ..., ak, and b0 = v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased:
<image>
Help Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path.
Input
The first line of input contains the number of vertices n (2 ≤ n ≤ 2·105).
Next n - 1 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 ≤ u, v ≤ n, u ≠ v) — indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree.
Output
If it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path.
Examples
Input
6
1 2
2 3
2 4
4 5
1 6
Output
3
Input
7
1 2
1 3
3 4
1 5
5 6
6 7
Output
-1
Note
In the first sample case, a path of three edges is obtained after merging paths 2 - 1 - 6 and 2 - 4 - 5.
It is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 - 3 - 4 and 1 - 5 - 6, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path.
### Input:
6
1 2
2 3
2 4
4 5
1 6
### Output:
3
### Input:
7
1 2
1 3
3 4
1 5
5 6
6 7
### Output:
-1
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time
sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7
def LI(): return list(map(int, input().split()))
def II(): return int(input())
def LS(): return input().split()
def S(): return input()
def main():
n = II()
d = collections.defaultdict(set)
for _ in range(n-1):
a,b = LI()
d[a].add(b)
d[b].add(a)
memo = [-1] * (n+1)
def path(t,s):
ps = set()
dt = list(d[t])
for k in dt:
if memo[k] < 0:
continue
ps.add(memo[k])
if s == -1 and len(ps) == 2:
memo[t] = sum(ps) + 2
return memo[t]
if len(ps) > 1:
return -t
if len(ps) == 0:
memo[t] = 0
return 0
memo[t] = list(ps)[0] + 1
return memo[t]
def _path(tt,ss):
q = [(tt,ss)]
tq = []
qi = 0
while len(q) > qi:
t,s = q[qi]
for k in d[t]:
if k == s:
continue
q.append((k,t))
qi += 1
for t,s in q[::-1]:
r = path(t,s)
if r < 0:
return r
return memo[tt]
def _path2(tt,ss):
q = [(tt,ss)]
tq = []
qi = 0
while len(q) > qi:
t,s = q[qi]
for k in d[t]:
if k == s or memo[k] >= 0:
continue
q.append((k,t))
qi += 1
for t,s in q[::-1]:
r = path(t,s)
if r < 0:
return r
return memo[tt]
t = _path(1,-1)
if t < 0:
t = _path2(-t,-1)
if t > 0:
while t%2 == 0:
t//=2
return t
return -1
print(main())
|
789_B. Masha and geometric depression_3187 | Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.
You are given geometric progression b defined by two integers b1 and q. Remind that a geometric progression is a sequence of integers b1, b2, b3, ..., where for each i > 1 the respective term satisfies the condition bi = bi - 1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m "bad" integers a1, a2, ..., am, and an integer l.
Masha writes all progression terms one by one onto the board (including repetitive) while condition |bi| ≤ l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.
But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers.
Input
The first line of input contains four integers b1, q, l, m (-109 ≤ b1, q ≤ 109, 1 ≤ l ≤ 109, 1 ≤ m ≤ 105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.
The second line contains m distinct integers a1, a2, ..., am (-109 ≤ ai ≤ 109) — numbers that will never be written on the board.
Output
Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise.
Examples
Input
3 2 30 4
6 14 25 48
Output
3
Input
123 1 2143435 4
123 11 -5453 141245
Output
0
Input
123 1 2143435 4
54343 -13 6 124
Output
inf
Note
In the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a "bad" integer. Terms bigger than 24 won't be written because they exceed l by absolute value.
In the second case, Masha won't write any number because all terms are equal 123 and this is a "bad" integer.
In the third case, Masha will write infinitely integers 123. | b1,q,l,m = map(int,input().split())
a = set(map(int,input().split()))
if q==0:
if 0 in a:
if b1 in a:
print(0)
elif abs(b1)<=l:
print(1)
else:
print(0)
elif abs(b1)<=l:
print("inf")
else:
print(0)
elif q==1:
if abs(b1)<=l and b1 not in a:
print("inf")
else:
print(0)
elif q==-1:
if abs(b1)<=l and (b1 not in a or -b1 not in a):
print('inf')
else:
print(0)
elif b1==0:
if 0 in a:
print(0)
else:
print("inf")
else:
cnt = 0
p = b1
while abs(p)<=l:
if p not in a:
cnt += 1
p *= q
print(cnt) | {
"input": [
"123 1 2143435 4\n123 11 -5453 141245\n",
"3 2 30 4\n6 14 25 48\n",
"123 1 2143435 4\n54343 -13 6 124\n",
"-100 0 50 1\n0\n",
"-1000 0 10 1\n5\n",
"-3 1 100 1\n3\n",
"1000000000 100000 1000000000 4\n5433 13 6 0\n",
"5 1 5 5\n1 2 3 4 0\n",
"2 -1 6 1\n2\n",
"3 2 30 3\n-691070108 -934106649 -220744807\n",
"0 8 5 1\n9\n",
"2 -1 1 1\n1\n",
"3 2 115 16\n24 48 12 96 3 720031148 -367712651 -838596957 558177735 -963046495 -313322487 -465018432 -618984128 -607173835 144854086 178041956\n",
"0 1 1 1\n0\n",
"-1000000000 -1000000000 1 1\n232512888\n",
"0 2 2143435 4\n54343 -13 6 124\n",
"0 69 12 1\n1\n",
"3 1 3 1\n5\n",
"0 5 8 1\n10\n",
"3 2 30 1\n3\n",
"2 -1 10 1\n2\n",
"-5 -1 10 1\n-5\n",
"-1 -1 2143435 4\n-1 -123 -5453 141245\n",
"11 0 228 5\n-1 0 1 5 -11245\n",
"123 -1 2143435 5\n-123 0 123 -5453 141245\n",
"2 2 4 1\n2\n",
"3 0 1 1\n3\n",
"0 4 1 1\n2\n",
"3 2 3 4\n6 14 25 48\n",
"3 2 25 2\n379195692 -69874783\n",
"-10 1 5 1\n100\n",
"1000000000 999999998 1000000000 1\n0\n",
"0 3 3 1\n1\n",
"1 0 2 1\n1\n",
"0 -3 2143435 5\n-1 0 1 5 -11245\n",
"11 0 1111 1\n11\n",
"2 0 3 1\n2\n",
"100 10 2 1\n100\n",
"0 5 10 1\n2\n",
"123 -1 10000 1\n123\n",
"1 5 10000 1\n125\n",
"123 0 2143435 4\n5433 0 -123 -645\n",
"11 0 228 5\n-1 -17 1 5 -11245\n",
"0 23 3 1\n3\n",
"3 0 3 1\n4\n",
"5 -1 3 1\n0\n",
"123 0 2143435 4\n5433 0 123 -645\n",
"2 -1 3 1\n2\n",
"2 -2 10 1\n1\n",
"-3 0 92055 36\n-92974174 -486557474 -663622151 695596393 177960746 -563227474 -364263320 -676254242 -614140218 71456762 -764104225 705056581 -106398436 332755134 -199942822 -732751692 658942664 677739866 886535704 183687802 -784248291 -22550621 -938674499 637055091 -704750213 780395802 778342470 -999059668 -794361783 796469192 215667969 354336794 -60195289 -885080928 -290279020 201221317\n",
"-1000 0 100 1\n2\n",
"123 -1 2143435 5\n-123 0 12 5 -11245\n",
"1 1 1000000000 1\n100\n",
"3 0 3 1\n0\n",
"1 0 2143435 4\n1 -123 -5453 141245\n",
"-3 0 1 1\n-3\n",
"2 0 2 1\n-1\n",
"123 -1 2143435 4\n54343 -13 6 123\n",
"-100 -1 1 1\n1\n",
"2 -1 100 1\n2\n",
"10 -1 2 1\n1\n",
"-1000 0 100 1\n-1000\n",
"0 3 100 1\n5\n",
"5 2 100 1\n5\n",
"-4 1 1 1\n0\n",
"-20 0 10 1\n0\n",
"-5 0 1 1\n1\n",
"10 -1 3 2\n10 8\n",
"0 35 2 1\n3\n",
"0 5 100 2\n34 56\n",
"11 0 2 5\n-1 0 1 5 -11245\n",
"0 2 100 1\n5\n",
"123 0 125 1\n123\n",
"100 0 100000 1\n100\n",
"1 -1 1 1\n1\n",
"1 -1 2143435 4\n1 -123 -5453 141245\n",
"2 2 4 1\n3\n",
"15 -1 15 4\n15 -15 1 2\n",
"3 2 24 4\n6 14 25 48\n",
"1 -1 2 1\n1\n",
"123 0 21 4\n543453 -123 6 1424\n",
"0 2 30 4\n6 14 25 48\n",
"10 10 10 1\n123\n",
"2 0 2 1\n2\n",
"0 4 1000 3\n5 6 7\n",
"-2 0 1 1\n1\n",
"0 10 10 1\n2\n",
"5 1 2 1\n2\n",
"3 3 104 17\n9 -73896485 -290898562 5254410 409659728 -916522518 -435516126 94354167 262981034 -375897180 -80186684 -173062070 -288705544 -699097793 -11447747 320434295 503414250\n",
"-10 0 5 1\n0\n",
"-3 1 100 1\n-3\n",
"0 8 10 1\n5\n",
"5 0 20 1\n5\n",
"0 0 2143435 5\n-1 -153 1 5 -11245\n",
"4 0 4 1\n0\n",
"2 0 1 1\n2\n",
"5 -1 100 1\n5\n",
"1 -2 1000000000 1\n0\n",
"0 2 5 1\n1\n",
"1 -1 10 1\n1\n",
"-1000 0 8 1\n5\n",
"-5 1 100 1\n3\n",
"1000000000 100000 1000000000 4\n3576 13 6 0\n",
"3 2 30 3\n-691070108 -136841328 -220744807\n",
"3 2 115 16\n24 20 12 96 3 720031148 -367712651 -838596957 558177735 -963046495 -313322487 -465018432 -618984128 -607173835 144854086 178041956\n",
"1 5 11000 1\n125\n",
"2 -2 10 1\n0\n",
"5 1 5 5\n2 2 3 4 0\n",
"2 -1 2 1\n2\n",
"0 1 5 1\n9\n",
"2 -2 1 1\n1\n",
"1 1 1 1\n0\n",
"-1000000000 -1000000000 1 1\n223032574\n",
"0 2 165061 4\n54343 -13 6 124\n",
"-1 69 12 1\n1\n",
"3 2 3 1\n5\n",
"-1 5 8 1\n10\n",
"2 2 30 1\n3\n",
"1 -1 10 1\n2\n",
"-5 0 10 1\n-5\n",
"11 -1 228 5\n-1 0 1 5 -11245\n",
"149 -1 2143435 5\n-123 0 123 -5453 141245\n",
"2 4 4 1\n2\n",
"3 0 0 1\n3\n",
"1 4 1 1\n2\n",
"3 4 25 2\n379195692 -69874783\n",
"-6 1 5 1\n100\n",
"1000000000 156695142 1000000000 1\n0\n",
"1 0 4 1\n1\n",
"0 -3 3086187 5\n-1 0 1 5 -11245\n",
"11 -1 1111 1\n11\n",
"000 10 2 1\n100\n",
"123 -1 10100 1\n123\n",
"67 0 2143435 4\n5433 0 -123 -645\n",
"11 0 228 5\n-1 -17 1 5 -20339\n",
"0 23 3 1\n2\n",
"1 0 3 1\n4\n",
"5 -1 3 1\n1\n",
"123 0 2143435 6\n5433 0 123 -645\n",
"2 -1 3 1\n0\n",
"-3 0 92055 36\n-92974174 -486557474 -663622151 695596393 177960746 -563227474 -364263320 -676254242 -614140218 71456762 -764104225 705056581 -106398436 96950257 -199942822 -732751692 658942664 677739866 886535704 183687802 -784248291 -22550621 -938674499 637055091 -704750213 780395802 778342470 -999059668 -794361783 796469192 215667969 354336794 -60195289 -885080928 -290279020 201221317\n",
"-1000 0 100 1\n1\n",
"123 -1 2143435 5\n-123 -1 12 5 -11245\n",
"1 1 1000000000 1\n110\n",
"6 0 3 1\n0\n",
"1 0 2143435 4\n1 -123 -5453 171108\n",
"-3 0 1 1\n-1\n",
"2 0 2 1\n-2\n",
"123 -1 3271850 4\n54343 -13 6 123\n",
"-146 -1 1 1\n1\n",
"2 -1 100 2\n2\n",
"19 -1 2 1\n1\n",
"-1723 0 100 1\n-1000\n",
"1 3 100 1\n5\n",
"5 2 100 1\n3\n",
"-7 1 1 1\n0\n",
"-20 0 4 1\n0\n",
"-10 0 1 1\n1\n",
"10 -1 3 2\n17 8\n",
"0 6 100 2\n34 56\n",
"11 0 2 5\n-2 0 1 5 -11245\n",
"0 2 110 1\n5\n",
"123 0 125 1\n148\n",
"100 0 100000 1\n101\n",
"1 -1 1 2\n1\n",
"2 -1 2143435 4\n1 -123 -5453 141245\n",
"2 2 4 2\n3\n",
"15 -1 24 4\n15 -15 1 2\n",
"3 4 24 4\n6 14 25 48\n",
"0 0 2 1\n1\n",
"123 0 21 4\n543453 -187 6 1424\n",
"0 2 30 4\n6 14 25 96\n",
"10 10 14 1\n123\n",
"2 0 4 1\n2\n",
"0 4 1000 3\n5 6 2\n",
"-2 0 2 1\n1\n",
"0 10 10 1\n0\n",
"3 3 104 17\n9 -73896485 -290898562 5254410 409659728 -916522518 -435516126 94354167 262981034 -375897180 -80186684 -173062070 -288705544 -410369619 -11447747 320434295 503414250\n",
"-10 0 5 1\n1\n",
"-3 1 100 1\n-5\n",
"5 0 12 1\n5\n"
],
"output": [
"0\n",
"3\n",
"inf\n",
"0\n",
"0\n",
"inf\n",
"1\n",
"inf\n",
"inf\n",
"4\n",
"inf\n",
"0\n",
"1\n",
"0\n",
"0\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"3\n",
"inf\n",
"inf\n",
"inf\n",
"1\n",
"0\n",
"1\n",
"0\n",
"inf\n",
"1\n",
"4\n",
"0\n",
"1\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"5\n",
"1\n",
"inf\n",
"inf\n",
"inf\n",
"0\n",
"0\n",
"inf\n",
"3\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"1\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"0\n",
"0\n",
"inf\n",
"4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"2\n",
"0\n",
"3\n",
"inf\n",
"0\n",
"inf\n",
"1\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"0\n",
"3\n",
"0\n",
"0\n",
"inf\n",
"inf\n",
"inf\n",
"1\n",
"0\n",
"inf\n",
"30\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"1\n",
"4\n",
"2\n",
"5\n",
"3\n",
"inf\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"0\n",
"inf\n",
"1\n",
"1\n",
"2\n",
"4\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"0\n",
"0\n",
"1\n",
"2\n",
"0\n",
"1\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"inf\n",
"1\n",
"inf\n",
"inf\n",
"inf\n",
"0\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"0\n",
"inf\n",
"0\n",
"0\n",
"5\n",
"5\n",
"0\n",
"0\n",
"0\n",
"0\n",
"inf\n",
"0\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"inf\n",
"2\n",
"0\n",
"2\n",
"inf\n",
"0\n",
"inf\n",
"1\n",
"inf\n",
"inf\n",
"inf\n",
"0\n",
"3\n",
"0\n",
"inf\n",
"inf\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise.
You are given geometric progression b defined by two integers b1 and q. Remind that a geometric progression is a sequence of integers b1, b2, b3, ..., where for each i > 1 the respective term satisfies the condition bi = bi - 1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m "bad" integers a1, a2, ..., am, and an integer l.
Masha writes all progression terms one by one onto the board (including repetitive) while condition |bi| ≤ l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.
But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers.
Input
The first line of input contains four integers b1, q, l, m (-109 ≤ b1, q ≤ 109, 1 ≤ l ≤ 109, 1 ≤ m ≤ 105) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.
The second line contains m distinct integers a1, a2, ..., am (-109 ≤ ai ≤ 109) — numbers that will never be written on the board.
Output
Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise.
Examples
Input
3 2 30 4
6 14 25 48
Output
3
Input
123 1 2143435 4
123 11 -5453 141245
Output
0
Input
123 1 2143435 4
54343 -13 6 124
Output
inf
Note
In the first sample case, Masha will write integers 3, 12, 24. Progression term 6 will be skipped because it is a "bad" integer. Terms bigger than 24 won't be written because they exceed l by absolute value.
In the second case, Masha won't write any number because all terms are equal 123 and this is a "bad" integer.
In the third case, Masha will write infinitely integers 123.
### Input:
123 1 2143435 4
123 11 -5453 141245
### Output:
0
### Input:
3 2 30 4
6 14 25 48
### Output:
3
### Code:
b1,q,l,m = map(int,input().split())
a = set(map(int,input().split()))
if q==0:
if 0 in a:
if b1 in a:
print(0)
elif abs(b1)<=l:
print(1)
else:
print(0)
elif abs(b1)<=l:
print("inf")
else:
print(0)
elif q==1:
if abs(b1)<=l and b1 not in a:
print("inf")
else:
print(0)
elif q==-1:
if abs(b1)<=l and (b1 not in a or -b1 not in a):
print('inf')
else:
print(0)
elif b1==0:
if 0 in a:
print(0)
else:
print("inf")
else:
cnt = 0
p = b1
while abs(p)<=l:
if p not in a:
cnt += 1
p *= q
print(cnt) |
80_D. Falling Anvils_3191 | For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.
Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!
It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.
Let the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root:
<image>
Determine the probability with which an aim can be successfully hit by an anvil.
You can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.
Input
The first line contains integer t (1 ≤ t ≤ 10000) — amount of testcases.
Each of the following t lines contain two space-separated integers a and b (0 ≤ a, b ≤ 106).
Pretests contain all the tests with 0 < a < 10, 0 ≤ b < 10.
Output
Print t lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed 10 - 6.
Examples
Input
2
4 2
1 2
Output
0.6250000000
0.5312500000 | t = int(input())
for i in range(t):
a, b = map(int, input().split())
denom = a * b * 2
if denom == 0:
if b == 0:
print('1')
else:
print('0.5')
continue
if a > 4 * b:
nom = 2 * b * b
else:
nom = (b - a / 4.0 + b) / 2.0 * a
print('%.9f' % ((denom - nom) * 1.0 / denom))
| {
"input": [
"2\n4 2\n1 2\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n3 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0\n8 0\n9 0\n",
"10\n4 6\n4 2\n10 3\n6 3\n7 8\n2 5\n0 3\n6 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n3 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 6\n3 2\n10 3\n6 3\n7 8\n2 5\n0 3\n6 1\n4 1\n10 9\n",
"2\n4 2\n0 2\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 6\n3 4\n10 3\n6 3\n7 8\n2 5\n0 3\n6 1\n4 1\n10 9\n",
"2\n4 0\n0 2\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 5\n3 4\n10 3\n6 3\n7 8\n2 5\n0 3\n6 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 5\n3 4\n10 3\n6 3\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 5\n3 4\n10 3\n6 2\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n",
"10\n2 5\n3 4\n10 3\n6 2\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n3 4\n10 5\n6 2\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n3 4\n10 5\n6 2\n7 8\n2 5\n0 3\n14 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n3 4\n10 5\n6 2\n7 13\n2 5\n0 3\n14 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n2 4\n10 5\n6 2\n7 13\n2 5\n0 3\n14 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n2 4\n10 5\n6 2\n7 13\n2 5\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n2 4\n9 5\n6 2\n7 13\n2 5\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n2 6\n9 5\n6 2\n7 13\n2 5\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n2 6\n9 5\n6 2\n7 13\n2 6\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n7 13\n2 6\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n7 13\n3 6\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n7 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n7 2\n3 6\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 1\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n7 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n7 2\n1 6\n0 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 8\n4 4\n5 4\n7 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n7 2\n1 6\n1 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 7\n4 4\n5 4\n7 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 3\n14 1\n4 1\n10 15\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 7\n4 4\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 3\n14 1\n4 1\n10 4\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 7\n4 4\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n9 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 3\n14 1\n4 1\n2 4\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 7\n4 4\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 3\n14 2\n4 1\n2 4\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 4\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 6\n14 2\n4 1\n2 4\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 9\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 6\n14 2\n4 1\n2 2\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n2 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 5\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n6 2\n14 2\n1 6\n1 6\n14 2\n4 1\n2 0\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n0 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 5\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n9 5\n11 2\n14 2\n1 6\n1 6\n14 2\n4 1\n2 0\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 4\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n0 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 5\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 10\n2 6\n1 5\n11 2\n14 2\n1 6\n1 6\n14 2\n4 1\n2 0\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n0 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 4\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n0 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 5\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"90\n1 1\n2 2\n3 1\n4 1\n10 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 1\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 2\n4 3\n5 3\n6 3\n7 3\n8 5\n9 3\n1 4\n4 4\n3 7\n4 2\n5 4\n7 4\n0 4\n8 4\n9 4\n0 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n2 7\n2 7\n5 7\n4 7\n5 7\n6 4\n7 7\n8 7\n9 7\n1 5\n2 8\n3 8\n4 8\n0 8\n6 8\n7 8\n8 8\n18 8\n1 9\n4 8\n3 5\n4 9\n5 9\n6 2\n7 9\n8 9\n15 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n0 1\n8 0\n9 0\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 0\n9 6\n1 7\n2 7\n3 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0\n8 0\n9 0\n",
"10\n4 6\n4 2\n10 3\n6 3\n7 8\n2 5\n0 3\n6 1\n2 1\n10 9\n",
"2\n0 2\n1 2\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n1 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n3 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 6\n3 2\n10 3\n6 3\n7 8\n2 5\n0 3\n2 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 3\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n2 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 6\n3 4\n10 3\n6 3\n7 8\n2 5\n0 3\n6 2\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 2\n4 1\n5 1\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 5\n3 4\n10 6\n6 3\n7 8\n2 5\n0 3\n6 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 2\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 2\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n4 5\n3 4\n10 3\n6 3\n7 8\n2 5\n0 3\n12 1\n7 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 2\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n7 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"10\n2 5\n3 4\n10 6\n6 2\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n",
"90\n1 1\n2 1\n3 1\n4 1\n5 2\n6 1\n7 1\n8 1\n9 1\n1 2\n2 2\n3 2\n4 2\n5 2\n6 2\n7 2\n8 4\n9 2\n1 3\n2 3\n3 3\n4 3\n5 3\n6 3\n7 3\n8 3\n9 3\n1 4\n4 4\n3 4\n4 4\n5 4\n6 4\n7 4\n8 4\n9 4\n1 5\n2 5\n3 5\n4 5\n5 5\n6 5\n7 5\n8 5\n9 5\n1 6\n2 6\n3 6\n4 6\n5 6\n6 6\n7 6\n8 6\n9 6\n1 7\n2 7\n5 7\n4 7\n5 7\n6 7\n7 7\n8 7\n9 7\n1 8\n2 8\n3 8\n4 8\n5 8\n6 8\n7 8\n8 8\n9 8\n1 9\n2 9\n3 9\n4 9\n5 9\n6 9\n7 9\n8 9\n9 9\n1 0\n2 0\n3 0\n8 0\n5 0\n6 0\n7 1\n8 0\n9 0\n",
"2\n4 2\n0 1\n",
"10\n4 10\n3 4\n10 3\n6 2\n7 8\n2 5\n0 3\n12 1\n4 1\n10 9\n"
],
"output": [
"0.6250000000\n0.5312500000\n",
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"0.5416666667\n0.6250000000\n0.7083333333\n0.6250000000\n0.5546875000\n0.5250000000\n0.5000000000\n0.8333333333\n0.7500000000\n0.5694444444\n",
"0.5625\n0.625\n0.6875\n0.75\n0.8\n0.8333333333333334\n0.8571428571428571\n0.875\n0.8888888888888888\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.75\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.53125\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5625\n0.575\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5267857142857143\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
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"0.5625\n0.625\n0.59375\n0.75\n0.8\n0.8333333333333334\n0.8571428571428571\n0.875\n0.8888888888888888\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.75\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.5625\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5625\n0.575\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5446428571428571\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
"0.55\n0.546875\n0.6041666666666666\n0.625\n0.5546875\n0.525\n0.5\n0.8333333333333334\n0.75\n0.5694444444444444\n",
"0.5625\n0.625\n0.6875\n0.75\n0.65625\n0.8333333333333334\n0.8571428571428571\n0.875\n0.7777777777777778\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.75\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.5625\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5625\n0.575\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5446428571428571\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
"0.55\n0.546875\n0.7083333333333334\n0.625\n0.5546875\n0.525\n0.5\n0.9166666666666666\n0.8571428571428571\n0.5694444444444444\n",
"0.5625\n0.625\n0.6875\n0.75\n0.65625\n0.8333333333333334\n0.8571428571428571\n0.875\n0.8888888888888888\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.625\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.5625\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5625\n0.6875\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5446428571428571\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
"0.5625\n0.625\n0.6875\n0.75\n0.65625\n0.8333333333333334\n0.8571428571428571\n0.875\n0.8888888888888888\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.625\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.5625\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5875\n0.575\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5446428571428571\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
"0.525\n0.546875\n0.6041666666666666\n0.6875\n0.5546875\n0.525\n0.5\n0.9166666666666666\n0.75\n0.5694444444444444\n",
"0.5625\n0.625\n0.6875\n0.75\n0.65625\n0.8333333333333334\n0.8571428571428571\n0.875\n0.8888888888888888\n0.53125\n0.5625\n0.59375\n0.625\n0.65625\n0.6875\n0.71875\n0.625\n0.7777777777777778\n0.5208333333333334\n0.5416666666666666\n0.5625\n0.5833333333333334\n0.6041666666666666\n0.625\n0.6458333333333334\n0.6666666666666666\n0.6875\n0.515625\n0.5625\n0.546875\n0.5625\n0.578125\n0.59375\n0.609375\n0.625\n0.640625\n0.5125\n0.525\n0.5375\n0.55\n0.5625\n0.575\n0.5875\n0.6\n0.6125\n0.5104166666666666\n0.5208333333333334\n0.53125\n0.5416666666666666\n0.5520833333333334\n0.5625\n0.5729166666666666\n0.5833333333333334\n0.59375\n0.5089285714285714\n0.5178571428571429\n0.5446428571428571\n0.5357142857142857\n0.5446428571428571\n0.5535714285714286\n0.5625\n0.5714285714285714\n0.5803571428571429\n0.5078125\n0.515625\n0.5234375\n0.53125\n0.5390625\n0.546875\n0.5546875\n0.5625\n0.5703125\n0.5069444444444444\n0.5138888888888888\n0.5208333333333334\n0.5277777777777778\n0.5347222222222222\n0.5416666666666666\n0.5486111111111112\n0.5555555555555556\n0.5625\n1\n1\n1\n1\n1\n1\n0.8571428571428571\n1\n1\n",
"0.625\n0.5\n",
"0.525\n0.546875\n0.7083333333333334\n0.6875\n0.5546875\n0.525\n0.5\n0.9166666666666666\n0.75\n0.5694444444444444\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.
Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!
It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.
Let the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root:
<image>
Determine the probability with which an aim can be successfully hit by an anvil.
You can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.
Input
The first line contains integer t (1 ≤ t ≤ 10000) — amount of testcases.
Each of the following t lines contain two space-separated integers a and b (0 ≤ a, b ≤ 106).
Pretests contain all the tests with 0 < a < 10, 0 ≤ b < 10.
Output
Print t lines — the probability of a successful anvil hit for each testcase. The absolute or relative error of the answer should not exceed 10 - 6.
Examples
Input
2
4 2
1 2
Output
0.6250000000
0.5312500000
### Input:
2
4 2
1 2
### Output:
0.6250000000
0.5312500000
### Input:
90
1 1
2 1
3 1
4 1
5 1
6 1
7 1
8 1
9 1
1 2
2 2
3 2
4 2
5 2
6 2
7 2
8 2
9 2
1 3
2 3
3 3
4 3
5 3
6 3
7 3
8 3
9 3
1 4
2 4
3 4
4 4
5 4
6 4
7 4
8 4
9 4
1 5
2 5
3 5
4 5
5 5
6 5
7 5
8 5
9 5
1 6
2 6
3 6
4 6
5 6
6 6
7 6
8 6
9 6
1 7
2 7
3 7
4 7
5 7
6 7
7 7
8 7
9 7
1 8
2 8
3 8
4 8
5 8
6 8
7 8
8 8
9 8
1 9
2 9
3 9
4 9
5 9
6 9
7 9
8 9
9 9
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
### Output:
0.5625000000
0.6250000000
0.6875000000
0.7500000000
0.8000000000
0.8333333333
0.8571428571
0.8750000000
0.8888888889
0.5312500000
0.5625000000
0.5937500000
0.6250000000
0.6562500000
0.6875000000
0.7187500000
0.7500000000
0.7777777778
0.5208333333
0.5416666667
0.5625000000
0.5833333333
0.6041666667
0.6250000000
0.6458333333
0.6666666667
0.6875000000
0.5156250000
0.5312500000
0.5468750000
0.5625000000
0.5781250000
0.5937500000
0.6093750000
0.6250000000
0.6406250000
0.5125000000
0.5250000000
0.5375000000
0.5500000000
0.5625000000
0.5750000000
0.5875000000
0.6000000000
0.6125000000
0.5104166667
0.5208333333
0.5312500000
0.5416666667
0.5520833333
0.5625000000
0.5729166667
0.5833333333
0.5937500000
0.5089285714
0.5178571429
0.5267857143
0.5357142857
0.5446428571
0.5535714286
0.5625000000
0.5714285714
0.5803571429
0.5078125000
0.5156250000
0.5234375000
0.5312500000
0.5390625000
0.5468750000
0.5546875000
0.5625000000
0.5703125000
0.5069444444
0.5138888889
0.5208333333
0.5277777778
0.5347222222
0.5416666667
0.5486111111
0.5555555556
0.5625000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
1.0000000000
### Code:
t = int(input())
for i in range(t):
a, b = map(int, input().split())
denom = a * b * 2
if denom == 0:
if b == 0:
print('1')
else:
print('0.5')
continue
if a > 4 * b:
nom = 2 * b * b
else:
nom = (b - a / 4.0 + b) / 2.0 * a
print('%.9f' % ((denom - nom) * 1.0 / denom))
|
835_B. The number on the board_3195 | Some natural number was written on the board. Its sum of digits was not less than k. But you were distracted a bit, and someone changed this number to n, replacing some digits with others. It's known that the length of the number didn't change.
You have to find the minimum number of digits in which these two numbers can differ.
Input
The first line contains integer k (1 ≤ k ≤ 109).
The second line contains integer n (1 ≤ n < 10100000).
There are no leading zeros in n. It's guaranteed that this situation is possible.
Output
Print the minimum number of digits in which the initial number and n can differ.
Examples
Input
3
11
Output
1
Input
3
99
Output
0
Note
In the first example, the initial number could be 12.
In the second example the sum of the digits of n is not less than k. The initial number could be equal to n. | """
Author : Arif Ahmad
Date :
Algo :
Difficulty :
"""
from sys import stdin, stdout
def main():
k = int(stdin.readline().strip())
n = stdin.readline().strip()
n = sorted(n)
total = 0
for c in n:
d = ord(c) - 48
total += d
ans = 0
for c in n:
if total >= k: break
d = ord(c) - 48
total = total - d + 9
ans += 1
stdout.write(str(ans) + '\n')
if __name__ == '__main__':
main()
| {
"input": [
"3\n11\n",
"3\n99\n",
"3\n21\n",
"3\n111\n",
"6\n33\n",
"6\n222\n",
"5\n5\n",
"2\n11\n",
"1\n1\n",
"500\n1899337170458531693764539600958943248270674811247191310452938511077656066239840703432499357537079035\n",
"900\n7570423817272967027553082464863962024635217372307919506594193055572300657732661146354209508997483330\n",
"10\n5205602270\n",
"45\n23456\n",
"700\n9307216756404590162143344901558545760612901767837570518638460182990196397856220673189163417019781185\n",
"9\n9\n",
"23\n12138\n",
"16\n333\n",
"108\n199999899899\n",
"2\n2\n",
"27\n888\n",
"1\n100\n",
"70\n3326631213\n",
"3\n12\n",
"200\n1000000010000000000000000000010000000000000001000001000000000000000000000000000000000000000000000000\n",
"42\n97779\n",
"18\n900\n",
"18\n99\n",
"17\n89\n",
"3\n25\n",
"3\n101\n",
"500\n912847954554043759533641650753636547262846968194243986164624835115915995453205463032991863345362751\n",
"900\n13595314340746721027884681972026445045155446054797436718350397773609081581610067818125738383867204953\n",
"700\n2827909885153614209536247937255907342223529877703181259853581714521705348785489110836222257304902083\n",
"108\n279537836291\n",
"27\n1303\n",
"70\n635283927\n",
"200\n1000000010000000000000000000010000000000000001000001000000000000010000000000000000000000000000000000\n",
"18\n117\n",
"500\n1518579087340116288937736599162465305202624412337518488197055281340561153696250883915352521725279445\n",
"900\n6761684374671474145370041824653392630068380810733017147939339046240643056768246793418122862717043873\n",
"700\n1820440427472754654005505510201511734837415681159646159223568238325009995518405552958176518558890038\n",
"700\n2421044298803518599175491131519646231498861226117474903459340692958777078643419274468107065406155492\n",
"108\n187335325377\n",
"6\n16\n",
"6\n344\n",
"5\n7\n",
"2\n4\n",
"1\n0\n",
"10\n9380242707\n",
"45\n31025\n",
"9\n17\n",
"23\n15494\n",
"16\n183\n",
"2\n3\n",
"1\n110\n",
"3\n13\n",
"42\n113672\n",
"18\n1685\n",
"17\n139\n",
"3\n0\n",
"3\n128\n",
"3\n1\n",
"3\n001\n",
"6\n0\n",
"6\n663\n",
"5\n14\n",
"2\n6\n",
"1\n2\n",
"10\n2517720454\n",
"9\n11\n",
"23\n28482\n",
"16\n77\n",
"108\n497278643619\n",
"2\n0\n",
"1\n010\n",
"70\n809579535\n",
"3\n2\n",
"200\n1000000010000000000000010000010000000000000001000001000000000000010000000000000000000000000000000000\n",
"42\n131479\n",
"18\n2752\n",
"18\n125\n",
"17\n115\n",
"3\n3\n",
"3\n221\n",
"3\n011\n",
"6\n1\n",
"6\n371\n",
"5\n15\n",
"2\n9\n",
"1\n3\n",
"500\n706462677389562675710135048975711250288549200563479007435388895878083268783135485467203952858871003\n",
"10\n1686851186\n",
"9\n2\n",
"23\n5804\n",
"16\n94\n",
"108\n139869568358\n",
"1\n000\n",
"70\n1461608712\n",
"3\n4\n",
"200\n1000000010000000000000010000010000000000000001000001000000000000010000000000000000000000000001000000\n",
"42\n226492\n",
"18\n3119\n",
"17\n163\n",
"3\n5\n",
"3\n406\n",
"3\n100\n",
"6\n2\n",
"6\n178\n",
"5\n23\n",
"2\n17\n",
"1\n4\n",
"500\n1365351811047316638577374736626193617865087279070847955122380370886930562732083201005251181562770410\n",
"10\n3124775247\n",
"700\n3993473126639854893598610789929709225198013139466801565924318044702332535342574254011166104230940309\n",
"9\n1\n",
"23\n11505\n",
"16\n75\n",
"1\n001\n",
"70\n165202738\n",
"200\n1000000010000000000000010000010000000000000001000001000000000010010000000000000000000000000001000000\n",
"42\n335392\n",
"18\n2219\n",
"17\n276\n",
"3\n6\n",
"3\n261\n"
],
"output": [
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"6\n",
"91\n",
"0\n",
"5\n",
"32\n",
"0\n",
"1\n",
"2\n",
"3\n",
"0\n",
"3\n",
"0\n",
"6\n",
"0\n",
"22\n",
"2\n",
"1\n",
"0\n",
"0\n",
"0\n",
"1\n",
"5\n",
"86\n",
"34\n",
"10\n",
"3\n",
"4\n",
"22\n",
"2\n",
"8\n",
"95\n",
"35\n",
"32\n",
"12\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"5\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"3\n",
"0\n",
"1\n",
"1\n",
"0\n",
"1\n",
"1\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"10\n",
"1\n",
"0\n",
"3\n",
"1\n",
"22\n",
"3\n",
"1\n",
"2\n",
"2\n",
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"4\n",
"0\n",
"1\n",
"1\n",
"1\n",
"10\n",
"1\n",
"5\n",
"0\n",
"22\n",
"3\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"10\n",
"0\n",
"35\n",
"1\n",
"2\n",
"1\n",
"0\n",
"5\n",
"22\n",
"3\n",
"1\n",
"1\n",
"0\n",
"0\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Some natural number was written on the board. Its sum of digits was not less than k. But you were distracted a bit, and someone changed this number to n, replacing some digits with others. It's known that the length of the number didn't change.
You have to find the minimum number of digits in which these two numbers can differ.
Input
The first line contains integer k (1 ≤ k ≤ 109).
The second line contains integer n (1 ≤ n < 10100000).
There are no leading zeros in n. It's guaranteed that this situation is possible.
Output
Print the minimum number of digits in which the initial number and n can differ.
Examples
Input
3
11
Output
1
Input
3
99
Output
0
Note
In the first example, the initial number could be 12.
In the second example the sum of the digits of n is not less than k. The initial number could be equal to n.
### Input:
3
11
### Output:
1
### Input:
3
99
### Output:
0
### Code:
"""
Author : Arif Ahmad
Date :
Algo :
Difficulty :
"""
from sys import stdin, stdout
def main():
k = int(stdin.readline().strip())
n = stdin.readline().strip()
n = sorted(n)
total = 0
for c in n:
d = ord(c) - 48
total += d
ans = 0
for c in n:
if total >= k: break
d = ord(c) - 48
total = total - d + 9
ans += 1
stdout.write(str(ans) + '\n')
if __name__ == '__main__':
main()
|
87_C. Interesting Game_3202 | Two best friends Serozha and Gena play a game.
Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.
The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?
Input
The single line contains a single integer n (1 ≤ n ≤ 105).
Output
If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.
If Gena wins, print "-1" (without the quotes).
Examples
Input
3
Output
2
Input
6
Output
-1
Input
100
Output
8 | import math
from collections import Counter
n = int(input())
g = [0 for i in range(n + 1)]
prefix_xor = g.copy()
def in_range(d, k):
if (2 * k - d * d + d) % (2 * d) != 0:
return -1
x = (2 * k - d * d + d) / (2 * d)
return int(x) if x > 0 else -1
def mex(arr):
counter = Counter()
for i in arr:
counter[i] += 1
for i in range(0, len(arr) + 1):
if counter[i] == 0:
return i
def find_move(arr):
for i in range(0, len(arr)):
if arr[i] == 0:
return i
return -1
if n < 3:
print(-1)
exit(0)
for i in range(3, n + 1):
for_range = range(2, int(math.sqrt(2 * i)) + 1)
filter_range = [l for l in for_range if in_range(l, i) > 0]
branches = [prefix_xor[in_range(d, i) + d - 1] ^ prefix_xor[in_range(d, i) - 1] for d in filter_range]
g[i] = mex(branches)
prefix_xor[i] = prefix_xor[i - 1] ^ g[i]
if i == n:
print(-1 if g[i] == 0 else filter_range[find_move(branches)])
| {
"input": [
"6\n",
"100\n",
"3\n",
"56\n",
"1\n",
"46\n",
"63478\n",
"7578\n",
"56056\n",
"78\n",
"66873\n",
"8149\n",
"35708\n",
"81207\n",
"41385\n",
"37317\n",
"74424\n",
"67817\n",
"684\n",
"15\n",
"96992\n",
"38798\n",
"19715\n",
"627\n",
"39509\n",
"45899\n",
"31893\n",
"1515\n",
"33\n",
"95298\n",
"27443\n",
"60879\n",
"99\n",
"34378\n",
"57113\n",
"36655\n",
"63359\n",
"873\n",
"67341\n",
"100000\n",
"42863\n",
"35\n",
"250\n",
"573\n",
"23\n",
"871\n",
"15748\n",
"92763\n",
"9564\n",
"42602\n",
"38\n",
"42237\n",
"70878\n",
"93764\n",
"303\n",
"28\n",
"43624\n",
"13800\n",
"60989\n",
"977\n",
"45190\n",
"90035\n",
"43956\n",
"72801\n",
"370\n",
"792\n",
"14577\n",
"10259\n",
"20\n",
"61946\n",
"74488\n",
"67748\n",
"2347\n",
"36488\n",
"14\n",
"64619\n",
"4083\n",
"707\n",
"34566\n",
"3359\n",
"2640\n",
"51\n",
"3947\n",
"43151\n",
"16\n",
"27223\n",
"52861\n",
"29112\n",
"1378\n",
"94967\n",
"13\n",
"36\n",
"653\n",
"19486\n",
"41407\n",
"6183\n",
"19\n",
"18133\n",
"3096\n",
"262\n",
"11\n",
"9\n",
"47\n",
"4055\n"
],
"output": [
"-1\n",
"8\n",
"2\n",
"-1\n",
"-1\n",
"4\n",
"-1\n",
"3\n",
"-1\n",
"4\n",
"2\n",
"2\n",
"-1\n",
"6\n",
"15\n",
"-1\n",
"21\n",
"73\n",
"-1\n",
"2\n",
"-1\n",
"76\n",
"-1\n",
"2\n",
"-1\n",
"-1\n",
"3\n",
"2\n",
"2\n",
"4\n",
"2\n",
"2\n",
"2\n",
"-1\n",
"2\n",
"-1\n",
"34\n",
"18\n",
"2\n",
"-1\n",
"-1\n",
"-1\n",
"5\n",
"3\n",
"-1\n",
"-1\n",
"8\n",
"22\n",
"3\n",
"17\n",
"-1\n",
"18\n",
"-1\n",
"-1\n",
"2\n",
"-1\n",
"16\n",
"15\n",
"142\n",
"2\n",
"4\n",
"22\n",
"9\n",
"6\n",
"20\n",
"3\n",
"113\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"2\n",
"2\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"2\n",
"-1\n",
"-1\n",
"-1\n",
"16\n",
"-1\n",
"-1\n",
"2\n",
"3\n",
"-1\n",
"-1\n",
"-1\n",
"2\n",
"-1\n",
"2\n",
"3\n",
"-1\n",
"2\n",
"2\n",
"2\n",
"-1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Two best friends Serozha and Gena play a game.
Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.
The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?
Input
The single line contains a single integer n (1 ≤ n ≤ 105).
Output
If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.
If Gena wins, print "-1" (without the quotes).
Examples
Input
3
Output
2
Input
6
Output
-1
Input
100
Output
8
### Input:
6
### Output:
-1
### Input:
100
### Output:
8
### Code:
import math
from collections import Counter
n = int(input())
g = [0 for i in range(n + 1)]
prefix_xor = g.copy()
def in_range(d, k):
if (2 * k - d * d + d) % (2 * d) != 0:
return -1
x = (2 * k - d * d + d) / (2 * d)
return int(x) if x > 0 else -1
def mex(arr):
counter = Counter()
for i in arr:
counter[i] += 1
for i in range(0, len(arr) + 1):
if counter[i] == 0:
return i
def find_move(arr):
for i in range(0, len(arr)):
if arr[i] == 0:
return i
return -1
if n < 3:
print(-1)
exit(0)
for i in range(3, n + 1):
for_range = range(2, int(math.sqrt(2 * i)) + 1)
filter_range = [l for l in for_range if in_range(l, i) > 0]
branches = [prefix_xor[in_range(d, i) + d - 1] ^ prefix_xor[in_range(d, i) - 1] for d in filter_range]
g[i] = mex(branches)
prefix_xor[i] = prefix_xor[i - 1] ^ g[i]
if i == n:
print(-1 if g[i] == 0 else filter_range[find_move(branches)])
|
903_E. Swapping Characters_3206 | We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string).
You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, k·n ≤ 5000).
Input
The first line contains two integers k and n (1 ≤ k ≤ 2500, 2 ≤ n ≤ 5000, k · n ≤ 5000) — the number of strings we obtained, and the length of each of these strings.
Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters.
Output
Print any suitable string s, or -1 if such string doesn't exist.
Examples
Input
3 4
abac
caab
acba
Output
acab
Input
3 4
kbbu
kbub
ubkb
Output
kbub
Input
5 4
abcd
dcba
acbd
dbca
zzzz
Output
-1
Note
In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character.
In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 — by swapping the second and the fourth, and s3 — by swapping the first and the third.
In the third example it's impossible to obtain given strings by aforementioned operations. | import collections
def swapCharacters(strings, k, n):
"""
Time: O(n^2 * k)
Space: O(1)
"""
if k == 1:
s0 = list(strings[0])
s0[0], s0[1] = s0[1], s0[0]
return ''.join(s0)
# Initial check for validity
freq = collections.Counter(strings[0])
canSame = (max(freq.values()) >= 2) # could swap two of the same characters ==> same string
for s in strings:
if collections.Counter(s) != freq:
return -1
# Find diff indices between first two strings
max_dist = 0
max_dist_s = None
s0 = strings[0]
for s1 in strings[1:]:
dist = HammingDistance(s0, s1, n)
if dist > max_dist:
max_dist = dist
max_dist_s = s1
# Hamming distance <= 2*2 between input strings to be valid
if max_dist > 4:
return -1
diffs = [i for i in range(n) if s0[i] != s1[i]]
# Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN))
s0 = list(s0)
for i in diffs:
for j in range(n):
# try swapping
s0[i], s0[j] = s0[j], s0[i]
# see if matches second string now
#dist = sum([s0[i] != s1[i] for i in diffs])
dist = HammingDistance(s0, s1, n)
if dist == 2 or (dist == 0 and canSame):
cand = ''.join(s0)
if verifyAll(strings, k, n, cand, canSame):
return cand
# revert
s0[i], s0[j] = s0[j], s0[i]
# nothing works
return -1
def HammingDistance(s0, s1, n):
count = 0
for i in range(n):
if s0[i] != s1[i]:
count += 1
return count
def verifyAll(strings, k, n, cand, canSame):
for s in strings:
dist = HammingDistance(s, cand, n)
if (dist != 0 or not canSame) and dist != 2:
return False
return True
k, n = [int(x) for x in input().split()]
strings = set() # discard duplicates
for _ in range(k):
strings.add(input())
strings = list(strings)
k = len(strings)
res = swapCharacters(strings, k, n)
print(res) | {
"input": [
"5 4\nabcd\ndcba\nacbd\ndbca\nzzzz\n",
"3 4\nabac\ncaab\nacba\n",
"3 4\nkbbu\nkbub\nubkb\n",
"3 4\nkbub\nkbbu\nubkb\n",
"5 5\nzbibx\nzbbix\nzbibx\nxbibz\nxbibz\n",
"100 2\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzs\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzs\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"5 5\neellh\nehlle\nehlle\nhelle\nhlele\n",
"2 3\nghn\nghn\n",
"2 4\nayax\nabac\n",
"2 6\nabcdef\nbadcef\n",
"1 2\nyu\n",
"2 4\najax\nazad\n",
"2 2\nnm\nnm\n",
"2 2\nac\nca\n",
"5 5\ngyvnn\ngnvny\nvygnn\ngynvn\ngnvny\n",
"2 2\nab\ncd\n",
"3 3\nuvh\nvhu\nhuv\n",
"3 2\nxh\nxh\nxh\n",
"3 2\ncg\ncg\ncg\n",
"8 23\nmgiomcytqdvoihhcirldmuj\nmgmoicytqdvoihhicrldmuj\nmgmomcytqdvoihhicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuj\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"8 6\nmnionk\nmnikno\ninmkno\nmnnkio\noniknm\noniknm\nmkinno\nmnikon\n",
"1 3\nvts\n",
"2 3\nabc\nabz\n",
"2 4\nabcd\nccdc\n",
"2 5\ndbcag\nacbdh\n",
"2 16\nhmlqgaepsgpdbzyk\nchhhburuvnyirrim\n",
"5 5\nzbibx\nzbbix\nxbibz\nxbibz\nxbibz\n",
"100 2\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nzq\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\nqz\n",
"1 2\nnm\nnm\n",
"2 2\nac\nac\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzs\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzs\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"5 5\neellh\nehlle\nehlke\nhelle\nhlele\n",
"2 4\najax\ndaza\n",
"2 2\nab\ncc\n",
"3 3\nuvh\nvhv\nhuv\n",
"3 2\ncg\ncg\ngc\n",
"8 23\nmgiomcytqdvoihhcirldmuj\nogmmicytqdvoihhicrldmuj\nmgmomcytqdvoihhicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuj\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"8 6\nmnionk\nmnikno\ninmkno\nmnnkio\noniknm\noniknm\nmkjnno\nmnikon\n",
"2 3\ncba\nabz\n",
"2 5\ndbcag\nabbdh\n",
"5 4\nabcd\ndcba\nacbd\nebca\nzzzz\n",
"3 4\nkbbu\nkbub\nubka\n",
"5 5\nzbibx\nzbbix\nxbibz\nxzibb\nxbibz\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzs\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"2 4\najax\nzada\n",
"2 2\nac\nba\n",
"3 3\nuvh\nwhv\nhuv\n",
"8 21\nmgiomcytqdvoihhcirldmuj\nogmmicytqdvoihhicrldmuj\nmgmomcytqdvoihhicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuj\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"8 6\nmnionk\nmnikno\nimmkno\nmnnkio\noniknm\noniknm\nmkjnno\nmnikon\n",
"2 5\ndbbag\nabbdh\n",
"3 4\nkbbu\nkbbu\nubka\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"2 2\najax\nzada\n",
"2 2\nac\naa\n",
"3 3\nhvu\nwhv\nhuv\n",
"8 21\nmgiomcytqdvoihhcirldmuj\nogmmicytqdvoihhicrldmuj\nmgmomcytqdvoihhicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuk\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"3 4\nkbbu\nkbbu\nbuka\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nszk\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"2 2\nxaja\nzada\n",
"2 2\nbc\naa\n",
"3 3\nhvu\nvhw\nhuv\n",
"8 21\nmgiomcytqdvoihhcirldmuj\nogmmicytqdvoihhicrldmuj\nmghomcytqdvoihmicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuk\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"3 1\nkbbu\nkbbu\nbuka\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nszk\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsk\nskz\nzsk\nkzs\nszk\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"3 3\nhuu\nvhw\nhuv\n",
"8 21\nmgiomcytqdvoihjcirldmuh\nogmmicytqdvoihhicrldmuj\nmghomcytqdvoihmicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuk\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nszk\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsj\nskz\nzsk\nkzs\nszk\nskz\nkzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"3 3\nhuu\nvhw\nvuh\n",
"8 21\nmgiomcytqdvoihjcirldmuh\nogmmicysqdvoihhicrldmuj\nmghomcytqdvoihmicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuk\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nszk\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsj\nskz\nzsk\nkzs\nszk\nskz\njzs\nkzs\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"3 3\nhut\nvhw\nvuh\n",
"8 21\nmgiomcytqdvoihjcirldmuh\nogmmicysqdvoihhicrldmuj\nmgholcytqdvoihmicrldiuj\nmgcomcytqdvoihhiirldmuj\nmgiimcytqdvoihhocrldmuk\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n",
"100 3\nzsk\nzsk\nzsk\nzsk\nskz\nskz\nkzt\nskz\nkzs\nkzs\nzsk\nkzs\nkzs\nlzs\nskz\nkzs\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nkzs\nskz\nskz\nskz\nzsk\nskz\nzsk\nskz\nkzs\nskz\nskz\nskz\nkzs\nzsk\nzsk\nkzs\nskz\nskz\nszk\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nskz\nkzs\nkzs\nskz\nkzs\nkzs\nkzs\nkzr\nskz\nkzs\nskz\nskz\nskz\nskz\nzsk\nkzs\nskz\nzsk\nkzs\nskz\nskz\nskz\nkzs\nkzs\nskz\nskz\nkzs\nkzs\nskz\nzsj\nskz\nzsk\nkzs\nszk\nskz\njzs\nszk\nkzs\nzsk\nkzs\nkzs\nzsk\nkzs\nskz\nzsk\nskz\nskz\nskz\nkzs\nzsk\nkzs\nkzs\nskz\n",
"3 3\nhvt\nvhw\nvuh\n",
"8 21\nmgiomcytqdvoihjcirldmuh\nogmmicysqdvoihhicrldmuj\nmgholcytqdvoihmicrldiuj\nmgcomcytqdvoihhiirldmuj\nkumdlrcohhiovdqtycmiigm\nmgioicytqdvoihhmcrldmuj\nmgiomcytqdvodhhicrlimuj\nmgiomcytjdvoihhicrldmuq\n"
],
"output": [
"-1\n",
"acab\n",
"kbub\n",
"kbub\n",
"zbibx\n",
"zq\n",
"szk\n",
"helle\n",
"hgn\n",
"-1\n",
"bacdef\n",
"uy\n",
"-1\n",
"mn\n",
"-1\n",
"gyvnn\n",
"-1\n",
"vuh\n",
"hx\n",
"gc\n",
"mgiomcytqdvoihhicrldmuj\n",
"mnikno\n",
"tvs\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"zbibx\n",
"-1\n",
"mn\n",
"ca\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
We had a string s consisting of n lowercase Latin letters. We made k copies of this string, thus obtaining k identical strings s1, s2, ..., sk. After that, in each of these strings we swapped exactly two characters (the characters we swapped could be identical, but they had different indices in the string).
You are given k strings s1, s2, ..., sk, and you have to restore any string s so that it is possible to obtain these strings by performing aforementioned operations. Note that the total length of the strings you are given doesn't exceed 5000 (that is, k·n ≤ 5000).
Input
The first line contains two integers k and n (1 ≤ k ≤ 2500, 2 ≤ n ≤ 5000, k · n ≤ 5000) — the number of strings we obtained, and the length of each of these strings.
Next k lines contain the strings s1, s2, ..., sk, each consisting of exactly n lowercase Latin letters.
Output
Print any suitable string s, or -1 if such string doesn't exist.
Examples
Input
3 4
abac
caab
acba
Output
acab
Input
3 4
kbbu
kbub
ubkb
Output
kbub
Input
5 4
abcd
dcba
acbd
dbca
zzzz
Output
-1
Note
In the first example s1 is obtained by swapping the second and the fourth character in acab, s2 is obtained by swapping the first and the second character, and to get s3, we swap the third and the fourth character.
In the second example s1 is obtained by swapping the third and the fourth character in kbub, s2 — by swapping the second and the fourth, and s3 — by swapping the first and the third.
In the third example it's impossible to obtain given strings by aforementioned operations.
### Input:
5 4
abcd
dcba
acbd
dbca
zzzz
### Output:
-1
### Input:
3 4
abac
caab
acba
### Output:
acab
### Code:
import collections
def swapCharacters(strings, k, n):
"""
Time: O(n^2 * k)
Space: O(1)
"""
if k == 1:
s0 = list(strings[0])
s0[0], s0[1] = s0[1], s0[0]
return ''.join(s0)
# Initial check for validity
freq = collections.Counter(strings[0])
canSame = (max(freq.values()) >= 2) # could swap two of the same characters ==> same string
for s in strings:
if collections.Counter(s) != freq:
return -1
# Find diff indices between first two strings
max_dist = 0
max_dist_s = None
s0 = strings[0]
for s1 in strings[1:]:
dist = HammingDistance(s0, s1, n)
if dist > max_dist:
max_dist = dist
max_dist_s = s1
# Hamming distance <= 2*2 between input strings to be valid
if max_dist > 4:
return -1
diffs = [i for i in range(n) if s0[i] != s1[i]]
# Checks all possible strings which match first two -- Finding strings (O(N)), testing string (O(KN))
s0 = list(s0)
for i in diffs:
for j in range(n):
# try swapping
s0[i], s0[j] = s0[j], s0[i]
# see if matches second string now
#dist = sum([s0[i] != s1[i] for i in diffs])
dist = HammingDistance(s0, s1, n)
if dist == 2 or (dist == 0 and canSame):
cand = ''.join(s0)
if verifyAll(strings, k, n, cand, canSame):
return cand
# revert
s0[i], s0[j] = s0[j], s0[i]
# nothing works
return -1
def HammingDistance(s0, s1, n):
count = 0
for i in range(n):
if s0[i] != s1[i]:
count += 1
return count
def verifyAll(strings, k, n, cand, canSame):
for s in strings:
dist = HammingDistance(s, cand, n)
if (dist != 0 or not canSame) and dist != 2:
return False
return True
k, n = [int(x) for x in input().split()]
strings = set() # discard duplicates
for _ in range(k):
strings.add(input())
strings = list(strings)
k = len(strings)
res = swapCharacters(strings, k, n)
print(res) |
954_G. Castle Defense_3210 | Today you are going to lead a group of elven archers to defend the castle that is attacked by an army of angry orcs. Three sides of the castle are protected by impassable mountains and the remaining side is occupied by a long wall that is split into n sections. At this moment there are exactly ai archers located at the i-th section of this wall. You know that archer who stands at section i can shoot orcs that attack section located at distance not exceeding r, that is all such sections j that |i - j| ≤ r. In particular, r = 0 means that archers are only capable of shooting at orcs who attack section i.
Denote as defense level of section i the total number of archers who can shoot at the orcs attacking this section. Reliability of the defense plan is the minimum value of defense level of individual wall section.
There is a little time left till the attack so you can't redistribute archers that are already located at the wall. However, there is a reserve of k archers that you can distribute among wall sections in arbitrary way. You would like to achieve maximum possible reliability of the defence plan.
Input
The first line of the input contains three integers n, r and k (1 ≤ n ≤ 500 000, 0 ≤ r ≤ n, 0 ≤ k ≤ 1018) — the number of sections of the wall, the maximum distance to other section archers can still shoot and the number of archers yet to be distributed along the wall. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the current number of archers at each section.
Output
Print one integer — the maximum possible value of defense plan reliability, i.e. the maximum possible value of minimum defense level if we distribute k additional archers optimally.
Examples
Input
5 0 6
5 4 3 4 9
Output
5
Input
4 2 0
1 2 3 4
Output
6
Input
5 1 1
2 1 2 1 2
Output
3 | import sys
border = 1 << 30
def build(x=0):
res = [0, 0]
i = 0
while x and i < 30:
if x & 1:
res[1] += (1 << i)
x >>= 1
i += 1
i = 0
while x:
if x & 1:
res[0] += (1 << i)
x >>= 1
i += 1
return res
n, r, k = map(int, sys.stdin.buffer.readline().decode('utf-8').split())
a = list(map(int, sys.stdin.buffer.readline().decode('utf-8').split()))
k_big, k_small = build(k)
left = build(sum(a[:r]))
minus_big, minus_small = [0]*n, [0]*n
w = 2*r+1
def solve(level_big, level_small):
used_big = used_small = 0
acc_big, acc_small = left
for i in range(n):
if minus_small[i] or minus_big[i]:
acc_big -= minus_big[i]
acc_small -= minus_small[i]
if acc_small < 0:
acc_small += border
acc_big -= 1
elif acc_small >= border:
acc_small -= border
acc_big += 1
minus_big[i] = minus_small[i] = 0
acc_small += (a[i+r] if i+r < n else 0) - (a[i-r-1] if i-r >= 1 else 0)
if acc_small >= border:
acc_small -= border
acc_big += 1
elif acc_small < 0:
acc_small += border
acc_big -= 1
if acc_big < level_big or acc_big == level_big and acc_small < level_small:
used_big += level_big - acc_big
used_small += level_small - acc_small
if used_small >= border:
used_small -= border
used_big += 1
elif used_small < 0:
used_small += border
used_big -= 1
if used_big > k_big or used_big == k_big and used_small > k_small:
break
if i+w < n:
minus_big[i+w] = level_big - acc_big
minus_small[i+w] = level_small - acc_small
acc_big = level_big
acc_small = level_small
for i in range(i+1, n):
if minus_small[i] or minus_big[i]:
minus_small[i] = minus_big[i] = 0
return used_big < k_big or used_big == k_big and used_small <= k_small
ok, ng = min(a), k + sum(a) + 1
while abs(ok - ng) > 1:
mid = (ok + ng) >> 1
if solve(*build(mid)):
ok = mid
else:
ng = mid
print(ok)
| {
"input": [
"4 2 0\n1 2 3 4\n",
"5 0 6\n5 4 3 4 9\n",
"5 1 1\n2 1 2 1 2\n",
"1 0 0\n1\n",
"1 1 10\n23\n",
"100 0 0\n607 169 477 518 368 54 15 471 604 138 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 752 446 204 509 816 313 900 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 100 0\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 64 804 441 957 288 112 790 239 919 216 885 527 381 749 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\n",
"2 0 100\n98 2\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 883 524 46 542 898 984 859 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 934 320 331 700 638\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 141 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 69 522 104 451 443 239 171 22 346 227 525 807\n",
"1 0 0\n0\n",
"100 0 1000\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 702 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 589 563 905 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 616 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 359 405 927 934 211 828 587 896 722 34 936 355 958 541 308 463 404 709 654 248\n",
"1 0 1000000000000000000\n1000000000\n",
"2 0 1\n1 1\n",
"100 3 0\n483 655 856 10 354 917 853 843 968 309 819 150 532 993 693 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 932 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\n",
"3 1 1000\n0 0 0\n",
"100 1 1000\n923 286 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 5 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 604 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"1 1 10\n20\n",
"100 0 0\n607 169 477 518 368 54 15 471 604 138 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 900 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 100 0\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 64 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 96 524 46 542 898 984 859 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 934 320 331 700 638\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 141 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 52 522 104 451 443 239 171 22 346 227 525 807\n",
"1 1 0\n0\n",
"100 0 1000\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 702 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 589 563 609 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 616 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 355 958 541 308 463 404 709 654 248\n",
"1 0 1000000000000000000\n1010000000\n",
"2 0 1\n1 0\n",
"100 3 0\n483 655 856 10 354 917 853 843 968 309 819 150 532 993 646 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 932 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\n",
"3 1 1000\n0 0 1\n",
"100 1 1000\n923 286 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 5 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"5 0 6\n5 4 3 4 11\n",
"5 1 1\n0 1 2 1 2\n",
"100 100 0\n739 293 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 141 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 52 522 104 451 443 82 171 22 346 227 525 807\n",
"100 1 1000\n923 286 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 9 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"5 1 6\n5 4 3 4 11\n",
"5 1 2\n0 1 2 1 2\n",
"100 100 0\n739 330 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 192 358 111 956 73 761 547\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 194 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 975 136 796 124 4 346 884 810 103 52 522 104 451 443 82 171 22 346 227 525 807\n",
"5 1 6\n5 6 3 4 11\n",
"100 100 0\n739 330 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 353 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 14 358 111 956 73 761 547\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 194 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 389 758 491 340 185 183 719 1492 136 796 124 4 346 884 810 103 52 522 104 451 443 82 171 22 346 227 525 807\n",
"5 1 0\n5 6 3 4 11\n",
"100 100 0\n739 330 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 341 903 43 659 290 422 426 390 132 242 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 14 358 111 956 73 761 547\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 194 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 260 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 340 758 491 340 185 183 719 1492 136 796 124 4 346 884 810 103 52 522 104 451 443 82 171 22 346 227 525 807\n",
"100 1 1000\n923 68 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 9 360 95 1671 725 107 727 5 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"100 100 0\n739 330 477 291 132 717 231 695 659 586 352 224 246 945 698 827 972 959 348 183 809 169 781 847 543 990 150 69 807 926 460 704 248 697 825 63 69 168 256 571 341 903 43 659 290 422 426 390 132 125 514 696 728 1 423 927 360 517 774 816 24 46 804 441 957 288 112 790 239 919 216 885 527 381 821 488 836 36 668 500 558 694 493 836 191 903 192 603 51 589 552 752 812 14 358 111 956 73 761 547\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 137 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 784 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 718 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 1348 320 331 700 638\n",
"100 100 1000\n814 165 709 628 263 653 940 749 331 437 129 547 575 73 480 429 396 688 489 312 425 946 444 228 547 512 477 849 53 241 643 416 194 502 449 58 686 111 171 844 113 790 79 107 399 846 945 427 361 68 295 630 52 939 679 458 485 738 202 141 166 940 5 73 108 351 245 998 640 772 604 123 340 758 491 340 185 183 719 1492 136 796 124 4 346 884 810 103 52 522 104 451 443 82 171 22 346 227 525 807\n",
"4 0 0\n1 2 3 4\n",
"100 0 0\n607 169 477 518 368 54 15 471 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 900 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 934 320 331 700 638\n",
"100 0 1000\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 702 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 832 563 609 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 355 958 541 308 463 404 709 654 248\n",
"100 3 0\n483 655 856 10 55 917 853 843 968 309 819 150 532 993 646 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 932 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\n",
"100 0 0\n607 169 477 518 368 54 15 471 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 661 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 953 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 1348 320 331 700 638\n",
"100 0 1000\n328 12 814 345 865 163 256 233 778 3 425 264 632 323 78 747 566 591 696 729 499 649 643 553 732 730 758 194 338 694 407 506 218 408 242 979 924 70 298 59 899 252 38 438 577 594 498 364 355 492 851 712 900 25 34 890 215 360 536 797 418 864 739 823 853 363 734 224 874 537 471 422 592 460 963 832 563 609 437 426 411 948 968 417 31 828 917 829 591 886 429 512 160 252 982 921 276 285 155 422\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 311 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 266 958 541 308 463 404 709 654 248\n",
"100 3 0\n483 655 856 10 55 917 853 843 968 309 819 150 532 993 646 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 564 39 278 866 866 515 793 151 110 991 725 989 96 21 931 653\n",
"100 1 1000\n923 68 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 9 360 95 951 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"5 0 2\n0 1 2 1 2\n",
"100 0 0\n607 169 477 518 368 54 29 471 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 661 669 86 400 186 565 951 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 784 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 663 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 1348 320 331 700 638\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 385 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 106 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 266 958 541 308 463 404 709 654 248\n",
"100 3 0\n483 655 856 10 55 917 853 843 968 309 819 150 532 993 646 498 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 564 39 278 866 866 515 942 151 110 991 725 989 96 21 931 653\n",
"100 1 1000\n923 68 937 954 258 701 953 262 346 809 109 678 963 496 245 110 75 633 900 434 608 144 574 425 646 458 188 991 341 293 121 513 548 323 139 9 360 95 1671 725 107 727 892 139 493 206 433 390 733 568 629 525 303 570 539 151 266 273 459 178 724 682 411 187 763 624 610 596 383 447 376 671 479 815 2 192 270 245 187 790 159 359 561 541 66 882 809 595 980 421 753 795 551 331 296 872 929 77 207 447\n",
"5 0 2\n0 2 2 1 2\n",
"100 0 0\n607 169 477 518 368 54 29 471 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 661 669 86 400 186 565 578 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 1 0\n724 108 796 141 159 89 957 672 396 460 791 468 147 431 700 934 298 95 131 53 676 96 361 438 413 23 171 529 258 834 612 398 120 429 296 231 273 159 936 623 85 72 598 550 205 345 1 414 772 912 464 784 909 96 524 46 542 898 984 245 432 551 972 763 310 233 399 358 875 660 992 946 883 96 20 626 718 234 896 233 790 644 6 563 341 201 980 391 619 508 610 534 698 110 468 1348 320 331 700 638\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 328 15 753 161 472 385 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 35 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 266 958 541 308 463 404 709 654 248\n",
"100 3 0\n483 655 856 10 55 917 853 843 968 309 819 150 532 993 646 729 124 303 121 186 938 587 184 859 440 665 314 751 346 999 593 396 48 119 327 902 540 107 722 641 263 853 113 209 832 379 250 501 395 379 928 57 260 589 156 763 254 591 395 356 459 996 720 544 49 59 149 442 188 628 438 774 639 474 355 669 739 957 757 906 692 27 464 256 564 39 278 866 866 515 942 151 110 991 725 989 96 21 931 653\n",
"5 1 0\n5 6 3 4 9\n",
"5 0 2\n0 2 3 1 2\n",
"100 0 0\n607 169 477 518 368 54 29 117 604 257 982 836 563 886 466 118 366 670 257 37 868 142 14 666 670 624 427 281 995 133 914 413 356 852 63 894 430 310 634 253 281 938 975 272 821 247 626 294 25 829 919 340 728 461 864 756 157 798 474 513 760 107 519 102 69 519 443 65 402 133 1222 446 204 509 816 313 661 669 86 400 186 565 578 101 396 822 130 153 980 848 910 219 876 581 35 756 513 314 804 887\n",
"100 3 1000\n391 145 605 150 641 788 1000 471 357 15 753 161 472 385 963 398 687 81 309 316 87 346 798 59 411 608 437 697 665 264 673 546 10 688 749 302 824 661 693 357 870 560 874 265 185 628 402 534 1000 649 551 412 384 273 249 324 54 204 946 811 478 35 1024 981 219 280 432 838 149 155 385 3 883 81 892 70 736 137 309 787 453 405 927 934 211 828 587 896 722 34 936 266 958 541 308 463 404 709 654 248\n"
],
"output": [
"6\n",
"5\n",
"3\n",
"1\n",
"33\n",
"14\n",
"50490\n",
"100\n",
"279\n",
"44706\n",
"0\n",
"150\n",
"2050\n",
"1000000001000000000\n",
"1\n",
"1701\n",
"1000\n",
"739\n",
"30",
"14",
"50562",
"279",
"44689",
"0",
"150",
"2050",
"1000000001010000000",
"1",
"1701",
"1000",
"739",
"5",
"2",
"50544",
"44532",
"740",
"15",
"3",
"50581",
"44585",
"16",
"50403",
"45102",
"11",
"50391",
"45053",
"723",
"50274",
"285",
"44845",
"1",
"14",
"279",
"150",
"2050",
"1701",
"14",
"279",
"150",
"2050",
"1701",
"740",
"1",
"14",
"279",
"2050",
"1701",
"740",
"1",
"14",
"279",
"2050",
"1701",
"11",
"1",
"14",
"2050"
]
} | 2CODEFORCES
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Today you are going to lead a group of elven archers to defend the castle that is attacked by an army of angry orcs. Three sides of the castle are protected by impassable mountains and the remaining side is occupied by a long wall that is split into n sections. At this moment there are exactly ai archers located at the i-th section of this wall. You know that archer who stands at section i can shoot orcs that attack section located at distance not exceeding r, that is all such sections j that |i - j| ≤ r. In particular, r = 0 means that archers are only capable of shooting at orcs who attack section i.
Denote as defense level of section i the total number of archers who can shoot at the orcs attacking this section. Reliability of the defense plan is the minimum value of defense level of individual wall section.
There is a little time left till the attack so you can't redistribute archers that are already located at the wall. However, there is a reserve of k archers that you can distribute among wall sections in arbitrary way. You would like to achieve maximum possible reliability of the defence plan.
Input
The first line of the input contains three integers n, r and k (1 ≤ n ≤ 500 000, 0 ≤ r ≤ n, 0 ≤ k ≤ 1018) — the number of sections of the wall, the maximum distance to other section archers can still shoot and the number of archers yet to be distributed along the wall. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the current number of archers at each section.
Output
Print one integer — the maximum possible value of defense plan reliability, i.e. the maximum possible value of minimum defense level if we distribute k additional archers optimally.
Examples
Input
5 0 6
5 4 3 4 9
Output
5
Input
4 2 0
1 2 3 4
Output
6
Input
5 1 1
2 1 2 1 2
Output
3
### Input:
4 2 0
1 2 3 4
### Output:
6
### Input:
5 0 6
5 4 3 4 9
### Output:
5
### Code:
import sys
border = 1 << 30
def build(x=0):
res = [0, 0]
i = 0
while x and i < 30:
if x & 1:
res[1] += (1 << i)
x >>= 1
i += 1
i = 0
while x:
if x & 1:
res[0] += (1 << i)
x >>= 1
i += 1
return res
n, r, k = map(int, sys.stdin.buffer.readline().decode('utf-8').split())
a = list(map(int, sys.stdin.buffer.readline().decode('utf-8').split()))
k_big, k_small = build(k)
left = build(sum(a[:r]))
minus_big, minus_small = [0]*n, [0]*n
w = 2*r+1
def solve(level_big, level_small):
used_big = used_small = 0
acc_big, acc_small = left
for i in range(n):
if minus_small[i] or minus_big[i]:
acc_big -= minus_big[i]
acc_small -= minus_small[i]
if acc_small < 0:
acc_small += border
acc_big -= 1
elif acc_small >= border:
acc_small -= border
acc_big += 1
minus_big[i] = minus_small[i] = 0
acc_small += (a[i+r] if i+r < n else 0) - (a[i-r-1] if i-r >= 1 else 0)
if acc_small >= border:
acc_small -= border
acc_big += 1
elif acc_small < 0:
acc_small += border
acc_big -= 1
if acc_big < level_big or acc_big == level_big and acc_small < level_small:
used_big += level_big - acc_big
used_small += level_small - acc_small
if used_small >= border:
used_small -= border
used_big += 1
elif used_small < 0:
used_small += border
used_big -= 1
if used_big > k_big or used_big == k_big and used_small > k_small:
break
if i+w < n:
minus_big[i+w] = level_big - acc_big
minus_small[i+w] = level_small - acc_small
acc_big = level_big
acc_small = level_small
for i in range(i+1, n):
if minus_small[i] or minus_big[i]:
minus_small[i] = minus_big[i] = 0
return used_big < k_big or used_big == k_big and used_small <= k_small
ok, ng = min(a), k + sum(a) + 1
while abs(ok - ng) > 1:
mid = (ok + ng) >> 1
if solve(*build(mid)):
ok = mid
else:
ng = mid
print(ok)
|
p02549 AtCoder Beginner Contest 179 - Leaping Tak_3226 | There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.
Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.
You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.
* When you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.
To help Tak, find the number of ways to go to Cell N, modulo 998244353.
Constraints
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \min(N, 10)
* 1 \leq L_i \leq R_i \leq N
* [L_i, R_i] and [L_j, R_j] do not intersect (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
L_1 R_1
L_2 R_2
:
L_K R_K
Output
Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.
Examples
Input
5 2
1 1
3 4
Output
4
Input
5 2
3 3
5 5
Output
0
Input
5 1
1 2
Output
5
Input
60 3
5 8
1 3
10 15
Output
221823067 | import sys
input = sys.stdin.readline
N,K=map(int,input().split())
K=[tuple(map(int,input().split())) for i in range(K)]
mod=998244353
DP=[0]*(4*10**5+100)
DP[1]=1
DP[2]=-1
for i in range(1,N+1):
DP[i]+=DP[i-1]
DP[i]%=mod
for l,r in K:
DP[i+l]+=DP[i]
DP[i+l]%=mod
DP[i+r+1]-=DP[i]
DP[i+r+1]%=mod
#print(DP[:10])
print(DP[N])
| {
"input": [
"5 2\n3 3\n5 5",
"5 1\n1 2",
"60 3\n5 8\n1 3\n10 15",
"5 2\n1 1\n3 4",
"5 2\n3 3\n5 9",
"60 3\n5 4\n1 3\n10 15",
"10 2\n1 1\n3 4",
"60 3\n5 4\n1 3\n10 20",
"50 3\n5 4\n1 3\n10 20",
"5 1\n1 2\n5 9",
"60 3\n5 8\n1 0\n10 15",
"3 2\n1 1\n3 4",
"60 3\n5 4\n1 6\n10 15",
"10 2\n1 2\n3 4",
"5 2\n1 3\n5 9",
"60 3\n5 4\n1 1\n10 20",
"50 3\n5 4\n1 3\n1 20",
"15 2\n1 2\n3 4",
"5 2\n1 3\n4 9",
"60 3\n5 4\n2 1\n10 20",
"84 3\n5 4\n1 3\n1 20",
"60 3\n2 4\n2 1\n10 20",
"84 3\n5 4\n1 2\n1 20",
"5 2\n1 3\n3 9",
"60 3\n2 4\n2 1\n9 20",
"84 3\n5 4\n1 2\n1 27",
"60 3\n2 4\n2 1\n12 20",
"84 3\n5 4\n1 1\n1 27",
"60 3\n2 4\n2 2\n12 20",
"84 3\n5 4\n2 1\n1 27",
"45 3\n2 4\n2 2\n12 20",
"45 3\n2 4\n2 2\n13 20",
"45 3\n2 4\n2 1\n13 20",
"45 3\n2 2\n2 1\n13 20",
"45 3\n2 2\n2 1\n13 35",
"45 3\n2 2\n2 1\n5 35",
"5 2\n3 3\n2 5",
"60 3\n5 8\n1 3\n10 9",
"60 2\n5 4\n1 3\n10 15",
"60 3\n5 4\n1 4\n10 20",
"49 3\n5 8\n1 0\n10 15",
"60 3\n5 4\n2 6\n10 15",
"10 2\n1 2\n5 4",
"50 3\n5 4\n2 3\n1 20",
"84 3\n5 4\n1 3\n1 10",
"60 3\n2 4\n2 1\n9 10",
"60 3\n2 3\n2 1\n12 20",
"45 3\n2 4\n1 1\n13 20",
"45 3\n2 2\n2 1\n13 47",
"5 2\n1 3\n2 5",
"60 3\n5 8\n1 3\n10 11",
"103 2\n5 4\n1 3\n10 15",
"60 3\n5 4\n1 6\n10 20",
"60 3\n5 4\n2 6\n3 15",
"50 3\n5 4\n4 3\n1 20",
"15 1\n1 2\n0 21",
"14 1\n1 2\n-1 21",
"60 3\n2 3\n2 1\n14 20",
"16 3\n2 2\n2 1\n13 47",
"60 3\n5 8\n1 6\n10 20",
"5 2\n1 4\n3 9",
"50 3\n5 4\n4 5\n1 20",
"5 2\n1 4\n2 9",
"60 3\n5 8\n1 3\n10 20",
"50 3\n5 4\n3 5\n1 20",
"60 3\n5 8\n1 3\n10 26",
"10 2\n3 4\n5 17",
"96 3\n5 4\n3 5\n1 20",
"4 1\n1 3\n0 4",
"60 3\n5 8\n1 2\n10 26",
"15 2\n1 0\n3 33",
"96 3\n4 4\n3 5\n1 20",
"60 3\n9 8\n1 2\n10 26",
"17 2\n1 0\n3 33",
"96 3\n4 4\n3 4\n1 20",
"60 3\n9 16\n1 2\n10 26",
"96 3\n4 4\n3 4\n1 5",
"60 3\n11 16\n1 2\n10 26",
"93 3\n4 4\n3 4\n1 5",
"5 0\n1 2",
"5 1\n3 3\n5 9",
"5 1\n3 2\n5 9",
"5 1\n1 2\n5 17",
"5 1\n1 0\n5 17",
"10 1\n1 0\n5 17",
"10 1\n1 0\n7 17",
"10 1\n1 0\n7 24",
"10 1\n1 0\n7 21",
"5 2\n3 3\n5 4",
"5 0\n3 3\n5 9",
"5 0\n1 3",
"5 1\n3 2\n0 9",
"5 1\n1 2\n5 13",
"5 0\n1 2\n5 17",
"5 1\n1 0\n2 17",
"10 1\n1 0\n7 30",
"10 1\n1 0\n7 45",
"16 1\n1 0\n7 21",
"5 2\n2 3\n5 4",
"3 0\n1 1\n3 4",
"8 0\n3 3\n5 9",
"5 1\n3 2\n0 6",
"5 0\n1 2\n5 13",
"5 0\n1 2\n2 17"
],
"output": [
"0",
"5",
"221823067",
"4",
"0\n",
"903929718\n",
"40\n",
"917017175\n",
"614976987\n",
"5\n",
"742066\n",
"1\n",
"980971792\n",
"208\n",
"7\n",
"3543464\n",
"465231607\n",
"5536\n",
"8\n",
"1598\n",
"613452135\n",
"292126669\n",
"281307714\n",
"10\n",
"693162917\n",
"282478460\n",
"690528981\n",
"894733340\n",
"877034906\n",
"425974918\n",
"866471222\n",
"694270313\n",
"9189590\n",
"974\n",
"1423\n",
"2168498\n",
"2\n",
"768416799\n",
"430890364\n",
"560835629\n",
"40986\n",
"887645468\n",
"55\n",
"421969935\n",
"679877201\n",
"622019656\n",
"35661246\n",
"508986960\n",
"1438\n",
"16\n",
"294018064\n",
"883576557\n",
"266040191\n",
"754365377\n",
"981187987\n",
"610\n",
"377\n",
"17712531\n",
"3\n",
"190978532\n",
"11\n",
"951713208\n",
"17\n",
"217313924\n",
"335832333\n",
"749094228\n",
"6\n",
"180683974\n",
"4\n",
"397629130\n",
"41\n",
"310942914\n",
"944871132\n",
"88\n",
"112718204\n",
"634479161\n",
"76115092\n",
"469563953\n",
"754902149\n",
"0\n",
"0\n",
"0\n",
"5\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"5\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.
Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.
You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.
* When you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.
To help Tak, find the number of ways to go to Cell N, modulo 998244353.
Constraints
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \min(N, 10)
* 1 \leq L_i \leq R_i \leq N
* [L_i, R_i] and [L_j, R_j] do not intersect (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
L_1 R_1
L_2 R_2
:
L_K R_K
Output
Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.
Examples
Input
5 2
1 1
3 4
Output
4
Input
5 2
3 3
5 5
Output
0
Input
5 1
1 2
Output
5
Input
60 3
5 8
1 3
10 15
Output
221823067
### Input:
5 2
3 3
5 5
### Output:
0
### Input:
5 1
1 2
### Output:
5
### Code:
import sys
input = sys.stdin.readline
N,K=map(int,input().split())
K=[tuple(map(int,input().split())) for i in range(K)]
mod=998244353
DP=[0]*(4*10**5+100)
DP[1]=1
DP[2]=-1
for i in range(1,N+1):
DP[i]+=DP[i-1]
DP[i]%=mod
for l,r in K:
DP[i+l]+=DP[i]
DP[i+l]%=mod
DP[i+r+1]-=DP[i]
DP[i+r+1]%=mod
#print(DP[:10])
print(DP[N])
|
p02680 AtCoder Beginner Contest 168 - . (Single Dot)_3229 | There is a grass field that stretches infinitely.
In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).
There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).
What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print `INF` instead.
Constraints
* All values in input are integers between -10^9 and 10^9 (inclusive).
* 1 \leq N, M \leq 1000
* A_i < B_i\ (1 \leq i \leq N)
* E_j < F_j\ (1 \leq j \leq M)
* The point (0, 0) does not lie on any of the given segments.
Input
Input is given from Standard Input in the following format:
N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M
Output
If the area of the region the cow can reach is infinite, print `INF`; otherwise, print an integer representing the area in \mathrm{cm^2}.
(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)
Examples
Input
5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4
Output
13
Input
6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4
Output
INF | I=lambda:map(int,input().split());F=1e21;r=range;n,m=I();f=[-F,F];X=[0]+f;Y=X[:];R=[(f,F),(f,-F)];H=[(F,f),(-F,f)]
for i in r(n):*a,c=I();R+=[(a,c)];Y+=c,;X+=a
for i in r(m):a,*b=I();H+=[(a,b)];X+=a,;Y+=b
def g(X):s=dict(enumerate(sorted(set(X))));return{s[i]:i for i in s},s,len(s)+1
h,s,K=g(X);w,t,L=g(Y);j=lambda:[[0]*-~K for i in r(L+1)];V=j();U=j();v=j()
for(a,b),c in R:U[w[c]][h[a]]+=1;U[w[c]][h[b]]+=-1
for d,(e,f)in H:V[w[e]][h[d]]+=1;V[w[f]][h[d]]+=-1
for i in r(L):
for j in r(K):U[i][j+1]+=U[i][j];V[i+1][j]+=V[i][j]
q=[(h[0],w[0])];v[w[0]][h[0]]=1;a=0
while q:
x,y=q.pop();a+=(s[x]-s[x+1])*(t[y]-t[y+1])
for e,f in[(-1,0),(1,0),(0,1),(0,-1)]:
c=x+e;d=y+f
if 0==v[d][c]and(U[(f>0)+y][x]|e==0)|(V[y][(e>0)+x]|f==0):q+=[(c,d)];v[d][c]=1
print([a,'INF'][a>F]) | {
"input": [
"6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4",
"6 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"5 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"5 6\n1 0 1\n0 1 1\n0 4 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 5\n3 -2 6\n1 2 4",
"5 6\n1 0 1\n0 1 1\n0 4 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 10\n6 -2 6\n1 2 4",
"5 6\n2 0 0\n-1 1 1\n0 4 2\n-2 7 -1\n0 2 3\n1 -1 1\n1 1 1\n1 0 2\n-1 -7 10\n3 -2 6\n1 4 6",
"3 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4",
"3 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 4",
"5 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-3 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 4",
"5 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-6 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 2 -1\n1 4 1\n3 1 0",
"6 1\n-3 -1 -2\n-3 -1 1\n-2 -1 2\n1 4 -3\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 6\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4",
"6 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -4\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 4 4",
"3 1\n-3 0 -4\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4",
"2 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -5\n-3 -1 1\n-2 -1 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 4",
"4 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-3 -1 1\n-2 0 2\n1 1 -2\n1 6 -1\n1 4 1\n3 1 4",
"2 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-3 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 1 1\n3 1 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n6 -2 6\n1 2 4",
"3 1\n-3 -1 -7\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 10\n3 -2 6\n1 2 4",
"3 0\n-3 -1 0\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -13 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 4 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 10\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 6 -1\n0 4 1\n3 1 0",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 2 -1\n1 4 2\n3 1 0",
"6 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -3\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 6\n2 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4",
"5 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n1 4 -4\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 1\n-1 -4 5\n3 -2 6\n1 4 4",
"3 1\n-3 0 -4\n-3 -1 1\n-2 0 2\n1 4 -2\n1 4 -1\n1 4 1\n3 1 4",
"2 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n4 -2 6\n1 2 4",
"3 1\n-3 -1 -5\n-3 0 1\n-2 -1 2\n1 4 -2\n1 6 -1\n1 4 1\n3 1 4",
"4 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 0\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-3 -1 1\n-2 0 2\n1 1 -2\n1 6 -1\n1 4 1\n3 1 4",
"2 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n4 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 1 1\n3 1 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n6 -2 6\n1 2 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 10\n3 -2 6\n1 2 4",
"3 0\n-3 -1 0\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 1 1\n3 1 0",
"5 6\n1 0 1\n0 0 1\n0 2 2\n-3 4 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -13 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n2 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 4 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 10\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 12 -1\n0 4 1\n3 1 0",
"6 1\n-3 -1 -4\n-3 -1 1\n-2 -1 2\n0 4 -3\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 3 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 6\n2 0 1\n0 1 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4",
"5 1\n-3 -1 -4\n-3 -1 1\n-3 -1 2\n1 4 -4\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 2 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 1\n-1 -1 5\n3 -2 6\n1 4 4",
"3 1\n-3 0 -4\n-3 -1 1\n-2 0 2\n1 5 -2\n1 4 -1\n1 4 1\n3 1 4",
"2 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n4 0 6\n1 2 4",
"3 1\n-3 -1 -5\n-3 0 1\n-2 -1 2\n1 1 -2\n1 6 -1\n1 4 1\n3 1 4",
"4 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n1 0 0\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-3 -1 1\n-2 0 2\n1 1 -2\n1 6 -1\n1 6 1\n3 1 4",
"2 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -2\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n4 -2 6\n1 2 4",
"3 1\n-3 -1 -4\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n1 1 1\n3 0 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n8 -2 6\n1 2 0",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n1 0 2\n-1 -4 10\n3 -2 6\n1 2 4",
"3 0\n-3 -1 0\n-3 0 1\n-2 0 2\n1 4 -2\n1 6 -1\n2 1 1\n3 1 0",
"3 1\n-3 -2 0\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n2 4 1\n3 1 0",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 12 -1\n0 4 1\n4 1 0",
"6 1\n-3 0 -4\n-3 -1 1\n-2 -1 2\n0 4 -3\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 3 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 6\n2 0 1\n0 2 2\n2 0 2\n-1 -4 5\n3 -2 4\n1 2 4",
"5 1\n-3 -1 -8\n-3 -1 1\n-3 -1 2\n1 4 -4\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 1\n-1 -1 5\n3 -2 6\n1 4 4",
"3 1\n-3 0 -4\n-3 -1 1\n-2 0 2\n1 5 -2\n1 4 -1\n1 4 2\n3 1 4",
"2 6\n1 0 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n4 0 6\n1 2 4",
"3 1\n-3 -1 -5\n-3 0 1\n-2 -1 2\n1 1 -2\n1 6 -1\n1 4 1\n5 1 4",
"4 6\n2 1 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n1 0 0\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-3 -1 1\n-2 0 2\n1 1 -2\n1 9 -1\n1 6 1\n3 1 4",
"2 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -2\n-2 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n4 -2 6\n0 2 4",
"3 1\n-3 -1 -4\n-6 -1 1\n-2 0 2\n0 4 -2\n1 6 -1\n1 1 1\n3 0 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n1 0 2\n-1 -4 17\n3 -2 6\n1 2 4",
"2 1\n-3 -2 0\n-6 -1 1\n-2 0 2\n1 4 -2\n1 6 -1\n2 4 1\n3 1 0",
"5 6\n1 0 1\n0 1 1\n0 4 2\n-3 7 -1\n-1 6 3\n1 0 1\n1 1 2\n2 0 2\n-1 -7 10\n6 -2 6\n1 2 6",
"3 1\n-3 -1 0\n-6 1 1\n-2 0 2\n1 4 -2\n1 12 -1\n0 4 0\n4 1 0",
"6 1\n-3 0 -4\n-3 -1 1\n-2 -1 2\n0 8 -3\n1 4 -1\n1 4 1\n3 1 4",
"5 1\n-3 0 -8\n-3 -1 1\n-3 -1 2\n1 4 -4\n1 4 -1\n1 4 1\n3 1 4",
"5 6\n1 1 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 1\n-1 -1 5\n3 -1 6\n1 4 4",
"3 1\n-2 0 -4\n-3 -1 1\n-2 0 2\n1 5 -2\n1 4 -1\n1 4 2\n3 1 4",
"2 6\n1 0 0\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n2 0 2\n-1 -4 5\n4 0 6\n1 0 4",
"3 1\n-3 -1 -5\n-3 0 1\n-2 -1 2\n1 1 -2\n1 6 -1\n1 4 1\n5 1 7",
"4 6\n2 0 1\n0 1 1\n0 2 2\n-3 4 -1\n-2 6 3\n1 0 1\n0 1 2\n1 0 0\n-1 -4 5\n3 -2 6\n1 2 4",
"3 1\n-3 -1 0\n-3 -1 1\n-2 0 2\n1 1 -2\n1 14 -1\n1 6 1\n3 1 4",
"2 6\n1 1 1\n0 1 1\n0 2 2\n-3 4 -2\n-2 0 3\n1 0 1\n1 1 2\n2 0 2\n-1 -4 5\n4 -2 6\n0 2 4",
"3 1\n-3 -1 -4\n-6 -1 1\n-2 0 2\n0 4 -2\n2 6 -1\n1 1 1\n3 0 4",
"5 6\n1 0 1\n0 1 1\n0 2 2\n-3 7 -1\n-1 9 3\n1 0 1\n1 1 2\n1 0 2\n-1 -4 17\n3 -2 6\n1 2 4"
],
"output": [
"INF",
"13",
"INF\n",
"13\n",
"16\n",
"14\n",
"28\n",
"4\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"13\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"14\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"16\n",
"INF\n",
"14\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"28\n",
"INF\n",
"INF\n",
"INF\n",
"16\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"INF\n",
"16\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There is a grass field that stretches infinitely.
In this field, there is a negligibly small cow. Let (x, y) denote the point that is x\ \mathrm{cm} south and y\ \mathrm{cm} east of the point where the cow stands now. The cow itself is standing at (0, 0).
There are also N north-south lines and M east-west lines drawn on the field. The i-th north-south line is the segment connecting the points (A_i, C_i) and (B_i, C_i), and the j-th east-west line is the segment connecting the points (D_j, E_j) and (D_j, F_j).
What is the area of the region the cow can reach when it can move around as long as it does not cross the segments (including the endpoints)? If this area is infinite, print `INF` instead.
Constraints
* All values in input are integers between -10^9 and 10^9 (inclusive).
* 1 \leq N, M \leq 1000
* A_i < B_i\ (1 \leq i \leq N)
* E_j < F_j\ (1 \leq j \leq M)
* The point (0, 0) does not lie on any of the given segments.
Input
Input is given from Standard Input in the following format:
N M
A_1 B_1 C_1
:
A_N B_N C_N
D_1 E_1 F_1
:
D_M E_M F_M
Output
If the area of the region the cow can reach is infinite, print `INF`; otherwise, print an integer representing the area in \mathrm{cm^2}.
(Under the constraints, it can be proved that the area of the region is always an integer if it is not infinite.)
Examples
Input
5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4
Output
13
Input
6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4
Output
INF
### Input:
6 1
-3 -1 -2
-3 -1 1
-2 -1 2
1 4 -2
1 4 -1
1 4 1
3 1 4
### Output:
INF
### Input:
5 6
1 2 0
0 1 1
0 2 2
-3 4 -1
-2 6 3
1 0 1
0 1 2
2 0 2
-1 -4 5
3 -2 4
1 2 4
### Output:
13
### Code:
I=lambda:map(int,input().split());F=1e21;r=range;n,m=I();f=[-F,F];X=[0]+f;Y=X[:];R=[(f,F),(f,-F)];H=[(F,f),(-F,f)]
for i in r(n):*a,c=I();R+=[(a,c)];Y+=c,;X+=a
for i in r(m):a,*b=I();H+=[(a,b)];X+=a,;Y+=b
def g(X):s=dict(enumerate(sorted(set(X))));return{s[i]:i for i in s},s,len(s)+1
h,s,K=g(X);w,t,L=g(Y);j=lambda:[[0]*-~K for i in r(L+1)];V=j();U=j();v=j()
for(a,b),c in R:U[w[c]][h[a]]+=1;U[w[c]][h[b]]+=-1
for d,(e,f)in H:V[w[e]][h[d]]+=1;V[w[f]][h[d]]+=-1
for i in r(L):
for j in r(K):U[i][j+1]+=U[i][j];V[i+1][j]+=V[i][j]
q=[(h[0],w[0])];v[w[0]][h[0]]=1;a=0
while q:
x,y=q.pop();a+=(s[x]-s[x+1])*(t[y]-t[y+1])
for e,f in[(-1,0),(1,0),(0,1),(0,-1)]:
c=x+e;d=y+f
if 0==v[d][c]and(U[(f>0)+y][x]|e==0)|(V[y][(e>0)+x]|f==0):q+=[(c,d)];v[d][c]=1
print([a,'INF'][a>F]) |
p02808 Dwango Programming Contest 6th - Cookie Distribution_3232 | There are N children, numbered 1,2,\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)
Let us define the happiness of the children as c_1 \times c_2 \times \ldots \times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \binom{N}{a_1} \times \binom{N}{a_2} \times \ldots \times \binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).
Constraints
* 1 \leq N \leq 1000
* 1 \leq K \leq 20
* 1 \leq a_i \leq N
Input
Input is given from Standard Input in the following format:
N K
a_1 a_2 \ldots a_K
Output
Print the answer.
Examples
Input
3 2
3 2
Output
12
Input
856 16
399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63
Output
337587117 | n,k = map(int,input().split())
a = tuple(map(int,input().split()))
mod = 10**9+7
rng = 1001
fctr = [1]
finv = [1]
for i in range(1,rng):
fctr.append(fctr[-1]*i%mod)
finv.append(pow(fctr[i],mod-2,mod))
dp = [[0 for i in range(n+1)] for j in range(k+1)]
dp[0][0] = 1
for i in range(1,k+1):
x = a[i-1]
for j in range(n+1):
if dp[i-1][j] == 0:
continue
y = dp[i-1][j]*fctr[n-j]*finv[n-x]%mod
for t in range(min(n-j,x)+1):
dp[i][j+t]=(dp[i][j+t]+y*fctr[n-t]*finv[n-j-t]*finv[t]*finv[x-t])%mod
print(dp[k][n]) | {
"input": [
"3 2\n3 2",
"856 16\n399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63",
"3 2\n1 2",
"856 16\n399 491 665 432 206 61 784 548 422 313 848 478 827 26 398 63",
"4 2\n1 2",
"856 16\n399 491 665 432 206 0 784 548 422 313 848 478 827 26 398 63",
"2 2\n1 2",
"856 16\n399 491 665 432 206 0 784 548 422 514 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 0 784 548 422 514 94 478 827 26 398 63",
"856 16\n399 491 665 432 206 0 784 548 143 514 94 478 827 26 398 63",
"3 2\n3 3",
"856 16\n399 263 665 432 206 61 784 548 422 24 848 478 827 26 398 63",
"3 2\n2 2",
"856 16\n399 491 665 432 206 61 784 548 422 313 848 478 827 23 398 63",
"4 2\n2 2",
"856 16\n399 491 665 432 206 0 784 246 422 313 848 478 827 26 398 63",
"2 2\n1 1",
"856 16\n399 491 665 432 206 0 784 548 422 514 848 478 827 2 398 63",
"856 16\n399 833 665 432 206 0 784 548 422 514 94 478 827 26 398 63",
"856 16\n399 491 665 432 107 0 784 548 143 514 94 478 827 26 398 63",
"856 16\n399 263 747 432 206 61 784 548 422 24 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 61 784 548 422 313 848 478 827 23 222 63",
"4 2\n2 3",
"856 16\n399 491 665 329 206 0 784 246 422 313 848 478 827 26 398 63",
"856 16\n399 833 665 432 206 0 784 548 422 514 70 478 827 26 398 63",
"856 16\n399 263 747 432 206 61 784 548 422 47 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 61 784 548 422 79 848 478 827 23 222 63",
"856 16\n399 491 665 329 206 0 784 246 508 313 848 478 827 26 398 63",
"2 1\n2 8",
"856 16\n399 263 747 432 206 61 784 548 422 30 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 61 784 548 422 79 848 478 827 23 222 94",
"856 16\n399 263 747 432 206 61 784 548 422 40 848 478 827 26 398 63",
"856 16\n399 491 665 564 206 61 784 548 422 79 848 478 827 23 222 94",
"856 16\n399 263 747 376 206 61 784 548 422 40 848 478 827 26 398 63",
"856 16\n399 263 234 376 206 61 784 548 422 40 848 478 827 26 398 63",
"856 16\n399 263 234 376 206 61 784 548 774 40 848 478 827 26 398 63",
"856 16\n399 350 234 376 206 61 784 548 774 40 848 478 827 26 398 63",
"856 16\n214 350 234 376 206 61 784 548 774 40 848 478 827 26 398 63",
"7 2\n1 7",
"856 16\n399 263 665 432 206 61 816 548 422 313 848 478 827 26 398 63",
"856 16\n399 491 665 432 170 0 784 548 422 313 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 1 784 548 422 514 848 478 827 26 398 63",
"856 16\n399 491 665 432 206 0 784 548 422 514 60 478 827 26 398 63",
"856 16\n399 491 665 432 206 0 784 855 143 514 94 478 827 26 398 63",
"856 16\n399 263 665 418 206 61 784 548 422 313 848 478 827 26 398 63",
"856 16\n399 263 665 418 206 61 784 315 422 313 848 478 827 26 398 63",
"856 16\n399 263 11 418 206 61 354 315 82 313 848 478 827 26 398 64",
"856 16\n399 263 11 418 206 61 354 315 82 313 848 478 827 42 398 64",
"856 16\n399 263 11 418 206 61 201 315 82 313 848 478 827 42 398 64",
"856 16\n399 263 11 418 206 61 201 530 82 313 848 478 827 42 398 64",
"856 16\n399 263 11 418 206 61 201 13 82 313 848 478 827 42 398 64",
"856 16\n399 263 11 418 206 61 201 6 82 313 848 478 827 42 398 64",
"856 16\n399 263 21 418 206 61 201 6 82 313 848 478 827 42 398 64",
"856 16\n399 263 21 204 206 61 201 6 82 313 848 478 827 42 398 64",
"856 7\n399 263 21 204 206 61 201 6 82 313 848 478 827 42 398 64",
"856 7\n399 389 21 204 206 61 201 6 82 313 848 478 827 42 398 64",
"856 14\n399 389 21 204 206 61 201 5 82 313 848 478 631 42 398 64",
"856 14\n399 389 21 204 206 61 201 5 39 313 848 478 631 42 398 64",
"856 12\n399 389 21 204 206 61 201 5 39 313 848 478 631 42 398 64",
"856 12\n399 389 37 204 206 61 201 5 39 313 848 478 631 42 398 64",
"856 12\n399 389 37 204 206 61 201 1 39 313 848 478 631 42 398 64",
"856 12\n399 389 37 204 206 61 195 1 39 313 848 478 631 42 398 64",
"856 12\n399 389 37 204 366 61 195 1 39 313 848 478 631 42 398 64",
"856 12\n399 389 24 204 366 61 195 1 39 313 848 478 631 42 398 80",
"2 2\n2 2",
"2 2\n2 3",
"2 2\n2 5",
"2 4\n2 5",
"2 5\n2 5",
"2 5\n0 5",
"2 5\n0 8",
"2 5\n1 8",
"2 5\n1 16",
"2 5\n1 22",
"2 9\n1 22",
"1 9\n1 22",
"1 9\n2 22",
"1 9\n3 22",
"1 9\n4 22",
"1 9\n6 22",
"1 9\n6 31",
"1 9\n6 26",
"1 1\n6 26",
"1 0\n6 26",
"2 2\n4 2",
"2 2\n3 5",
"2 2\n1 5",
"2 4\n4 5",
"2 6\n2 5",
"2 5\n1 5",
"1 5\n0 8",
"1 5\n1 8",
"2 5\n1 30",
"2 5\n1 28",
"2 9\n1 8",
"2 9\n2 22",
"1 9\n2 14",
"1 14\n3 22",
"1 9\n1 29",
"0 9\n6 22",
"1 14\n6 31",
"0 9\n6 26"
],
"output": [
"12",
"337587117",
"3\n",
"652418319\n",
"0\n",
"860269823\n",
"4\n",
"293299401\n",
"366370911\n",
"24060500\n",
"8\n",
"310476415\n",
"12\n",
"25729710\n",
"6\n",
"314510353\n",
"2\n",
"25600194\n",
"23647064\n",
"973833970\n",
"756052596\n",
"293415485\n",
"24\n",
"281860830\n",
"150176430\n",
"944589618\n",
"731138031\n",
"601992298\n",
"1\n",
"279486415\n",
"452204876\n",
"816722626\n",
"68373623\n",
"397893539\n",
"368478426\n",
"983214695\n",
"654286888\n",
"726149561\n",
"14\n",
"307328341\n",
"421014311\n",
"5274556\n",
"305060096\n",
"957106834\n",
"800357371\n",
"772960854\n",
"453626014\n",
"928059710\n",
"872873967\n",
"292836983\n",
"351295606\n",
"509183906\n",
"727532698\n",
"591111976\n",
"113519286\n",
"557731190\n",
"691045396\n",
"129825796\n",
"830635867\n",
"959556031\n",
"280903391\n",
"634652159\n",
"418267134\n",
"767801877\n",
"4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N children, numbered 1,2,\ldots,N. In the next K days, we will give them some cookies. In the i-th day, we will choose a_i children among the N with equal probability, and give one cookie to each child chosen. (We make these K choices independently.)
Let us define the happiness of the children as c_1 \times c_2 \times \ldots \times c_N, where c_i is the number of cookies received by Child i in the K days. Find the expected happiness multiplied by \binom{N}{a_1} \times \binom{N}{a_2} \times \ldots \times \binom{N}{a_K} (we can show that this value is an integer), modulo (10^{9}+7).
Constraints
* 1 \leq N \leq 1000
* 1 \leq K \leq 20
* 1 \leq a_i \leq N
Input
Input is given from Standard Input in the following format:
N K
a_1 a_2 \ldots a_K
Output
Print the answer.
Examples
Input
3 2
3 2
Output
12
Input
856 16
399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63
Output
337587117
### Input:
3 2
3 2
### Output:
12
### Input:
856 16
399 263 665 432 206 61 784 548 422 313 848 478 827 26 398 63
### Output:
337587117
### Code:
n,k = map(int,input().split())
a = tuple(map(int,input().split()))
mod = 10**9+7
rng = 1001
fctr = [1]
finv = [1]
for i in range(1,rng):
fctr.append(fctr[-1]*i%mod)
finv.append(pow(fctr[i],mod-2,mod))
dp = [[0 for i in range(n+1)] for j in range(k+1)]
dp[0][0] = 1
for i in range(1,k+1):
x = a[i-1]
for j in range(n+1):
if dp[i-1][j] == 0:
continue
y = dp[i-1][j]*fctr[n-j]*finv[n-x]%mod
for t in range(min(n-j,x)+1):
dp[i][j+t]=(dp[i][j+t]+y*fctr[n-t]*finv[n-j-t]*finv[t]*finv[x-t])%mod
print(dp[k][n]) |
p03081 ExaWizards 2019 - Snuke the Wizard_3238 | There are N squares numbered 1 to N from left to right. Each square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.
Snuke cast Q spells to move the golems.
The i-th spell consisted of two characters t_i and d_i, where d_i is `L` or `R`. When Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is `L`, and moved to the square adjacent to the right if d_i is `R`.
However, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.
Find the number of golems remaining after Snuke cast the Q spells.
Constraints
* 1 \leq N,Q \leq 2 \times 10^{5}
* |s| = N
* s_i and t_i are uppercase English letters.
* d_i is `L` or `R`.
Input
Input is given from Standard Input in the following format:
N Q
s
t_1 d_1
\vdots
t_{Q} d_Q
Output
Print the answer.
Examples
Input
3 4
ABC
A L
B L
B R
A R
Output
2
Input
8 3
AABCBDBA
A L
B R
A R
Output
5
Input
10 15
SNCZWRCEWB
B R
R R
E R
W R
Z L
S R
Q L
W L
B R
C L
A L
N L
E R
Z L
S L
Output
3 | n, q = map(int, input().split())
s = input()
o = []
for _ in range(q):
t, d = input().split()
o.append((t, d))
def check(x):
cur = s[x]
ind = x
for i in range(q):
if o[i][0] == cur:
if o[i][1] == 'L':
ind -= 1
if ind < 0:
return "LEFT"
cur = s[ind]
else:
ind += 1
if ind > n-1:
return "RIGHT"
cur = s[ind]
return "MID"
ans = n
bottom = -1
top = n
while top - bottom > 1:
mid = (top+bottom)//2
if check(mid) == "LEFT":
bottom = mid
else:
top = mid
ans -= 1+bottom
bottom = -1
top = n
while top - bottom > 1:
mid = (top+bottom)//2
if check(mid) == "RIGHT":
top = mid
else:
bottom = mid
ans -= n-top
print(ans) | {
"input": [
"10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nS L",
"3 4\nABC\nA L\nB L\nB R\nA R",
"8 3\nAABCBDBA\nA L\nB R\nA R",
"10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nR L",
"3 4\nACB\nA L\nB L\nB R\nA R",
"8 3\nAABBBDBA\nA L\nB R\nA R",
"3 3\nACB\nB L\nB L\nA R\n@ S",
"3 3\nBCA\nB L\nB L\nA R\n@ S",
"8 0\nAABCBDBA\nA L\nB R\n@ S",
"8 3\nAABCBDBA\nC L\nB R\nA R",
"10 15\nBWECRWZCNS\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nA L\nN L\nE R\nZ L\nR L",
"10 0\nSNCZWRCEWB\nB R\nR R\nE R\nX R\nZ L\nS R\nQ L\nW L\nB R\nC L\nB L\nN L\nE R\nZ L\nS L",
"3 4\nCBB\nA L\nC L\nB R\nB R",
"8 3\nAABCBDBA\nA L\nB R\n@ R",
"3 4\nACB\nA L\nB L\nB R\n@ R",
"8 3\nAABCBDCA\nA L\nB R\n@ R",
"3 3\nACB\nA L\nB L\nB R\n@ R",
"3 3\nACB\nA L\nB L\nA R\n@ R",
"3 3\nACB\nA L\nB L\nA R\n@ S",
"10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nD L\nA L\nN L\nE R\nZ L\nR L",
"3 4\nACB\nA L\nB L\nB Q\nA R",
"8 3\nAABCBDBA\nA L\nB R\n@ S",
"3 4\nADB\nA L\nB L\nB R\n@ R",
"8 3\nAABCBDCA\nA L\nB R\n@ S",
"3 3\nBCA\nA L\nB L\nB R\n@ R",
"3 4\nACB\nA L\nB L\nB Q\nA S",
"8 3\nAACCBDBA\nA L\nB R\nA R",
"3 4\nBCA\nA L\nB L\nB R\nA R",
"3 4\nABB\nA L\nB L\nB R\n@ R",
"3 3\nABC\nA L\nB L\nA R\n@ R",
"3 3\nACB\nA L\nB L\nB R\n@ S",
"8 3\nAABBBDBA\nA L\nB R\nB R",
"3 4\nACC\nA L\nB L\nB Q\nA R",
"3 4\nADB\nA L\nB L\nB Q\n@ R",
"3 3\nCCA\nA L\nB L\nB R\n@ R",
"3 3\nACB\nB L\nB K\nA R\n@ S",
"3 4\nBCA\nA L\nB L\nB Q\nA S",
"8 3\nACCABDBA\nA L\nB R\nA R",
"3 4\nABB\nA L\nB L\nB R\nA R",
"3 3\nBAC\nA L\nB L\nA R\n@ R",
"8 3\nAABBBDAA\nA L\nB R\nB R",
"8 0\nAABCBDBA\n@ L\nB R\n@ S",
"3 4\nACB\nA L\nB L\nB Q\n@ R",
"3 3\nCCA\nA L\nB L\nA R\n@ R",
"3 3\nBCA\nA L\nB L\nB Q\nA S",
"3 3\nBBC\nA L\nB L\nA R\n@ R",
"8 3\nAABBBDAA\nB L\nB R\nB R",
"8 0\nAABCBDBA\n@ L\nB S\n@ S",
"3 3\nCCA\nA L\nB L\nA R\n@ Q",
"3 3\nCBB\nA L\nB L\nA R\n@ R",
"8 1\nAABCBDBA\n@ L\nB S\n@ S",
"3 3\nCBB\nA L\nC L\nA R\n@ R",
"8 1\nAABCBDBA\n@ L\nA S\n@ S",
"3 3\nCBB\nA L\nC L\nA R\n@ S",
"8 1\nAABCBDBA\n? L\nA S\n@ S",
"8 1\nAABCBDBA\n? K\nA S\n@ S",
"8 1\nBABCBDBA\n? K\nA S\n@ S",
"8 0\nBABCBDBA\n? K\nA S\n@ S",
"10 15\nSNCZWRCEWB\nB R\nR R\nE R\nW R\nZ L\nS R\nQ L\nW L\nB R\nC L\nB L\nN L\nE R\nZ L\nS L",
"3 4\nBBC\nA L\nB L\nB R\nA R",
"8 3\nAABCBDBA\nB L\nB R\nA R",
"3 4\nACB\nA L\nB L\nB S\nA R",
"3 4\nACB\nA L\nB L\nB R\n@ Q",
"3 1\nACB\nA L\nB L\nB R\n@ R",
"3 3\nACB\nA L\nB L\nA R\n@ Q",
"3 3\nACB\nA L\nB L\nA Q\n@ S",
"3 4\nADB\nA L\nB L\nB R\nA R",
"8 1\nAABCBDCA\nA L\nB R\n@ S",
"3 3\nACB\nB L\nC L\nA R\n@ S",
"3 4\nACB\nA L\nB L\nB Q\nB S",
"3 3\nBCA\nB L\nB K\nA R\n@ S",
"8 2\nAACCBDBA\nA L\nB R\nA R",
"3 4\nBCA\nA L\nB L\nB R\nB R",
"3 4\nABB\nA L\nB L\nB R\n@ S",
"3 3\nABC\nA L\nC L\nA R\n@ R",
"3 4\nACC\nB L\nB L\nB Q\nA R",
"8 0\nAABCBDBA\nA L\nA R\n@ S",
"3 4\nADB\n@ L\nB L\nB Q\n@ R",
"3 3\nCCA\nA L\nB L\nC R\n@ R",
"3 3\nACB\nB L\nB K\nA R\n@ T",
"3 4\nBCA\nA L\nB L\nB P\nA S",
"8 3\nAACABDBC\nA L\nB R\nA R",
"3 4\nABB\nB L\nB L\nB R\nA R",
"8 3\nAABBBDAA\nA L\nA R\nB R",
"8 0\nAABCBDBA\n@ L\nB R\n? S",
"3 3\nCCA\nA L\nB L\nA R\n? R",
"3 3\nBBC\nA L\nA L\nA R\n@ R",
"8 0\nAABCBDBA\n@ L\nB T\n@ S",
"3 3\nACC\nA L\nB L\nA R\n@ Q",
"3 3\nCBB\nA L\nC L\n@ R\n@ R",
"3 3\nCBB\nA L\nB L\nA R\n@ S",
"8 1\nAABCBDBB\n? L\nA S\n@ S",
"8 1\nBABCBDBA\n? K\nA R\n@ S",
"10 15\nSNCZWRCEWB\nB R\nR R\nE R\nX R\nZ L\nS R\nQ L\nW L\nB R\nC L\nB L\nN L\nE R\nZ L\nS L",
"3 4\nBCB\nA L\nB L\nB R\nA R",
"3 4\nACC\nA L\nB L\nB S\nA R",
"3 4\nACB\nA L\nB L\nB R\nA Q",
"3 1\nACB\n@ L\nB L\nB R\n@ R",
"3 3\nACB\nA L\nB L\nA Q\n@ T",
"3 4\nBDA\nA L\nB L\nB R\nA R",
"8 1\nAABCBDCA\nA L\nC R\n@ S",
"3 4\nBCA\nA L\nB L\nC R\nB R",
"3 2\nABC\nA L\nC L\nA R\n@ R"
],
"output": [
"3",
"2",
"5",
"7\n",
"2\n",
"5\n",
"3\n",
"1\n",
"8\n",
"6\n",
"9\n",
"10\n",
"0\n",
"7\n",
"2\n",
"7\n",
"2\n",
"2\n",
"2\n",
"7\n",
"2\n",
"7\n",
"2\n",
"7\n",
"2\n",
"2\n",
"5\n",
"2\n",
"2\n",
"2\n",
"2\n",
"7\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"5\n",
"2\n",
"1\n",
"7\n",
"8\n",
"2\n",
"3\n",
"2\n",
"2\n",
"8\n",
"8\n",
"3\n",
"3\n",
"8\n",
"2\n",
"8\n",
"2\n",
"8\n",
"8\n",
"8\n",
"8\n",
"3\n",
"2\n",
"7\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"7\n",
"3\n",
"2\n",
"1\n",
"7\n",
"2\n",
"2\n",
"2\n",
"3\n",
"8\n",
"3\n",
"3\n",
"3\n",
"2\n",
"7\n",
"3\n",
"7\n",
"8\n",
"3\n",
"3\n",
"8\n",
"2\n",
"2\n",
"3\n",
"8\n",
"8\n",
"5\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"2\n",
"7\n",
"2\n",
"2\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N squares numbered 1 to N from left to right. Each square has a character written on it, and Square i has a letter s_i. Besides, there is initially one golem on each square.
Snuke cast Q spells to move the golems.
The i-th spell consisted of two characters t_i and d_i, where d_i is `L` or `R`. When Snuke cast this spell, for each square with the character t_i, all golems on that square moved to the square adjacent to the left if d_i is `L`, and moved to the square adjacent to the right if d_i is `R`.
However, when a golem tried to move left from Square 1 or move right from Square N, it disappeared.
Find the number of golems remaining after Snuke cast the Q spells.
Constraints
* 1 \leq N,Q \leq 2 \times 10^{5}
* |s| = N
* s_i and t_i are uppercase English letters.
* d_i is `L` or `R`.
Input
Input is given from Standard Input in the following format:
N Q
s
t_1 d_1
\vdots
t_{Q} d_Q
Output
Print the answer.
Examples
Input
3 4
ABC
A L
B L
B R
A R
Output
2
Input
8 3
AABCBDBA
A L
B R
A R
Output
5
Input
10 15
SNCZWRCEWB
B R
R R
E R
W R
Z L
S R
Q L
W L
B R
C L
A L
N L
E R
Z L
S L
Output
3
### Input:
10 15
SNCZWRCEWB
B R
R R
E R
W R
Z L
S R
Q L
W L
B R
C L
A L
N L
E R
Z L
S L
### Output:
3
### Input:
3 4
ABC
A L
B L
B R
A R
### Output:
2
### Code:
n, q = map(int, input().split())
s = input()
o = []
for _ in range(q):
t, d = input().split()
o.append((t, d))
def check(x):
cur = s[x]
ind = x
for i in range(q):
if o[i][0] == cur:
if o[i][1] == 'L':
ind -= 1
if ind < 0:
return "LEFT"
cur = s[ind]
else:
ind += 1
if ind > n-1:
return "RIGHT"
cur = s[ind]
return "MID"
ans = n
bottom = -1
top = n
while top - bottom > 1:
mid = (top+bottom)//2
if check(mid) == "LEFT":
bottom = mid
else:
top = mid
ans -= 1+bottom
bottom = -1
top = n
while top - bottom > 1:
mid = (top+bottom)//2
if check(mid) == "RIGHT":
top = mid
else:
bottom = mid
ans -= n-top
print(ans) |
p03226 Tenka1 Programmer Contest - Circular_3241 | You are given a sequence of N integers: A_1,A_2,...,A_N.
Find the number of permutations p_1,p_2,...,p_N of 1,2,...,N that can be changed to A_1,A_2,...,A_N by performing the following operation some number of times (possibly zero), modulo 998244353:
* For each 1\leq i\leq N, let q_i=min(p_{i-1},p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.
Constraints
* 1 \leq N \leq 3 × 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the number of the sequences that satisfy the condition, modulo 998244353.
Examples
Input
3
1
2
1
Output
2
Input
5
3
1
4
1
5
Output
0
Input
8
4
4
4
1
1
1
2
2
Output
24
Input
6
1
1
6
2
2
2
Output
0 | import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)
from operator import itemgetter
MOD = 998244353
N,*A = map(int,read().split())
T = A.count(1)
if T == 0:
print(0)
exit()
if T == 1:
answer = 1 if len(set(A)) == N else 0
print(answer)
exit()
if T == N:
answer = 1
for n in range(1,N+1):
answer *= n
answer %= MOD
print(answer)
exit()
n = A.index(1)
while A[n-1] == 1:
n -= 1
A = A[n:] + A[:n]
# assert len(A) == N and A[0] == 1 and A[-1] != 1
L = [0] * (N+1)
R = [-1] * (N+1)
ctr = [0] * (N+1)
nums = []
prev = 0
for i,x in enumerate(A):
ctr[x] += 1
R[x] = i
if prev != x:
nums.append(x)
L[x] = i
prev = x
if any(y - x + 1 != z for x,y,z in zip(L,R,ctr)):
print(0)
exit()
if any(x > T for x in ctr[2:]):
print(0)
exit()
free = [0] * (N+1) # ある数値を書き込んだ時点で、死亡確定になってるマス数
answer = 1
for x,y,z in zip(nums,nums[1:],nums[2:]+[1]):
if x > y < z:
if ctr[y] != T:
answer = 0
break
elif x < y < z:
free[y] += ctr[y] - 1
elif x > y > z:
free[y] += ctr[y] - 1
else:
# x < y > z
answer *= (T + 1 - ctr[y])
answer %= MOD
free[y] += ctr[y] + T - 2
f = 0
for n in range(1,N+1):
if ctr[n] >= 1:
f += free[n]
continue
answer *= f
answer %= MOD
f -= 1
print(answer) | {
"input": [
"3\n1\n2\n1",
"8\n4\n4\n4\n1\n1\n1\n2\n2",
"6\n1\n1\n6\n2\n2\n2",
"5\n3\n1\n4\n1\n5",
"8\n4\n4\n4\n1\n2\n1\n2\n2",
"5\n3\n1\n4\n2\n5",
"6\n4\n1\n1\n2\n2\n4",
"6\n1\n1\n1\n2\n2\n2",
"6\n1\n1\n1\n2\n2\n1",
"6\n1\n1\n1\n1\n2\n1",
"6\n1\n1\n1\n1\n1\n1",
"3\n1\n1\n1",
"8\n4\n4\n5\n1\n1\n1\n2\n3",
"5\n1\n2\n2\n1\n1",
"6\n1\n1\n6\n2\n2\n4",
"5\n3\n1\n4\n1\n9",
"8\n4\n4\n3\n1\n2\n1\n2\n2",
"6\n1\n1\n12\n2\n2\n4",
"5\n3\n1\n4\n1\n2",
"6\n2\n1\n12\n2\n2\n4",
"5\n3\n2\n4\n1\n2",
"6\n2\n1\n12\n2\n2\n1",
"5\n3\n2\n8\n1\n2",
"5\n3\n2\n5\n1\n2",
"8\n8\n4\n4\n1\n1\n1\n2\n2",
"6\n2\n1\n6\n2\n2\n2",
"8\n5\n4\n3\n1\n2\n1\n2\n2",
"5\n3\n1\n4\n1\n3",
"6\n4\n1\n12\n2\n2\n4",
"5\n5\n2\n4\n1\n2",
"6\n2\n1\n12\n2\n2\n2",
"5\n3\n2\n8\n1\n1",
"6\n2\n1\n13\n2\n2\n2",
"5\n3\n2\n4\n2\n5",
"8\n5\n7\n3\n1\n2\n1\n2\n2",
"5\n2\n1\n4\n1\n3",
"6\n3\n1\n6\n2\n2\n2",
"6\n2\n1\n1\n2\n2\n2",
"5\n3\n3\n4\n2\n5",
"5\n3\n1\n4\n1\n1",
"5\n3\n4\n4\n2\n5",
"5\n3\n4\n4\n2\n10",
"6\n1\n1\n1\n2\n3\n1",
"5\n3\n4\n4\n2\n16",
"6\n1\n1\n1\n1\n3\n1",
"5\n3\n4\n4\n3\n16",
"6\n1\n2\n1\n2\n3\n1",
"5\n3\n8\n4\n3\n16",
"5\n3\n8\n7\n3\n16",
"3\n1\n3\n1",
"8\n4\n4\n4\n1\n1\n1\n1\n2",
"6\n1\n1\n6\n2\n1\n2",
"5\n3\n1\n3\n1\n5",
"8\n4\n4\n2\n1\n2\n1\n2\n2",
"6\n1\n1\n7\n2\n2\n2",
"5\n3\n1\n5\n1\n9",
"8\n4\n1\n3\n1\n2\n1\n2\n2",
"6\n2\n1\n19\n2\n2\n4",
"6\n2\n1\n12\n2\n4\n4",
"5\n2\n2\n8\n1\n2",
"8\n8\n4\n4\n1\n1\n1\n2\n3",
"6\n2\n2\n6\n2\n2\n2",
"5\n1\n1\n4\n2\n5",
"5\n3\n1\n5\n1\n1",
"5\n5\n3\n4\n1\n2",
"5\n4\n2\n8\n1\n1",
"6\n3\n1\n1\n2\n2\n2",
"5\n3\n2\n4\n2\n10",
"8\n5\n11\n3\n1\n2\n1\n2\n2",
"5\n2\n1\n4\n1\n2",
"6\n2\n1\n1\n2\n2\n4",
"5\n3\n3\n5\n2\n5",
"5\n3\n1\n3\n1\n1",
"6\n1\n1\n1\n2\n1\n1",
"5\n3\n3\n4\n2\n16",
"5\n3\n4\n4\n3\n32",
"5\n3\n8\n4\n3\n24",
"5\n3\n8\n7\n4\n16",
"8\n4\n1\n2\n1\n2\n1\n2\n2",
"5\n3\n1\n5\n2\n9",
"6\n3\n1\n12\n2\n4\n4",
"5\n4\n2\n8\n1\n2",
"8\n8\n8\n4\n1\n1\n1\n2\n3",
"6\n2\n2\n6\n2\n3\n2",
"5\n1\n2\n4\n2\n5",
"5\n3\n1\n5\n1\n2",
"5\n8\n2\n8\n1\n1",
"6\n3\n1\n2\n2\n2\n2",
"5\n3\n2\n4\n2\n8",
"8\n5\n11\n3\n1\n2\n1\n4\n2",
"5\n2\n2\n4\n1\n2",
"6\n2\n1\n2\n2\n2\n4",
"5\n3\n5\n5\n2\n5",
"5\n5\n1\n3\n1\n1",
"6\n1\n2\n1\n1\n2\n1",
"5\n3\n4\n4\n3\n8",
"5\n1\n8\n7\n4\n16",
"3\n1\n1\n2",
"8\n4\n1\n2\n1\n4\n1\n2\n2",
"5\n3\n1\n5\n2\n14",
"6\n3\n2\n12\n2\n4\n4",
"5\n4\n2\n15\n1\n2",
"6\n2\n2\n6\n2\n6\n2",
"5\n1\n2\n4\n3\n5"
],
"output": [
"2",
"24",
"0",
"0",
"0\n",
"1\n",
"2\n",
"24\n",
"72\n",
"120\n",
"720\n",
"6\n",
"18\n",
"12\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"24\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"120\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a sequence of N integers: A_1,A_2,...,A_N.
Find the number of permutations p_1,p_2,...,p_N of 1,2,...,N that can be changed to A_1,A_2,...,A_N by performing the following operation some number of times (possibly zero), modulo 998244353:
* For each 1\leq i\leq N, let q_i=min(p_{i-1},p_{i}), where p_0=p_N. Replace the sequence p with the sequence q.
Constraints
* 1 \leq N \leq 3 × 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the number of the sequences that satisfy the condition, modulo 998244353.
Examples
Input
3
1
2
1
Output
2
Input
5
3
1
4
1
5
Output
0
Input
8
4
4
4
1
1
1
2
2
Output
24
Input
6
1
1
6
2
2
2
Output
0
### Input:
3
1
2
1
### Output:
2
### Input:
8
4
4
4
1
1
1
2
2
### Output:
24
### Code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)
from operator import itemgetter
MOD = 998244353
N,*A = map(int,read().split())
T = A.count(1)
if T == 0:
print(0)
exit()
if T == 1:
answer = 1 if len(set(A)) == N else 0
print(answer)
exit()
if T == N:
answer = 1
for n in range(1,N+1):
answer *= n
answer %= MOD
print(answer)
exit()
n = A.index(1)
while A[n-1] == 1:
n -= 1
A = A[n:] + A[:n]
# assert len(A) == N and A[0] == 1 and A[-1] != 1
L = [0] * (N+1)
R = [-1] * (N+1)
ctr = [0] * (N+1)
nums = []
prev = 0
for i,x in enumerate(A):
ctr[x] += 1
R[x] = i
if prev != x:
nums.append(x)
L[x] = i
prev = x
if any(y - x + 1 != z for x,y,z in zip(L,R,ctr)):
print(0)
exit()
if any(x > T for x in ctr[2:]):
print(0)
exit()
free = [0] * (N+1) # ある数値を書き込んだ時点で、死亡確定になってるマス数
answer = 1
for x,y,z in zip(nums,nums[1:],nums[2:]+[1]):
if x > y < z:
if ctr[y] != T:
answer = 0
break
elif x < y < z:
free[y] += ctr[y] - 1
elif x > y > z:
free[y] += ctr[y] - 1
else:
# x < y > z
answer *= (T + 1 - ctr[y])
answer %= MOD
free[y] += ctr[y] + T - 2
f = 0
for n in range(1,N+1):
if ctr[n] >= 1:
f += free[n]
continue
answer *= f
answer %= MOD
f -= 1
print(answer) |
p03374 AtCoder Regular Contest 096 - Static Sushi_3244 | "Teishi-zushi", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.
Nakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.
Nakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.
Whenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger.
Constraints
* 1 ≤ N ≤ 10^5
* 2 ≤ C ≤ 10^{14}
* 1 ≤ x_1 < x_2 < ... < x_N < C
* 1 ≤ v_i ≤ 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N C
x_1 v_1
x_2 v_2
:
x_N v_N
Output
If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.
Examples
Input
3 20
2 80
9 120
16 1
Output
191
Input
3 20
2 80
9 1
16 120
Output
192
Input
1 100000000000000
50000000000000 1
Output
0
Input
15 10000000000
400000000 1000000000
800000000 1000000000
1900000000 1000000000
2400000000 1000000000
2900000000 1000000000
3300000000 1000000000
3700000000 1000000000
3800000000 1000000000
4000000000 1000000000
4100000000 1000000000
5200000000 1000000000
6600000000 1000000000
8000000000 1000000000
9300000000 1000000000
9700000000 1000000000
Output
6500000000 | N, C = map(int, input().split())
xv = [[int(i) for i in input().split()] for _ in range(N)]
av = 0
fa1 = 0
bv = 0
fb1 = 0
fa = []
fb = []
ga = []
gb = []
for i in range(N):
ax = xv[i][0]
av += xv[i][1]
bx = C - xv[-(i+1)][0]
bv += xv[-(i+1)][1]
fa1 = max(fa1, av-ax)
fa.append(fa1)
ga.append(av - 2*ax)
fb1 = max(fb1, bv-bx)
fb.append(fb1)
gb.append(bv - 2*bx)
p = max(0, fa[-1], fb[-1])
for i in range(N-1):
p = max(p, fa[i]+gb[N-i-2], ga[i]+fb[N-i-2])
print(p)
| {
"input": [
"15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000000\n9300000000 1000000000\n9700000000 1000000000",
"3 20\n2 80\n9 120\n16 1",
"3 20\n2 80\n9 1\n16 120",
"1 100000000000000\n50000000000000 1",
"3 20\n2 80\n5 120\n16 1",
"3 20\n2 1\n9 120\n16 1",
"3 20\n0 80\n9 1\n16 120",
"1 100100000000000\n50000000000000 1",
"15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000001\n9300000000 1000000000\n9700000000 1000000000",
"3 20\n4 80\n9 120\n16 1",
"3 20\n2 80\n8 1\n16 120",
"3 20\n2 80\n8 1\n16 82",
"3 20\n2 80\n9 1\n20 120",
"3 20\n4 50\n9 120\n16 1",
"3 20\n2 101\n8 1\n16 120",
"3 21\n2 80\n8 1\n16 82",
"3 20\n2 001\n8 1\n16 120",
"3 20\n2 80\n3 2\n20 120",
"3 20\n2 72\n8 120\n16 -1",
"3 20\n2 80\n3 2\n20 114",
"3 20\n2 72\n8 188\n16 -1",
"3 20\n4 80\n9 1\n16 120",
"15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000000\n6600000000 1000000000\n8000000000 1000000001\n9300000000 1000000100\n9700000000 1000000000",
"3 20\n4 80\n9 120\n29 1",
"3 20\n2 80\n9 165\n16 0",
"3 20\n3 80\n9 1\n20 120",
"3 20\n2 100\n8 1\n16 120",
"3 10\n2 80\n9 120\n16 0",
"3 20\n2 80\n3 2\n8 120",
"3 20\n2 101\n8 188\n16 -1",
"3 20\n4 80\n9 17\n29 1",
"3 20\n2 80\n9 327\n16 0",
"3 20\n3 66\n9 120\n16 1",
"3 20\n2 101\n8 316\n16 -1",
"3 22\n4 80\n9 17\n29 1",
"3 20\n3 66\n9 229\n16 1",
"3 24\n4 80\n9 17\n29 1",
"3 20\n8 80\n9 445\n16 0",
"3 24\n7 80\n9 17\n13 1",
"3 20\n0 66\n9 65\n16 2",
"3 20\n0 66\n4 65\n16 2",
"3 20\n0 56\n4 65\n16 2",
"3 20\n0 56\n2 65\n16 2",
"3 7\n0 56\n2 65\n16 2",
"3 7\n0 56\n2 65\n25 2",
"3 11\n0 56\n2 85\n25 2",
"3 13\n0 56\n2 85\n25 2",
"3 20\n2 80\n5 120\n16 2",
"1 100100000000000\n50000000000000 2",
"1 100100000100000\n50000000000000 2",
"1 100100000100000\n50000000000000 4",
"1 100100000100000\n46089894256444 4",
"1 100100000100000\n54080308945825 4",
"1 100100000100000\n54080308945825 7",
"1 100100000100000\n97477316051591 7",
"1 100000000000000\n50000000000000 0",
"1 100100000000000\n90630560822492 2",
"1 100100000100000\n50000000000000 1",
"1 100100000100000\n50000000000000 5",
"1 100100000100000\n36435423729333 4",
"1 100100010100000\n54080308945825 4",
"1 100000000000000\n50000000000000 -1",
"1 100100000000000\n7505783473189 2",
"1 100100000100010\n50000000000000 1",
"1 100100000100000\n50000000000000 8",
"1 100100000100000\n36435423729333 2",
"1 100100010100000\n54080308945825 1",
"1 100000000000000\n50000000000000 -2",
"1 100100000000000\n7505783473189 4",
"1 100100100100000\n50000000000000 4",
"1 100100000100000\n36435423729333 1",
"1 100000000000000\n2421261197873 -2",
"1 100100000000000\n7505783473189 8",
"1 100100100100000\n58327321578744 4",
"1 100100000100000\n19822786627217 1",
"1 100000000000000\n1741598310499 -2",
"1 100100000000000\n7505783473189 3",
"1 100100100100000\n22913237067823 4",
"1 100000000000000\n1741598310499 -3",
"1 100100001000000\n7505783473189 3",
"1 100100100100000\n41461083252438 4",
"1 100000000000000\n2678773713496 -3",
"1 100100001000000\n7505783473189 0",
"1 100000000000000\n2801735506425 -3",
"1 100100001000000\n4623623015161 0",
"1 100100001010000\n4623623015161 0",
"1 100100001110000\n4623623015161 0",
"1 100100001110000\n2938818569659 0",
"1 100100011110000\n2938818569659 0",
"3 20\n2 80\n9 120\n16 0",
"1 100000000100000\n50000000000000 1",
"1 100100000000000\n6783797980409 1",
"1 100100000000000\n54911871768050 2",
"1 100100000100000\n10677651247468 4",
"1 100100000100000\n42933082280305 4",
"15 10000000000\n400000000 1000000000\n800000000 1000000000\n1900000000 1000000000\n2400000000 1000000000\n2900000000 1000000000\n3300000000 1000000000\n3700000000 1000000000\n3800000000 1000000000\n4000000000 1000000000\n4100000000 1000000000\n5200000000 1000000001\n6600000000 1000000000\n8000000000 1000000001\n9300000000 1000000000\n9700000000 1000000000",
"1 100000000000000\n74834431600491 0",
"1 100100000000000\n21109961939239 2",
"1 100100001100000\n50000000000000 5",
"1 100100000100000\n66407103008160 4",
"1 100100010100000\n56740499990362 4",
"1 100100000000000\n50000000000000 -1",
"1 100100000000000\n1198784427126 2",
"1 100000000100010\n50000000000000 1"
],
"output": [
"6500000000",
"191",
"192",
"0",
"195\n",
"112\n",
"196\n",
"0\n",
"6500000000\n",
"191\n",
"192\n",
"154\n",
"198\n",
"161\n",
"213\n",
"153\n",
"116\n",
"199\n",
"184\n",
"193\n",
"252\n",
"188\n",
"6500000100\n",
"210\n",
"236\n",
"197\n",
"212\n",
"203\n",
"194\n",
"281\n",
"107\n",
"398\n",
"177\n",
"409\n",
"103\n",
"286\n",
"99\n",
"516\n",
"88\n",
"122\n",
"127\n",
"117\n",
"119\n",
"139\n",
"157\n",
"169\n",
"165\n",
"195\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"191\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"6500000000\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
"Teishi-zushi", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter.
Nakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories.
Nakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter.
Whenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger.
Constraints
* 1 ≤ N ≤ 10^5
* 2 ≤ C ≤ 10^{14}
* 1 ≤ x_1 < x_2 < ... < x_N < C
* 1 ≤ v_i ≤ 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N C
x_1 v_1
x_2 v_2
:
x_N v_N
Output
If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c.
Examples
Input
3 20
2 80
9 120
16 1
Output
191
Input
3 20
2 80
9 1
16 120
Output
192
Input
1 100000000000000
50000000000000 1
Output
0
Input
15 10000000000
400000000 1000000000
800000000 1000000000
1900000000 1000000000
2400000000 1000000000
2900000000 1000000000
3300000000 1000000000
3700000000 1000000000
3800000000 1000000000
4000000000 1000000000
4100000000 1000000000
5200000000 1000000000
6600000000 1000000000
8000000000 1000000000
9300000000 1000000000
9700000000 1000000000
Output
6500000000
### Input:
15 10000000000
400000000 1000000000
800000000 1000000000
1900000000 1000000000
2400000000 1000000000
2900000000 1000000000
3300000000 1000000000
3700000000 1000000000
3800000000 1000000000
4000000000 1000000000
4100000000 1000000000
5200000000 1000000000
6600000000 1000000000
8000000000 1000000000
9300000000 1000000000
9700000000 1000000000
### Output:
6500000000
### Input:
3 20
2 80
9 120
16 1
### Output:
191
### Code:
N, C = map(int, input().split())
xv = [[int(i) for i in input().split()] for _ in range(N)]
av = 0
fa1 = 0
bv = 0
fb1 = 0
fa = []
fb = []
ga = []
gb = []
for i in range(N):
ax = xv[i][0]
av += xv[i][1]
bx = C - xv[-(i+1)][0]
bv += xv[-(i+1)][1]
fa1 = max(fa1, av-ax)
fa.append(fa1)
ga.append(av - 2*ax)
fb1 = max(fb1, bv-bx)
fb.append(fb1)
gb.append(bv - 2*bx)
p = max(0, fa[-1], fb[-1])
for i in range(N-1):
p = max(p, fa[i]+gb[N-i-2], ga[i]+fb[N-i-2])
print(p)
|
p03535 CODE FESTIVAL 2017 Final (Parallel) - Time Gap_3248 | In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.
Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours. The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours. Here, we are using 24-hour notation. That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.
Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.
Find the maximum possible value of s.
Constraints
* 1 \leq N \leq 50
* 0 \leq D_i \leq 12
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
D_1 D_2 ... D_N
Output
Print the maximum possible value of s.
Examples
Input
3
7 12 8
Output
4
Input
2
11 11
Output
2
Input
1
0
Output
0 | N = int(input())
D = [int(x) for x in input().split()]
D.append(0)
D.sort()
ans = []
for i in range(N + 1):
if i % 2 == 0:
ans.append(D[i])
else:
ans.append((24 - D[i]) % 24)
ans.sort()
print(min(min(ans[i + 1] - ans[i] for i in range(N)), 24 - ans[-1]))
| {
"input": [
"2\n11 11",
"3\n7 12 8",
"1\n0",
"2\n11 8",
"3\n7 12 11",
"2\n8 8",
"2\n10 2",
"2\n2 0",
"3\n9 12 8",
"2\n6 8",
"2\n12 8",
"2\n9 7",
"1\n11",
"1\n9",
"1\n10",
"3\n8 12 11",
"2\n8 1",
"2\n10 1",
"2\n4 2",
"2\n8 2",
"2\n2 1",
"2\n3 0",
"2\n8 6",
"3\n8 12 0",
"2\n8 0",
"2\n17 1",
"2\n10 0",
"2\n4 1",
"2\n14 1",
"2\n2 2",
"2\n3 1",
"2\n5 0",
"2\n6 6",
"2\n9 1",
"2\n0 1",
"2\n15 0",
"2\n4 0",
"2\n14 0",
"2\n4 3",
"2\n3 2",
"2\n12 12",
"2\n6 11",
"2\n1 1",
"2\n11 0",
"2\n6 0",
"2\n0 3",
"2\n3 3",
"2\n3 12",
"2\n0 0",
"2\n19 0",
"2\n0 4",
"2\n6 3",
"2\n5 12",
"2\n17 0",
"2\n1 4",
"2\n6 1",
"2\n12 0",
"2\n7 0",
"2\n12 1",
"2\n7 1",
"2\n12 2",
"2\n21 1",
"2\n11 7",
"3\n10 12 8",
"2\n0 8",
"2\n13 1",
"2\n16 1",
"2\n10 4",
"2\n1 2",
"2\n1 0",
"2\n5 1",
"3\n4 12 8",
"2\n8 11",
"2\n9 0",
"2\n13 0",
"2\n4 6",
"2\n11 1",
"2\n5 2",
"2\n6 2",
"2\n1 8",
"2\n1 6",
"2\n16 2",
"2\n2 11",
"2\n7 2",
"2\n20 1",
"2\n0 5",
"2\n5 3",
"2\n5 7",
"2\n0 2",
"2\n0 6",
"2\n7 12",
"2\n1 7",
"2\n7 3",
"2\n12 4",
"2\n0 7",
"2\n0 15",
"2\n16 0",
"2\n5 4",
"2\n14 2",
"2\n1 3",
"2\n2 4",
"2\n24 0",
"2\n11 2"
],
"output": [
"2",
"4",
"0",
"5\n",
"1\n",
"8\n",
"2\n",
"0\n",
"3\n",
"6\n",
"4\n",
"7\n",
"11\n",
"9\n",
"10\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"0\n",
"6\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"1\n",
"2\n",
"1\n",
"0\n",
"6\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"3\n",
"2\n",
"0\n",
"6\n",
"1\n",
"0\n",
"0\n",
"0\n",
"3\n",
"3\n",
"0\n",
"0\n",
"0\n",
"3\n",
"5\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"1\n",
"2\n",
"1\n",
"6\n",
"2\n",
"0\n",
"1\n",
"1\n",
"4\n",
"1\n",
"0\n",
"1\n",
"4\n",
"5\n",
"0\n",
"0\n",
"4\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"0\n",
"3\n",
"5\n",
"0\n",
"0\n",
"5\n",
"1\n",
"3\n",
"4\n",
"0\n",
"0\n",
"0\n",
"4\n",
"2\n",
"1\n",
"2\n",
"0\n",
"2\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.
Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours. The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours. Here, we are using 24-hour notation. That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.
Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.
Find the maximum possible value of s.
Constraints
* 1 \leq N \leq 50
* 0 \leq D_i \leq 12
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
D_1 D_2 ... D_N
Output
Print the maximum possible value of s.
Examples
Input
3
7 12 8
Output
4
Input
2
11 11
Output
2
Input
1
0
Output
0
### Input:
2
11 11
### Output:
2
### Input:
3
7 12 8
### Output:
4
### Code:
N = int(input())
D = [int(x) for x in input().split()]
D.append(0)
D.sort()
ans = []
for i in range(N + 1):
if i % 2 == 0:
ans.append(D[i])
else:
ans.append((24 - D[i]) % 24)
ans.sort()
print(min(min(ans[i + 1] - ans[i] for i in range(N)), 24 - ans[-1]))
|
p03695 AtCoder Beginner Contest 064 - Colorful Leaderboard_3252 | In AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:
* Rating 1-399 : gray
* Rating 400-799 : brown
* Rating 800-1199 : green
* Rating 1200-1599 : cyan
* Rating 1600-1999 : blue
* Rating 2000-2399 : yellow
* Rating 2400-2799 : orange
* Rating 2800-3199 : red
Other than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.
Currently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.
Find the minimum and maximum possible numbers of different colors of the users.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ a_i ≤ 4800
* a_i is an integer.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.
Examples
Input
4
2100 2500 2700 2700
Output
2 2
Input
5
1100 1900 2800 3200 3200
Output
3 5
Input
20
800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990
Output
1 1 | n,a=open(0)
s=set();x=0
for i in map(int,a.split()):
j=i//400
if j<8:s.add(j)
else:x+=1
print(max(1,len(s)),len(s)+x) | {
"input": [
"4\n2100 2500 2700 2700",
"20\n800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990",
"5\n1100 1900 2800 3200 3200",
"4\n2100 2500 4217 2700",
"20\n800 810 820 830 840 850 860 870 880 890 900 1771 920 930 940 950 960 970 980 990",
"5\n1100 3348 2800 3200 3200",
"20\n800 810 820 830 840 850 860 870 880 890 900 1771 920 930 120 950 960 970 980 990",
"5\n1101 3348 2955 3200 2889",
"5\n1101 3348 2302 3200 2889",
"4\n2100 4691 248 409",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 950 960 970 980 990",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 2243 960 970 980 990",
"20\n800 2108 443 830 840 1093 116 614 398 92 399 1139 1229 646 92 2243 960 970 1914 990",
"20\n800 990 78 2271 36 2722 116 68 620 99 118 1335 454 486 157 1328 82 1387 1914 573",
"20\n975 990 000 2271 28 3273 196 38 68 22 118 1335 875 971 3 1328 65 1173 1914 573",
"20\n975 290 000 3026 28 3273 372 38 48 22 255 1335 875 1250 3 2010 79 1173 1914 573",
"20\n975 147 000 4828 55 3273 372 38 48 22 255 754 875 1250 3 2010 79 1173 1914 890",
"20\n975 147 000 4828 55 3273 372 38 9 22 255 754 875 1703 3 2010 79 1173 1914 890",
"4\n3422 2500 2700 2700",
"20\n800 2054 820 830 840 850 116 433 398 259 399 1139 920 1007 92 2243 960 970 3670 990",
"20\n975 990 000 290 28 3273 196 38 68 22 118 1335 875 971 3 1328 65 1173 1914 573",
"20\n1304 147 010 4828 55 3273 372 3 9 22 255 754 875 3080 0 2010 79 512 1914 427",
"4\n2100 3371 4217 2127",
"20\n975 990 000 2271 28 3273 372 53 68 22 118 1335 875 1250 3 3842 79 1173 3241 573",
"20\n975 147 000 4828 55 3273 372 6 9 22 255 163 875 44 3 2010 79 1173 1914 356",
"5\n1111 1141 830 1005 946",
"4\n2100 2500 4217 2612",
"5\n1100 3348 2800 3200 5007",
"4\n2100 2500 248 2612",
"20\n800 810 820 830 840 850 860 870 880 890 900 1771 920 1028 120 950 960 970 980 990",
"5\n1100 3348 2955 3200 5007",
"4\n2100 2500 248 2218",
"20\n800 810 820 830 840 850 860 870 880 890 900 1303 920 1028 120 950 960 970 980 990",
"5\n1101 3348 2955 3200 5007",
"4\n2100 4691 248 2218",
"20\n800 810 820 830 840 850 860 870 880 890 900 1303 920 1028 92 950 960 970 980 990",
"4\n2100 4691 248 3862",
"20\n800 810 820 830 840 850 860 870 1213 890 900 1303 920 1028 92 950 960 970 980 990",
"20\n800 1586 820 830 840 850 860 870 1213 890 900 1303 920 1028 92 950 960 970 980 990",
"5\n1101 3348 2302 1173 2889",
"4\n2100 3230 248 409",
"20\n800 1586 820 830 840 850 860 870 1213 259 900 1303 920 1028 92 950 960 970 980 990",
"5\n1001 3348 2302 1173 2889",
"4\n2100 3230 248 21",
"5\n1001 3348 2302 2089 2889",
"4\n2100 3230 248 26",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1303 920 1028 92 1189 960 970 980 990",
"5\n1001 831 2302 2089 2889",
"4\n2100 3992 248 26",
"5\n1011 831 2302 2089 2889",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1138 920 1028 92 2243 960 970 980 990",
"5\n1011 1444 2302 2089 2889",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1138 920 1052 92 2243 960 970 980 990",
"5\n1010 1444 2302 2089 2889",
"20\n800 1586 820 830 840 850 860 433 1213 259 900 1139 920 1052 92 2243 960 970 980 990",
"5\n1011 1444 2302 2089 2555",
"20\n800 1586 820 830 840 850 384 433 1213 259 900 1139 920 1052 92 2243 960 970 980 990",
"5\n0011 1444 2302 2089 2555",
"20\n800 1586 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 980 990",
"5\n0011 1444 2302 2089 1070",
"20\n800 2054 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 980 990",
"5\n0011 1444 2302 2089 344",
"20\n800 2054 820 830 840 850 384 433 1213 259 900 1139 920 1007 92 2243 960 970 1357 990",
"5\n0001 1444 2302 2089 344",
"20\n800 2054 820 830 840 850 384 433 398 259 900 1139 920 1007 92 2243 960 970 1357 990",
"5\n0001 1444 2302 2089 194",
"20\n800 2054 820 830 840 850 116 433 398 259 900 1139 920 1007 92 2243 960 970 1357 990",
"5\n0001 1444 2302 1373 194",
"20\n800 2054 820 830 840 850 116 433 398 259 900 1139 920 1007 92 2243 960 970 1914 990",
"5\n0001 2597 2302 1373 194",
"20\n800 2054 820 830 840 850 116 433 398 259 399 1139 920 1007 92 2243 960 970 1914 990",
"5\n0001 2597 2302 1585 194",
"20\n800 2054 820 830 840 850 116 433 398 92 399 1139 920 1007 92 2243 960 970 1914 990",
"5\n0001 2396 2302 1585 194",
"20\n800 2054 820 830 840 850 116 614 398 92 399 1139 920 1007 92 2243 960 970 1914 990",
"5\n0001 2396 1904 1585 194",
"20\n800 2054 820 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990",
"5\n0001 3918 1904 1585 194",
"20\n800 2108 820 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990",
"5\n0001 3918 1904 1005 194",
"20\n800 2108 443 830 840 850 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990",
"5\n0001 3918 2121 1005 194",
"20\n800 2108 443 830 840 1093 116 614 398 92 399 1139 920 646 92 2243 960 970 1914 990",
"5\n0001 3918 3916 1005 194",
"20\n800 2108 443 830 840 1093 116 614 398 92 399 1139 768 646 92 2243 960 970 1914 990",
"5\n0001 2696 3916 1005 194",
"5\n0101 2696 3916 1005 194",
"20\n800 2108 443 830 840 1093 116 614 398 92 399 1139 1229 646 92 2243 96 970 1914 990",
"5\n0101 2696 3916 1005 379",
"20\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 96 970 1914 990",
"5\n1101 2696 3916 1005 379",
"20\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 174 970 1914 990",
"5\n1101 1141 3916 1005 379",
"20\n800 2108 443 830 840 1093 116 614 311 92 399 1139 1229 646 92 2243 174 857 1914 990",
"5\n1111 1141 3916 1005 379",
"20\n800 2108 443 830 840 1093 116 614 620 92 399 1139 1229 646 92 2243 174 857 1914 990",
"5\n1111 1141 3916 1005 185",
"20\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 857 1914 990",
"20\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 1254 1914 990",
"20\n800 2108 443 830 840 2012 116 614 620 92 399 1139 1229 646 92 2243 174 1254 1914 625",
"20\n800 2108 443 830 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 625",
"20\n800 2108 443 1329 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 625",
"20\n800 2108 443 1329 840 2012 116 614 620 92 65 1139 1229 646 92 2243 174 1254 1914 573"
],
"output": [
"2 2",
"1 1",
"3 5",
"2 3\n",
"2 2\n",
"2 5\n",
"3 3\n",
"2 4\n",
"3 5\n",
"3 4\n",
"4 4\n",
"5 5\n",
"6 6\n",
"7 7\n",
"6 7\n",
"7 8\n",
"6 8\n",
"5 7\n",
"1 2\n",
"4 5\n",
"5 6\n",
"7 9\n",
"1 3\n",
"5 8\n",
"4 6\n",
"1 1\n",
"2 3\n",
"2 5\n",
"3 3\n",
"3 3\n",
"2 5\n",
"3 3\n",
"3 3\n",
"2 5\n",
"2 3\n",
"3 3\n",
"2 4\n",
"3 3\n",
"3 3\n",
"3 4\n",
"3 4\n",
"3 3\n",
"3 4\n",
"2 3\n",
"3 4\n",
"2 3\n",
"4 4\n",
"3 3\n",
"2 3\n",
"3 3\n",
"5 5\n",
"4 4\n",
"5 5\n",
"4 4\n",
"5 5\n",
"4 4\n",
"5 5\n",
"4 4\n",
"5 5\n",
"4 4\n",
"5 5\n",
"3 3\n",
"5 5\n",
"3 3\n",
"5 5\n",
"3 3\n",
"5 5\n",
"3 3\n",
"5 5\n",
"4 4\n",
"5 5\n",
"4 4\n",
"5 5\n",
"3 3\n",
"5 5\n",
"4 4\n",
"5 5\n",
"3 4\n",
"5 5\n",
"3 4\n",
"5 5\n",
"3 4\n",
"5 5\n",
"2 4\n",
"5 5\n",
"3 4\n",
"3 4\n",
"6 6\n",
"3 4\n",
"6 6\n",
"3 4\n",
"6 6\n",
"2 3\n",
"6 6\n",
"2 3\n",
"6 6\n",
"2 3\n",
"6 6\n",
"6 6\n",
"6 6\n",
"6 6\n",
"6 6\n",
"6 6\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:
* Rating 1-399 : gray
* Rating 400-799 : brown
* Rating 800-1199 : green
* Rating 1200-1599 : cyan
* Rating 1600-1999 : blue
* Rating 2000-2399 : yellow
* Rating 2400-2799 : orange
* Rating 2800-3199 : red
Other than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.
Currently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.
Find the minimum and maximum possible numbers of different colors of the users.
Constraints
* 1 ≤ N ≤ 100
* 1 ≤ a_i ≤ 4800
* a_i is an integer.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.
Examples
Input
4
2100 2500 2700 2700
Output
2 2
Input
5
1100 1900 2800 3200 3200
Output
3 5
Input
20
800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990
Output
1 1
### Input:
4
2100 2500 2700 2700
### Output:
2 2
### Input:
20
800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990
### Output:
1 1
### Code:
n,a=open(0)
s=set();x=0
for i in map(int,a.split()):
j=i//400
if j<8:s.add(j)
else:x+=1
print(max(1,len(s)),len(s)+x) |
p03850 AtCoder Regular Contest 066 - Addition and Subtraction Hard_3256 | Joisino has a formula consisting of N terms: A_1 op_1 A_2 ... op_{N-1} A_N. Here, A_i is an integer, and op_i is an binary operator either `+` or `-`. Because Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula. Opening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer. It is allowed to insert any number of parentheses at a position. Your task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.
Constraints
* 1≦N≦10^5
* 1≦A_i≦10^9
* op_i is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
N
A_1 op_1 A_2 ... op_{N-1} A_N
Output
Print the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.
Examples
Input
3
5 - 1 - 3
Output
7
Input
5
1 - 2 + 3 - 4 + 5
Output
5
Input
5
1 - 20 - 13 + 14 - 5
Output
13 | #!/usr/bin/env python3
def solve(n):
s = input()
sum_a = 0
sum_n = 0
sum_np = 0
min_sum_np = 10 ** 15
j = s.find('-')
if j < 0:
return sum(list(map(int, s.split(' + '))))
sum_a = sum(list(map(int, s[:j - 1].split(' + '))))
j += 2
s += ' '
len_s = len(s)
sign = -1
w = ''
while j < len_s:
ch = s[j]
j += 1
if ch == ' ':
if len(w):
a = int(w)
sum_a += a
w = ''
if sign < 0:
sum_n += a
sum_np = 0
else:
sum_np += a
elif ch == '+':
sign = 1
elif ch == '-':
min_sum_np = min(min_sum_np, sum_n + sum_np)
sign = -1
else:
w += ch
min_sum_np = min(min_sum_np, sum_n + sum_np)
return sum_a - 2 * min_sum_np
def main():
n = input()
n = int(n)
print(solve(n))
if __name__ == '__main__':
main()
| {
"input": [
"5\n1 - 2 + 3 - 4 + 5",
"3\n5 - 1 - 3",
"5\n1 - 20 - 13 + 14 - 5",
"5\n1 - 2 + 2 - 4 + 5",
"5\n1 - 38 - 13 + 14 - 5",
"5\n1 - 45 - 13 + 14 - 5",
"5\n2 - 45 - 13 + 14 - 5",
"5\n2 - 80 - 13 + 14 - 5",
"5\n2 - 57 - 13 + 14 - 5",
"5\n2 - 39 - 13 + 9 - 5",
"5\n1 - 2 + 0 - 4 + 5",
"5\n1 - 6 - 13 + 14 - 5",
"5\n2 - 45 - 7 + 14 - 5",
"5\n2 - 119 - 13 + 14 - 5",
"5\n2 - 39 - 14 + 14 - 5",
"5\n2 - 15 - 13 + 9 - 4",
"5\n1 - 9 - 6 + 14 - 5",
"5\n1 - 2 + 1 - 4 + 5",
"5\n1 - 6 - 13 + 14 - 4",
"5\n2 - 119 - 13 + 19 - 5",
"5\n2 - 39 - 14 + 14 - 9",
"5\n1 - 6 - 13 + 4 - 4",
"5\n1 - 119 - 13 + 19 - 5",
"5\n1 - 6 - 13 + 4 - 6",
"5\n1 - 119 - 13 + 19 - 9",
"5\n2 - 39 - 14 + 3 - 4",
"5\n1 - 6 - 13 + 6 - 6",
"5\n2 - 39 - 19 + 5 - 4",
"3\n5 - 1 - 6",
"5\n1 - 20 - 22 + 14 - 5",
"5\n1 - 2 + 2 - 7 + 5",
"5\n1 - 38 - 10 + 14 - 5",
"5\n0 - 45 - 13 + 14 - 5",
"5\n2 - 49 - 13 + 14 - 5",
"5\n2 - 80 - 13 + 21 - 5",
"5\n1 - 119 - 13 + 14 - 5",
"5\n4 - 39 - 14 + 14 - 5",
"5\n3 - 15 - 13 + 9 - 4",
"5\n1 - 4 + 1 - 4 + 5",
"5\n1 - 6 - 24 + 14 - 4",
"5\n1 - 119 - 13 + 2 - 5",
"5\n1 - 6 - 13 + 5 - 6",
"5\n1 - 119 - 13 + 1 - 9",
"5\n1 - 6 - 13 + 9 - 6",
"3\n5 - 1 - 8",
"5\n0 - 45 - 13 + 14 - 0",
"5\n2 - 159 - 13 + 21 - 5",
"5\n1 - 119 - 8 + 14 - 5",
"5\n0 - 4 + 1 - 4 + 5",
"5\n2 - 119 - 9 + 19 - 5",
"5\n1 - 119 - 13 + 4 - 5",
"5\n1 - 6 - 13 + 18 - 6",
"3\n4 - 1 - 8",
"5\n1 - 38 - 1 + 14 - 3",
"5\n0 - 45 - 6 + 14 - 0",
"5\n0 - 49 - 13 + 24 - 5",
"5\n0 - 6 - 13 + 18 - 6",
"5\n0 - 45 - 0 + 14 - 0",
"5\n0 - 49 - 6 + 24 - 5",
"5\n2 - 119 - 13 + 6 - 5",
"5\n1 - 5 - 13 + 18 - 6",
"5\n0 - 45 - 0 + 3 - 0",
"5\n1 - 2 + 3 - 4 + 3",
"5\n0 - 38 - 13 + 14 - 5",
"5\n1 - 20 - 6 + 14 - 1",
"5\n2 - 80 - 7 + 14 - 5",
"5\n2 - 119 - 13 + 9 - 5",
"5\n2 - 119 - 13 + 30 - 5",
"5\n1 - 119 - 1 + 19 - 9",
"5\n2 - 39 - 6 + 3 - 4",
"5\n1 - 83 - 13 + 14 - 5",
"5\n2 - 57 - 13 + 17 - 5",
"5\n1 - 6 - 24 + 14 - 6",
"5\n2 - 119 - 8 + 19 - 3",
"5\n1 - 6 - 13 + 14 - 6",
"5\n2 - 159 - 9 + 21 - 5",
"5\n2 - 171 - 9 + 19 - 5",
"5\n1 - 3 - 13 + 18 - 6",
"5\n1 - 5 - 13 + 18 - 11",
"5\n2 - 80 - 1 + 14 - 5",
"5\n2 - 167 - 13 + 9 - 5",
"5\n3 - 119 - 13 + 30 - 5",
"5\n2 - 78 - 28 + 14 - 4",
"5\n1 - 119 - 2 + 19 - 9",
"5\n2 - 6 - 23 + 5 - 6",
"5\n1 - 90 - 13 + 14 - 5",
"5\n0 - 39 - 13 + 0 - 4",
"5\n1 - 6 - 24 + 22 - 6",
"5\n2 - 49 - 13 + 39 - 10",
"5\n1 - 3 - 20 + 18 - 6",
"5\n2 - 73 - 1 + 14 - 3",
"5\n0 - 81 - 13 + 24 - 1",
"5\n2 - 119 - 9 + 11 - 5",
"5\n0 - 6 - 21 + 32 - 6",
"5\n2 - 131 - 1 + 14 - 5",
"5\n1 - 167 - 13 + 9 - 5",
"5\n2 - 78 - 14 + 14 - 4",
"5\n2 - 54 - 6 + 3 - 2",
"5\n1 - 157 - 13 + 14 - 5",
"5\n0 - 76 - 13 + 0 - 4",
"5\n1 - 3 - 20 + 18 - 10",
"5\n0 - 81 - 11 + 24 - 1",
"5\n0 - 6 - 17 + 32 - 6"
],
"output": [
"5",
"7",
"13",
"6\n",
"-5\n",
"-12\n",
"-11\n",
"-46\n",
"-23\n",
"-10\n",
"8\n",
"27\n",
"-17\n",
"-85\n",
"-4\n",
"13\n",
"17\n",
"7\n",
"26\n",
"-80\n",
"0\n",
"16\n",
"-81\n",
"18\n",
"-77\n",
"-16\n",
"20\n",
"-9\n",
"10\n",
"22\n",
"9\n",
"-8\n",
"-13\n",
"-15\n",
"-39\n",
"-86\n",
"-2\n",
"14\n",
"5\n",
"37\n",
"-98\n",
"19\n",
"-95\n",
"23\n",
"12\n",
"-18\n",
"-118\n",
"-91\n",
"4\n",
"-84\n",
"-96\n",
"32\n",
"11\n",
"-19\n",
"-25\n",
"-7\n",
"31\n",
"-31\n",
"-14\n",
"-93\n",
"33\n",
"-42\n",
"3\n",
"-6\n",
"2\n",
"-52\n",
"-90\n",
"-69\n",
"-89\n",
"-24\n",
"-50\n",
"-20\n",
"39\n",
"-87\n",
"28\n",
"-122\n",
"-136\n",
"35\n",
"38\n",
"-58\n",
"-138\n",
"-68\n",
"-30\n",
"-88\n",
"30\n",
"-57\n",
"-22\n",
"47\n",
"15\n",
"42\n",
"-53\n",
"-43\n",
"-92\n",
"53\n",
"-109\n",
"-139\n",
"-44\n",
"-41\n",
"-124\n",
"-59\n",
"46\n",
"-45\n",
"49\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Joisino has a formula consisting of N terms: A_1 op_1 A_2 ... op_{N-1} A_N. Here, A_i is an integer, and op_i is an binary operator either `+` or `-`. Because Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula. Opening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer. It is allowed to insert any number of parentheses at a position. Your task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.
Constraints
* 1≦N≦10^5
* 1≦A_i≦10^9
* op_i is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
N
A_1 op_1 A_2 ... op_{N-1} A_N
Output
Print the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.
Examples
Input
3
5 - 1 - 3
Output
7
Input
5
1 - 2 + 3 - 4 + 5
Output
5
Input
5
1 - 20 - 13 + 14 - 5
Output
13
### Input:
5
1 - 2 + 3 - 4 + 5
### Output:
5
### Input:
3
5 - 1 - 3
### Output:
7
### Code:
#!/usr/bin/env python3
def solve(n):
s = input()
sum_a = 0
sum_n = 0
sum_np = 0
min_sum_np = 10 ** 15
j = s.find('-')
if j < 0:
return sum(list(map(int, s.split(' + '))))
sum_a = sum(list(map(int, s[:j - 1].split(' + '))))
j += 2
s += ' '
len_s = len(s)
sign = -1
w = ''
while j < len_s:
ch = s[j]
j += 1
if ch == ' ':
if len(w):
a = int(w)
sum_a += a
w = ''
if sign < 0:
sum_n += a
sum_np = 0
else:
sum_np += a
elif ch == '+':
sign = 1
elif ch == '-':
min_sum_np = min(min_sum_np, sum_n + sum_np)
sign = -1
else:
w += ch
min_sum_np = min(min_sum_np, sum_n + sum_np)
return sum_a - 2 * min_sum_np
def main():
n = input()
n = int(n)
print(solve(n))
if __name__ == '__main__':
main()
|
p04017 AtCoder Regular Contest 060 - Tak and Hotels_3260 | N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.
Tak the traveler has the following two personal principles:
* He never travels a distance of more than L in a single day.
* He never sleeps in the open. That is, he must stay at a hotel at the end of a day.
You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j. For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles. It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq L \leq 10^9
* 1 \leq Q \leq 10^5
* 1 \leq x_i < x_2 < ... < x_N \leq 10^9
* x_{i+1} - x_i \leq L
* 1 \leq a_j,b_j \leq N
* a_j \neq b_j
* N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q
Output
Print Q lines. The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.
Example
Input
9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5
Output
4
2
1
2 | import bisect
N = int(input())
x = list(map(int, input().split()))
L = int(input())
dest = []
dest_1 = [0] * N
for i in range(N):
dest_1[i] = bisect.bisect_left(x, x[i] + L + 0.5) - 1
dest.append(dest_1)
for i in range(1, len(bin(N - 1)) - 1):
dest_prev = dest[i - 1]
dest_i = [0] * N
for j in range(N):
dest_i[j] = dest_prev[dest_prev[j]]
dest.append(dest_i)
Q = int(input())
for _ in range(Q):
a, b = map(int, input().split())
a -= 1
b -= 1
if a > b:
a, b = b, a
k = len(dest) - 1
ans = 0
while True:
d = dest[k][a]
if d >= b:
if k > 0:
k -= 1
else:
ans += 1
break
else:
ans += 2 ** k
a = d
print(ans)
| {
"input": [
"9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 5",
"9\n1 3 6 13 15 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 5",
"9\n1 6 6 13 23 18 19 29 31\n10\n3\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 5\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 9\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 8\n1 3\n9 7\n8 7",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n8 7",
"9\n1 6 6 13 23 18 27 29 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 31\n10\n3\n1 9\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 58\n10\n2\n1 2\n7 5\n6 7\n8 5",
"9\n1 7 6 13 23 18 19 29 31\n18\n3\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 3\n1 5\n9 7\n8 1",
"9\n1 3 6 13 15 13 19 29 31\n10\n2\n2 8\n9 3\n1 7\n8 5",
"9\n1 3 6 13 15 18 19 29 40\n10\n3\n1 6\n7 3\n6 3\n8 5",
"9\n1 3 6 13 15 18 19 29 40\n10\n3\n2 6\n7 3\n6 3\n8 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n2\n1 9\n7 6\n6 7\n8 5",
"9\n1 3 6 13 15 18 19 29 31\n10\n4\n1 8\n7 3\n6 7\n8 3",
"9\n1 3 5 15 23 18 19 29 31\n10\n1\n1 8\n7 3\n9 7\n8 5",
"9\n1 7 6 13 23 18 19 29 31\n10\n3\n1 8\n7 3\n6 1\n8 10",
"9\n1 8 6 13 23 18 19 22 31\n10\n3\n1 8\n7 3\n6 7\n5 10",
"9\n1 1 6 13 15 13 19 29 31\n10\n2\n2 8\n9 3\n1 7\n8 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n1\n1 9\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n17\n2\n1 8\n1 3\n2 7\n8 7",
"9\n0 3 1 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n6 7",
"9\n1 7 6 13 23 18 19 29 31\n10\n3\n2 8\n7 3\n6 1\n8 10",
"9\n1 7 6 13 23 18 19 29 31\n18\n3\n1 2\n1 3\n6 7\n8 10",
"9\n1 6 6 24 15 15 19 29 31\n10\n2\n2 8\n8 3\n1 2\n5 5",
"9\n1 6 6 24 7 15 19 29 31\n10\n3\n2 8\n8 3\n1 2\n5 5",
"9\n1 3 6 13 23 18 19 29 31\n12\n4\n1 8\n1 5\n9 7\n8 7",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 4\n7 3\n1 2\n5 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n3\n1 9\n2 3\n6 7\n8 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n4\n1 9\n7 6\n6 7\n8 5",
"9\n1 3 10 13 15 18 19 29 40\n10\n3\n2 6\n7 2\n6 3\n8 5",
"9\n1 3 6 13 15 18 19 29 31\n10\n3\n1 8\n7 5\n6 7\n8 3",
"9\n1 4 6 20 15 18 22 60 40\n10\n1\n1 6\n5 4\n6 4\n1 1",
"9\n2 5 6 13 23 34 29 39 48\n18\n3\n1 2\n2 6\n6 7\n1 10",
"9\n0 3 4 13 5 18 17 27 55\n21\n1\n1 4\n1 8\n9 4\n22 10",
"9\n1 3 6 13 15 15 19 29 31\n10\n1\n1 4\n7 3\n1 2\n5 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n4\n1 9\n7 6\n6 7\n8 1",
"9\n1 3 4 13 7 18 36 29 55\n12\n2\n1 6\n1 7\n9 4\n15 11",
"9\n1 2 7 13 14 23 19 29 31\n10\n4\n1 8\n7 3\n3 7\n8 5",
"9\n2 5 6 13 23 18 27 29 31\n18\n3\n1 2\n2 5\n2 7\n1 10",
"9\n1 3 6 13 23 19 19 29 31\n16\n3\n1 9\n7 6\n6 7\n8 1",
"9\n1 3 6 13 23 18 23 31 31\n10\n3\n1 9\n6 1\n6 7\n22 11",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n9 7\n8 5",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 15 23 18 19 29 31\n10\n2\n1 8\n7 3\n9 7\n8 5",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n1 7\n8 5",
"9\n1 6 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 5 15 23 18 19 29 31\n10\n2\n1 8\n7 3\n9 7\n8 5",
"9\n1 3 7 13 15 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n9 7\n8 7",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n2 7\n8 5",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n1 2\n8 5",
"9\n1 8 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 58\n10\n2\n1 8\n7 5\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n1 3\n9 7\n8 7",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 9\n7 2\n6 7\n8 10",
"9\n1 8 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n14 10",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 9\n7 2\n6 7\n16 10",
"9\n1 8 6 13 23 18 19 29 42\n10\n2\n1 8\n7 3\n6 7\n14 10",
"9\n1 3 6 13 23 18 19 29 30\n10\n2\n1 9\n7 2\n6 7\n16 10",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n6 7",
"9\n1 3 4 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n6 7",
"9\n1 3 6 13 15 18 19 29 31\n10\n2\n1 6\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n2 7\n8 5",
"9\n1 3 6 13 15 13 19 29 31\n10\n2\n1 8\n7 3\n1 7\n8 5",
"9\n1 7 6 13 23 18 19 29 31\n10\n3\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 7 13 15 18 19 29 31\n10\n2\n1 8\n7 3\n3 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 5\n6 11\n8 5",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n1 2\n5 5",
"9\n1 8 6 13 23 18 19 22 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 9\n7 2\n10 7\n8 10",
"9\n1 3 6 13 13 18 19 29 31\n10\n2\n1 9\n7 2\n6 7\n16 10",
"9\n1 8 6 13 23 18 19 29 42\n10\n2\n1 8\n7 3\n0 7\n14 10",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n8 1",
"9\n1 3 6 13 23 18 19 29 31\n12\n2\n1 8\n2 5\n9 7\n6 7",
"9\n1 3 4 13 23 18 19 29 31\n12\n2\n1 8\n1 5\n9 7\n8 7",
"9\n1 3 6 13 15 18 19 29 40\n10\n2\n1 6\n7 3\n6 7\n8 5",
"9\n1 3 6 13 15 13 19 29 31\n10\n2\n2 8\n7 3\n1 7\n8 5",
"9\n1 6 6 13 23 18 27 29 31\n10\n2\n1 8\n7 3\n6 7\n8 19",
"9\n1 3 6 13 23 19 19 29 31\n10\n3\n1 9\n7 3\n6 7\n8 10",
"9\n1 8 6 13 23 18 19 22 31\n10\n2\n1 8\n7 3\n6 7\n5 10",
"9\n1 3 0 13 23 18 19 29 58\n10\n2\n1 2\n7 5\n6 7\n8 5",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 9\n7 2\n10 2\n8 10",
"9\n1 3 6 13 13 18 19 29 31\n10\n2\n1 9\n7 2\n12 7\n16 10",
"9\n1 8 6 13 23 18 19 29 42\n10\n2\n1 8\n7 3\n0 2\n14 10",
"9\n1 3 6 13 15 18 19 29 40\n10\n2\n1 6\n7 3\n6 3\n8 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n3\n1 9\n7 3\n6 7\n8 5",
"9\n1 3 6 13 23 19 19 29 31\n10\n2\n1 9\n7 3\n6 7\n8 5",
"9\n1 3 10 13 15 18 19 29 40\n10\n3\n2 6\n7 3\n6 3\n8 5",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n6 10\n8 5",
"9\n2 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 7\n8 10",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n7 3\n1 7\n8 1",
"9\n1 3 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n9 10\n8 7",
"9\n1 3 6 13 15 15 19 29 31\n10\n2\n1 8\n4 3\n2 7\n8 5",
"9\n1 3 6 6 15 15 19 29 31\n10\n2\n1 8\n7 3\n1 2\n8 5",
"9\n1 8 6 13 23 18 19 29 31\n10\n2\n1 8\n7 3\n6 14\n8 10",
"9\n1 1 6 13 23 18 19 29 31\n10\n2\n1 8\n1 3\n9 7\n8 7"
],
"output": [
"4\n2\n1\n2",
"4\n2\n",
"4\n2\n1\n",
"4\n1\n",
"5\n2\n",
"3\n1\n",
"3\n2\n",
"5\n3\n",
"5\n2\n1\n",
"1\n1\n",
"2\n1\n1\n",
"1\n2\n",
"3\n4\n",
"3\n2\n2\n",
"2\n2\n2\n",
"5\n1\n",
"4\n2\n1\n3\n",
"4\n",
"4\n2\n3\n",
"3\n2\n1\n",
"4\n4\n",
"5\n",
"2\n1\n",
"4\n3\n",
"3\n2\n3\n",
"1\n1\n1\n",
"3\n3\n",
"3\n3\n1\n",
"3\n2\n1\n1\n",
"2\n2\n",
"5\n1\n1\n",
"5\n1\n1\n1\n",
"2\n2\n1\n",
"4\n1\n1\n",
"3\n",
"1\n2\n1\n",
"1\n",
"2\n",
"5\n1\n1\n4\n",
"2\n3\n",
"4\n2\n2\n2\n",
"1\n1\n2\n",
"3\n1\n1\n",
"4\n3\n1\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n1\n",
"4\n1\n",
"5\n2\n",
"4\n2\n",
"5\n2\n",
"4\n2\n",
"5\n2\n",
"3\n2\n",
"3\n2\n",
"3\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n1\n",
"4\n2\n",
"4\n1\n",
"4\n2\n",
"3\n2\n",
"5\n2\n",
"5\n2\n",
"4\n2\n",
"3\n2\n",
"3\n2\n",
"3\n2\n",
"3\n2\n",
"3\n2\n",
"5\n3\n",
"5\n2\n1\n",
"3\n2\n",
"1\n1\n",
"5\n2\n",
"5\n2\n",
"4\n2\n",
"3\n2\n",
"5\n2\n1\n",
"5\n2\n",
"2\n1\n1\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n2\n",
"4\n1\n",
"4\n2\n",
"4\n2\n",
"4\n1\n"
]
} | 5ATCODER
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.
Tak the traveler has the following two personal principles:
* He never travels a distance of more than L in a single day.
* He never sleeps in the open. That is, he must stay at a hotel at the end of a day.
You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j. For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles. It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.
Constraints
* 2 \leq N \leq 10^5
* 1 \leq L \leq 10^9
* 1 \leq Q \leq 10^5
* 1 \leq x_i < x_2 < ... < x_N \leq 10^9
* x_{i+1} - x_i \leq L
* 1 \leq a_j,b_j \leq N
* a_j \neq b_j
* N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q
Output
Print Q lines. The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.
Example
Input
9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5
Output
4
2
1
2
### Input:
9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5
### Output:
4
2
1
2
### Input:
9
1 3 6 13 15 18 19 29 31
10
2
1 8
7 3
6 7
8 5
### Output:
4
2
### Code:
import bisect
N = int(input())
x = list(map(int, input().split()))
L = int(input())
dest = []
dest_1 = [0] * N
for i in range(N):
dest_1[i] = bisect.bisect_left(x, x[i] + L + 0.5) - 1
dest.append(dest_1)
for i in range(1, len(bin(N - 1)) - 1):
dest_prev = dest[i - 1]
dest_i = [0] * N
for j in range(N):
dest_i[j] = dest_prev[dest_prev[j]]
dest.append(dest_i)
Q = int(input())
for _ in range(Q):
a, b = map(int, input().split())
a -= 1
b -= 1
if a > b:
a, b = b, a
k = len(dest) - 1
ans = 0
while True:
d = dest[k][a]
if d >= b:
if k > 0:
k -= 1
else:
ans += 1
break
else:
ans += 2 ** k
a = d
print(ans)
|
p00101 Aizu PR_3264 | An English booklet has been created for publicizing Aizu to the world. When you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says "Hoshino" not "Hoshina".
Your task is to write a program which replace all the words "Hoshino" with "Hoshina". You can assume that the number of characters in a text is less than or equal to 1000.
Input
The input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.
Output
For each dataset, print the converted texts in a line.
Example
Input
3
Hoshino
Hashino
Masayuki Hoshino was the grandson of Ieyasu Tokugawa.
Output
Hoshina
Hashino
Masayuki Hoshina was the grandson of Ieyasu Tokugawa. | [print(input().replace("Hoshino","Hoshina")) for i in range(int(input()))]
| {
"input": [
"3\nHoshino\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.",
"3\nHoshimo\nHashino\nMasayuki Hoshino was the grandson of Ieyasu Tokugawa.",
"3\nHoshimo\nHashino\nMasayuki Hoshino was the grandspn of Ieyasu Tokugawa.",
"3\nHoshimo\nHashino\nMasayuki Hoshino was the grandspn of ueyasI Tokugawa.",
"3\nHoshimo\nHashino\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.",
"3\nHoshimo\nHashoni\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.",
"3\nHoshimo\nHashoni\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.",
"3\nHmshioo\nHashoni\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.",
"3\nHmshioo\nHashoni\nMasayuki omihsoH was the grandspn of uezasI Tokugawa.",
"3\nHmshioo\nHashoni\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.",
"3\nHmshjoo\nHashoni\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.",
"3\nHmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn of uezasI Tokugawa.",
"3\nHmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn fo uezasI Tokugawa.",
"3\nHmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn fo ufzasI Tokugawa.",
"3\nHmshjoo\nHashoni\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.",
"3\nHmshjoo\ninohsaH\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.",
"3\nHmshjoo\ninohsaH\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.",
"3\nHmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.",
"3\nHmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH Tokugawa.",
"3\nHmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT",
"3\nImshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT",
"3\nImshjoo\nHashoni\nikuy`saM onihsoH taw the grandspn fo ufzasH .awagukoT",
"3\nImshjoo\nHashoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT",
"3\nImshjoo\nhasHoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT",
"3\nImshjoo\nhatHoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT",
"3\nImshjoo\nhatHoni\nikuy`saM onihsoH taw the grandspn fo ufsazG .awagukoT",
"3\nImshjoo\nhatHoni\nMas`yuki onihsoH taw the grandspn fo ufsazG .awagukoT",
"3\nImshjoo\nhatHoni\nMas`yuki onihsoH taw the grandspn fo ufsazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`yuki onohsiH taw the grandspn fo ufsazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`yukj onohsiH taw the grandspn fo ufsazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH taw the grandspn fo ufsazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo ufsazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaguTok",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugok",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugpk",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH vat the grandspn fo uesazG .awaTugpk",
"3\nImshjoo\nhatHoni\nMas`ykuj onohsiH vat eht grandspn fo uesazG .awaTugpk",
"3\nImshjoo\nhatHoni\nMasaykuj onohsiH vat the grandspn fo uesazG .awaTugpk",
"3\nImshjoo\nhatHoni\nMasaykuj onohsiH vat the gr`ndspn fo uesazG .awaTugpk",
"3\nImshjoo\nhatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk",
"3\nImshioo\nhatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk",
"3\nImshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk",
"3\nImshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo ufsazG .awaTugpk",
"3\nImshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspo fo ufsazG .awaTugpk",
"3\nImshioo\niatHoni\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk",
"3\nImsiioo\niatHoni\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk",
"3\nImsiioo\niatHoni\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk",
"3\nImsiino\niatHoni\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk",
"3\nImsiino\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk",
"3\nImsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk",
"3\nImsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTugpk",
"3\nImsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTgupk",
"3\nImsiinp\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fo uftazG .awaTgupk",
"3\nImsiinp\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk",
"3\npniismI\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk",
"3\npniismI\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.",
"3\npniismI\ninoHtai\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.",
"3\nImsiinp\ninoHtai\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.",
"3\nImsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo fn uftazG kpugTawa.",
"3\nImsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo nf uftazG kpugTawa.",
"3\nImsiinp\ninoHtai\njukyasaM onohsiI vta huf gr`ncspo nf uftazG kpugTawa.",
"3\nImsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.",
"3\nImsiinp\ntnoHiai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.",
"3\nImsiinp\ntnoHiai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk",
"3\nImsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk",
"3\nImsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr`ncspo fn uftaGz .awaTgupk",
"3\nImsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn uftaGz .awaTgupk",
"3\nImsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI wta htf gr_ncspo fn ugtaGz .awaTgupk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgupk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgvpk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpk",
"3\npniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpl",
"3\npniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo nf ugtaGz .awaTgvpl",
"3\npniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo nf ugatGz .awaTgvpl",
"3\npniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl",
"3\npniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl",
"3\npniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaTgvpl",
"3\npniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg gr_ncspo me ugatGz .awaSgvpl",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg me ugatGz .awaSgvpl",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpl",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpm",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg nf ugatGz .awaSgvpm",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg fn ugatGz .awaSgvpm",
"3\npniismI\ntioHian\nitkyasaM onohsiI `tw htg ppscn_rg fn ugatGz .awaSgvpm",
"3\npniismI\ntioHian\nitkyasaM onohsiI `uw htg ppscn_rg fn ugatGz .awaSgvpm",
"3\npniismI\ntioHian\nitkyasaM onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohsiI `vw htg ppscn_rg fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohsiI `vw htg gr_ncspp fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohsiI v`w htg gr_ncspp fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz .awaSgvpm",
"3\npniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz mpvgSawa.",
"3\npniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.",
"3\npniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp nf zGtagv mpvgSawa.",
"3\npniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.",
"3\npniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGatgv mpvgSawa.",
"3\npniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp nf zGatgv mpvgSawa."
],
"output": [
"Hoshina\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.",
"Hoshimo\nHashino\nMasayuki Hoshina was the grandson of Ieyasu Tokugawa.\n",
"Hoshimo\nHashino\nMasayuki Hoshina was the grandspn of Ieyasu Tokugawa.\n",
"Hoshimo\nHashino\nMasayuki Hoshina was the grandspn of ueyasI Tokugawa.\n",
"Hoshimo\nHashino\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\n",
"Hoshimo\nHashoni\nMasayuki onihsoH was the grandspn of ueyasI Tokugawa.\n",
"Hoshimo\nHashoni\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\n",
"Hmshioo\nHashoni\nMasayuki omihsoH was the grandspn of ueyasI Tokugawa.\n",
"Hmshioo\nHashoni\nMasayuki omihsoH was the grandspn of uezasI Tokugawa.\n",
"Hmshioo\nHashoni\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\n",
"Hmshjoo\nHashoni\nMasayuki omihsoH saw the grandspn of uezasI Tokugawa.\n",
"Hmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn of uezasI Tokugawa.\n",
"Hmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn fo uezasI Tokugawa.\n",
"Hmshjoo\nHashoni\nMas`yuki omihsoH saw the grandspn fo ufzasI Tokugawa.\n",
"Hmshjoo\nHashoni\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\n",
"Hmshjoo\ninohsaH\nMas`yuki onihsoH saw the grandspn fo ufzasI Tokugawa.\n",
"Hmshjoo\ninohsaH\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\n",
"Hmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasI Tokugawa.\n",
"Hmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH Tokugawa.\n",
"Hmshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\n",
"Imshjoo\nHashoni\nikuy`saM onihsoH saw the grandspn fo ufzasH .awagukoT\n",
"Imshjoo\nHashoni\nikuy`saM onihsoH taw the grandspn fo ufzasH .awagukoT\n",
"Imshjoo\nHashoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\n",
"Imshjoo\nhasHoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\n",
"Imshjoo\nhatHoni\nikuy`saM onihsoH taw the grandspn fo ufsazH .awagukoT\n",
"Imshjoo\nhatHoni\nikuy`saM onihsoH taw the grandspn fo ufsazG .awagukoT\n",
"Imshjoo\nhatHoni\nMas`yuki onihsoH taw the grandspn fo ufsazG .awagukoT\n",
"Imshjoo\nhatHoni\nMas`yuki onihsoH taw the grandspn fo ufsazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`yuki onohsiH taw the grandspn fo ufsazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`yukj onohsiH taw the grandspn fo ufsazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH taw the grandspn fo ufsazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo ufsazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaguTok\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugok\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH tav the grandspn fo uesazG .awaTugpk\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH vat the grandspn fo uesazG .awaTugpk\n",
"Imshjoo\nhatHoni\nMas`ykuj onohsiH vat eht grandspn fo uesazG .awaTugpk\n",
"Imshjoo\nhatHoni\nMasaykuj onohsiH vat the grandspn fo uesazG .awaTugpk\n",
"Imshjoo\nhatHoni\nMasaykuj onohsiH vat the gr`ndspn fo uesazG .awaTugpk\n",
"Imshjoo\nhatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\n",
"Imshioo\nhatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\n",
"Imshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo uesazG .awaTugpk\n",
"Imshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspn fo ufsazG .awaTugpk\n",
"Imshioo\niatHoni\nMasaykuj onohsiH vat thf gr`ndspo fo ufsazG .awaTugpk\n",
"Imshioo\niatHoni\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\n",
"Imsiioo\niatHoni\nMasaykuj onohsiH vat htf gr`ndspo fo ufsazG .awaTugpk\n",
"Imsiioo\niatHoni\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\n",
"Imsiino\niatHoni\nMasaykuj onohsiH vta htf gr`ndspo fo ufsazG .awaTugpk\n",
"Imsiino\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\n",
"Imsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo ufsazG .awaTugpk\n",
"Imsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTugpk\n",
"Imsiinp\niatHoni\nMasaykuj onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\n",
"Imsiinp\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fo uftazG .awaTgupk\n",
"Imsiinp\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\n",
"pniismI\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG .awaTgupk\n",
"pniismI\niatHoni\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\n",
"pniismI\ninoHtai\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\n",
"Imsiinp\ninoHtai\njukyasaM onohsiH vta htf gr`ncspo fn uftazG kpugTawa.\n",
"Imsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo fn uftazG kpugTawa.\n",
"Imsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo nf uftazG kpugTawa.\n",
"Imsiinp\ninoHtai\njukyasaM onohsiI vta huf gr`ncspo nf uftazG kpugTawa.\n",
"Imsiinp\ninoHtai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\n",
"Imsiinp\ntnoHiai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz kpugTawa.\n",
"Imsiinp\ntnoHiai\njukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\n",
"Imsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr`ncspo nf uftaGz .awaTgupk\n",
"Imsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr`ncspo fn uftaGz .awaTgupk\n",
"Imsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn uftaGz .awaTgupk\n",
"Imsiinp\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI vta htf gr_ncspo fn ugtaGz .awaTgupk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI wta htf gr_ncspo fn ugtaGz .awaTgupk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgupk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI wt` htf gr_ncspo fn ugtaGz .awaTgvpk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpk\n",
"pniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo fn ugtaGz .awaTgvpl\n",
"pniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo nf ugtaGz .awaTgvpl\n",
"pniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo nf ugatGz .awaTgvpl\n",
"pniismI\ntnoHiai\niukyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\n",
"pniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo mf ugatGz .awaTgvpl\n",
"pniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaTgvpl\n",
"pniismI\ntnoHiai\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htf gr_ncspo me ugatGz .awaSgvpl\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg gr_ncspo me ugatGz .awaSgvpl\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg me ugatGz .awaSgvpl\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpl\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg ne ugatGz .awaSgvpm\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg nf ugatGz .awaSgvpm\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg opscn_rg fn ugatGz .awaSgvpm\n",
"pniismI\ntioHian\nitkyasaM onohsiI `tw htg ppscn_rg fn ugatGz .awaSgvpm\n",
"pniismI\ntioHian\nitkyasaM onohsiI `uw htg ppscn_rg fn ugatGz .awaSgvpm\n",
"pniismI\ntioHian\nitkyasaM onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohsiI `uw htg ppscn_rg fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohsiI `vw htg ppscn_rg fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohsiI `vw htg gr_ncspp fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohsiI v`w htg gr_ncspp fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz .awaSgvpm\n",
"pniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn vgatGz mpvgSawa.\n",
"pniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\n",
"pniismI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp nf zGtagv mpvgSawa.\n",
"pniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGtagv mpvgSawa.\n",
"pniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp fn zGatgv mpvgSawa.\n",
"pniisnI\ntioHian\nMasaykti onohisI v`w htg gr_ncspp nf zGatgv mpvgSawa.\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
An English booklet has been created for publicizing Aizu to the world. When you read it carefully, you found a misnomer (an error in writing) on the last name of Masayuki Hoshina, the lord of the Aizu domain. The booklet says "Hoshino" not "Hoshina".
Your task is to write a program which replace all the words "Hoshino" with "Hoshina". You can assume that the number of characters in a text is less than or equal to 1000.
Input
The input consists of several datasets. There will be the number of datasets n in the first line. There will be n lines. A line consisting of english texts will be given for each dataset.
Output
For each dataset, print the converted texts in a line.
Example
Input
3
Hoshino
Hashino
Masayuki Hoshino was the grandson of Ieyasu Tokugawa.
Output
Hoshina
Hashino
Masayuki Hoshina was the grandson of Ieyasu Tokugawa.
### Input:
3
Hoshino
Hashino
Masayuki Hoshino was the grandson of Ieyasu Tokugawa.
### Output:
Hoshina
Hashino
Masayuki Hoshina was the grandson of Ieyasu Tokugawa.
### Input:
3
Hoshimo
Hashino
Masayuki Hoshino was the grandson of Ieyasu Tokugawa.
### Output:
Hoshimo
Hashino
Masayuki Hoshina was the grandson of Ieyasu Tokugawa.
### Code:
[print(input().replace("Hoshino","Hoshina")) for i in range(int(input()))]
|
p00234 Aizu Buried Treasure_3267 | Aizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost.
The state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation:
1. A cell filled with soil. There is a fixed cost for each cell to dig.
2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen.
Only left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up.
You must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded.
Create a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output "NA".
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format.
W H
f m o
c1,1 c2,1 ... cW,1
c1,2 c2,2 ... cW,2
...
c1, H c2, H ... cW, H
The horizontal size W of the formation and the vertical size H (3 ≤ W, H ≤ 10) are given in the first line. The second line is the integer f (1 ≤ f ≤ 10000) that represents your excavation cost, the integer m (3 ≤ m ≤ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≤ m) is given.
The following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format:
If the value is negative, the cell is full of soil and the value represents the cost.
If the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen.
However, there are no more than 50 cells in which oxygen has accumulated.
The number of datasets does not exceed 50.
Output
Print the minimum cost or NA on one line for each dataset.
Example
Input
3 3
100 10 10
-100 -20 -100
-100 -20 -100
-100 -20 -100
3 3
100 10 10
-100 -20 -100
-100 -20 -20
-100 -60 -20
3 3
100 10 3
-100 -20 -100
-20 -20 -20
-20 -100 -20
3 3
100 3 3
-100 -20 -30
-100 -20 2
-100 -20 -20
4 5
1500 5 4
-10 -380 -250 -250
-90 2 -80 8
-250 -130 -330 -120
-120 -40 -50 -20
-250 -10 -20 -150
0 0
Output
60
80
NA
50
390 | import sys
sys.setrecursionlimit(1000000)
INF = 10 ** 20
def update_state(state, newx):
tmp = list(state)
tmp[newx] = 1
return tuple(tmp)
def get_co(x, y):
dc = do = 0
score = mp[y][x]
if score < 0:
dc = -score
else:
do = score
return dc, do
def minimum_cost(x, y, state, ox, goal, dic, w, m):
if (x, y, state, ox) in dic:
return dic[(x, y, state, ox)]
if y == goal:
return 0
if ox <= 1:
return INF
ret = INF
if x >= 1:
if state[x - 1] == 0:
dc, do = get_co(x - 1, y)
ret = min(ret, minimum_cost(x - 1, y, update_state(state, x - 1), min(ox + do - 1, m), goal, dic, w, m) + dc)
else:
ret = min(ret, minimum_cost(x - 1, y, state, ox - 1, goal, dic, w, m))
if x < w - 1:
if state[x + 1] == 0:
dc, do = get_co(x + 1, y)
ret = min(ret, minimum_cost(x + 1, y, update_state(state, x + 1), min(ox + do - 1, m), goal, dic, w, m) + dc)
else:
ret = min(ret, minimum_cost(x + 1, y, state, ox - 1, goal, dic, w, m))
dc, do = get_co(x, y + 1)
ret = min(ret, minimum_cost(x, y + 1, tuple((1 if i == x else 0 for i in range(w))), min(ox + do - 1, m), goal, dic, w, m) + dc)
dic[(x, y, state, ox)] = ret
return ret
while True:
w, h = map(int, input().split())
if w == 0:
break
f, m, o = map(int, input().split())
mp = [list(map(int, input().split())) for _ in range(h)]
if o <= 1:
print("NA")
continue
dic = {}
ans = INF
for i in range(w):
dc, do = get_co(i, 0)
state = tuple(1 if i == j else 0 for j in range(w))
ans = min(ans, minimum_cost(i, 0, state, min(o + do - 1, m), h - 1, dic, w, m) + dc)
if ans > f:
print("NA")
else:
print(ans)
| {
"input": [
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 0 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -14\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -18 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n6 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-8 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
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"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 4\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n6 3\n100 19 3\n-147 -20 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -62 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -28 -30\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-35 -40 -45 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-12 -60 -9\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -40 -50 -25\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-120 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -7\n3 3\n101 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -172 -11\n3 3\n100 1 3\n-100 0 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -107\n-90 2 -80 8\n-250 -130 -330 -166\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n6 3\n100 10 7\n-100 -20 -100\n-125 -29 -20\n-78 -60 -20\n3 3\n110 10 3\n-100 -20 -100\n-20 -20 -20\n-8 -29 -20\n3 3\n110 3 3\n-100 -8 0\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -63\n-130 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-146 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -33 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -162\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -32\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-274 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -10 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-49 -20 -100\n-227 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -40 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-207 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -22 -100\n-117 -20 -15\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -14\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -226 -312\n-90 2 -80 8\n-207 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -2 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-172 -20 -100\n-20 -20 -20\n-10 -100 -20\n3 3\n110 3 3\n-100 -38 -30\n-100 -20 2\n-127 -20 -20\n4 5\n883 5 4\n1 -380 -250 -312\n-90 2 -144 12\n-467 -130 -330 -29\n-56 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -35\n-117 -29 -15\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-122 -60 -20\n3 3\n110 19 3\n-289 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n000 3 3\n-78 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n89 5 4\n-10 -380 -250 -253\n-90 2 -80 8\n-207 -107 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n110 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -106\n-120 -40 -50 -20\n-250 -8 -13 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -4 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-22 -20 2\n-100 -20 -14\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 1\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -4 -32 -150\n0 0"
],
"output": [
"60\n80\nNA\n50\n390",
"60\n80\nNA\n50\n376\n",
"60\n80\nNA\n50\n388\n",
"60\n80\nNA\n50\n394\n",
"60\n80\nNA\n50\n390\n",
"60\n80\nNA\n50\nNA\n",
"60\n80\nNA\n44\n394\n",
"58\n80\nNA\n50\n376\n",
"60\n80\nNA\n50\n454\n",
"60\n40\nNA\n50\n388\n",
"60\n80\nNA\n50\n378\n",
"60\n80\nNA\n45\n394\n",
"60\n67\nNA\n50\n390\n",
"58\n80\nNA\n50\n386\n",
"64\n80\nNA\n45\n394\n",
"60\n69\nNA\n50\n390\n",
"60\n98\nNA\n50\n388\n",
"65\n80\nNA\n50\n390\n",
"60\n80\nNA\n50\n352\n",
"64\n80\nNA\n45\n439\n",
"60\n80\nNA\n50\n342\n",
"64\n80\nNA\n64\n439\n",
"60\n80\nNA\n50\n270\n",
"65\n80\nNA\nNA\n390\n",
"60\n80\nNA\n50\n258\n",
"74\n80\nNA\nNA\n390\n",
"74\n76\nNA\nNA\n390\n",
"60\n80\nNA\n50\n383\n",
"60\n70\nNA\n50\n388\n",
"60\n80\nNA\n50\n384\n",
"60\n80\nNA\n50\n386\n",
"60\n87\nNA\n50\n390\n",
"60\n80\nNA\nNA\n390\n",
"60\nNA\nNA\n50\n390\n",
"60\n80\nNA\n54\n388\n",
"60\n80\nNA\n50\n280\n",
"60\n71\nNA\n50\n390\n",
"NA\n80\nNA\n50\n390\n",
"53\n80\nNA\n50\n390\n",
"50\n80\nNA\n50\n454\n",
"64\n80\nNA\nNA\n394\n",
"60\n40\nNA\n50\n397\n",
"64\n80\nNA\n45\n399\n",
"60\n67\nNA\n50\n436\n",
"64\n80\nNA\n56\n439\n",
"60\n67\nNA\n50\n409\n",
"65\n80\nNA\n50\n380\n",
"60\n96\nNA\n50\n342\n",
"64\n80\nNA\n57\n439\n",
"60\n80\nNA\n50\n222\n",
"65\n80\nNA\nNA\n260\n",
"65\n80\nNA\nNA\n377\n",
"65\n76\nNA\nNA\n390\n",
"60\n70\nNA\n50\n314\n",
"60\n80\nNA\n50\n437\n",
"60\n80\nNA\n44\n554\n",
"52\n80\nNA\n50\n386\n",
"47\n80\nNA\n50\n376\n",
"60\n80\nNA\nNA\n388\n",
"60\n80\nNA\nNA\n380\n",
"58\n80\nNA\n50\n280\n",
"60\n100\nNA\n54\n388\n",
"60\n40\nNA\n50\n384\n",
"NA\n80\nNA\nNA\n390\n",
"60\n80\nNA\n50\n294\n",
"69\n80\nNA\n45\n394\n",
"60\n80\n40\nNA\n390\n",
"60\n100\nNA\n50\n388\n",
"60\n69\nNA\n50\n352\n",
"60\n67\nNA\nNA\n436\n",
"60\n67\nNA\n50\n280\n",
"60\n60\nNA\n50\n409\n",
"60\n80\nNA\n50\n277\n",
"65\nNA\nNA\n50\n390\n",
"65\n80\nNA\n50\n352\n",
"60\n68\nNA\n50\n270\n",
"43\n80\nNA\n50\n258\n",
"60\n80\nNA\n50\n345\n",
"60\n70\nNA\nNA\n314\n",
"60\n80\nNA\n50\n382\n",
"60\n86\nNA\n50\n390\n",
"47\n80\nNA\n50\n375\n",
"60\n80\nNA\n55\n388\n",
"60\n40\nNA\n45\n384\n",
"60\n65\nNA\n50\n390\n",
"NA\n80\nNA\nNA\n396\n",
"58\n80\nNA\n50\n390\n",
"69\n80\nNA\n45\nNA\n",
"60\n100\n40\nNA\n390\n",
"64\n80\nNA\n45\n389\n",
"60\n69\nNA\n50\n357\n",
"60\n67\nNA\nNA\n363\n",
"60\n40\nNA\n20\n388\n",
"64\n80\nNA\n45\n376\n",
"65\n92\nNA\n50\n380\n",
"65\n100\nNA\n50\n390\n",
"67\n80\nNA\n50\n390\n",
"42\n80\nNA\n50\n270\n",
"74\n80\nNA\nNA\nNA\n",
"60\n80\nNA\n50\n369\n",
"60\n64\nNA\n44\n554\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Aizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost.
The state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation:
1. A cell filled with soil. There is a fixed cost for each cell to dig.
2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen.
Only left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up.
You must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded.
Create a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output "NA".
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format.
W H
f m o
c1,1 c2,1 ... cW,1
c1,2 c2,2 ... cW,2
...
c1, H c2, H ... cW, H
The horizontal size W of the formation and the vertical size H (3 ≤ W, H ≤ 10) are given in the first line. The second line is the integer f (1 ≤ f ≤ 10000) that represents your excavation cost, the integer m (3 ≤ m ≤ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≤ m) is given.
The following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format:
If the value is negative, the cell is full of soil and the value represents the cost.
If the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen.
However, there are no more than 50 cells in which oxygen has accumulated.
The number of datasets does not exceed 50.
Output
Print the minimum cost or NA on one line for each dataset.
Example
Input
3 3
100 10 10
-100 -20 -100
-100 -20 -100
-100 -20 -100
3 3
100 10 10
-100 -20 -100
-100 -20 -20
-100 -60 -20
3 3
100 10 3
-100 -20 -100
-20 -20 -20
-20 -100 -20
3 3
100 3 3
-100 -20 -30
-100 -20 2
-100 -20 -20
4 5
1500 5 4
-10 -380 -250 -250
-90 2 -80 8
-250 -130 -330 -120
-120 -40 -50 -20
-250 -10 -20 -150
0 0
Output
60
80
NA
50
390
### Input:
3 3
100 10 10
-100 -20 -100
-100 -20 -100
-100 -20 -100
3 3
100 10 10
-100 -20 -100
-100 -20 -20
-100 -60 -20
3 3
100 10 3
-100 -20 -100
-20 -20 -20
-20 -100 -20
3 3
100 3 3
-100 -20 -30
-100 -20 2
-100 -20 -20
4 5
1500 5 4
-10 -380 -250 -250
-90 2 -80 8
-250 -130 -330 -120
-120 -40 -50 -20
-250 -10 -20 -150
0 0
### Output:
60
80
NA
50
390
### Input:
3 3
100 10 10
-100 -20 -100
-100 -20 -100
-100 -20 -100
3 3
100 10 10
-100 -20 -100
-100 -20 -20
-100 -60 -20
3 3
100 10 3
-100 -20 -100
-20 -20 -20
-20 -100 -20
3 3
100 3 3
-100 -20 -30
-100 -20 2
-100 -20 -20
4 5
1500 5 4
-10 -380 -250 -250
-90 2 -80 8
-250 -130 -330 -120
-120 -40 -50 -6
-250 -10 -20 -150
0 0
### Output:
60
80
NA
50
376
### Code:
import sys
sys.setrecursionlimit(1000000)
INF = 10 ** 20
def update_state(state, newx):
tmp = list(state)
tmp[newx] = 1
return tuple(tmp)
def get_co(x, y):
dc = do = 0
score = mp[y][x]
if score < 0:
dc = -score
else:
do = score
return dc, do
def minimum_cost(x, y, state, ox, goal, dic, w, m):
if (x, y, state, ox) in dic:
return dic[(x, y, state, ox)]
if y == goal:
return 0
if ox <= 1:
return INF
ret = INF
if x >= 1:
if state[x - 1] == 0:
dc, do = get_co(x - 1, y)
ret = min(ret, minimum_cost(x - 1, y, update_state(state, x - 1), min(ox + do - 1, m), goal, dic, w, m) + dc)
else:
ret = min(ret, minimum_cost(x - 1, y, state, ox - 1, goal, dic, w, m))
if x < w - 1:
if state[x + 1] == 0:
dc, do = get_co(x + 1, y)
ret = min(ret, minimum_cost(x + 1, y, update_state(state, x + 1), min(ox + do - 1, m), goal, dic, w, m) + dc)
else:
ret = min(ret, minimum_cost(x + 1, y, state, ox - 1, goal, dic, w, m))
dc, do = get_co(x, y + 1)
ret = min(ret, minimum_cost(x, y + 1, tuple((1 if i == x else 0 for i in range(w))), min(ox + do - 1, m), goal, dic, w, m) + dc)
dic[(x, y, state, ox)] = ret
return ret
while True:
w, h = map(int, input().split())
if w == 0:
break
f, m, o = map(int, input().split())
mp = [list(map(int, input().split())) for _ in range(h)]
if o <= 1:
print("NA")
continue
dic = {}
ans = INF
for i in range(w):
dc, do = get_co(i, 0)
state = tuple(1 if i == j else 0 for j in range(w))
ans = min(ans, minimum_cost(i, 0, state, min(o + do - 1, m), h - 1, dic, w, m) + dc)
if ans > f:
print("NA")
else:
print(ans)
|
p00396 Playing With Stones_3270 | Playing with Stones
Koshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:
1. Before starting the game, they define some small areas and place "one or more black stones and one or more white stones" in each of the areas.
2. Koshiro and Ukiko alternately select an area and perform one of the following operations.
(a) Remove a white stone from the area
(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area.
(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game.
3. If either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.
They played the game several times, with Koshiro’s first move and Ukiko’s second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.
Given the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.
Input
The input is given in the following format.
$N$
$w_1$ $b_1$
$w_2$ $b_2$
:
$w_N$ $b_N$
The first line provides the number of areas $N$ ($1 \leq N \leq 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 \leq w_i, b_i \leq 100$) in the $i$-th area.
Output
Output 0 if Koshiro wins and 1 if Ukiko wins.
Examples
Input
4
24 99
15 68
12 90
95 79
Output
0
Input
3
2 46
94 8
46 57
Output
1 | #!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
g = defaultdict(lambda : None)
g[(0,0)] = 0
def grundy(w,b):
if g[(w,b)] != None:
return g[(w,b)]
s = set()
if w:
s.add(grundy(w-1,b))
if b:
s.add(grundy(w+1,b-1))
for i in range(1,min(w,b)+1):
s.add(grundy(w,b-i))
i = 0
while i in s:
i += 1
g[(w,b)] = i
return i
n = I()
ans = 0
for _ in range(n):
w,b = LI()
ans ^= grundy(w,b)
print(0 if ans else 1)
return
#Solve
if __name__ == "__main__":
solve()
| {
"input": [
"4\n24 99\n15 68\n12 90\n95 79",
"3\n2 46\n94 8\n46 57",
"4\n24 99\n15 68\n12 90\n95 66",
"3\n0 46\n94 8\n46 57",
"4\n24 99\n15 44\n12 90\n95 66",
"3\n0 46\n9 8\n46 57",
"4\n18 99\n15 44\n12 90\n95 66",
"3\n1 46\n9 8\n46 57",
"4\n18 99\n15 44\n3 90\n95 66",
"3\n1 63\n9 8\n46 57",
"4\n18 99\n15 44\n3 90\n95 104",
"3\n1 63\n9 8\n46 21",
"4\n18 99\n15 15\n3 90\n95 104",
"3\n2 63\n9 8\n46 21",
"3\n2 63\n9 8\n46 15",
"3\n2 63\n9 8\n24 15",
"3\n2 32\n9 8\n24 15",
"3\n2 32\n9 8\n24 17",
"3\n2 32\n9 11\n24 17",
"3\n2 32\n9 11\n24 4",
"3\n2 32\n9 16\n24 4",
"3\n3 32\n9 16\n24 4",
"3\n3 32\n9 16\n35 4",
"3\n3 15\n9 16\n35 4",
"3\n0 15\n9 16\n35 4",
"3\n1 15\n9 16\n35 4",
"3\n2 15\n9 16\n35 4",
"3\n1 15\n9 32\n35 4",
"3\n1 15\n9 38\n35 4",
"3\n1 13\n9 38\n35 4",
"3\n1 13\n9 38\n35 1",
"3\n1 13\n9 38\n35 0",
"3\n1 13\n9 38\n46 0",
"3\n1 13\n9 38\n46 1",
"3\n1 13\n9 58\n46 1",
"3\n0 13\n9 58\n46 1",
"3\n0 5\n9 58\n46 1",
"3\n0 5\n9 23\n46 1",
"3\n0 5\n9 23\n66 1",
"3\n0 5\n9 19\n66 1",
"3\n0 5\n9 19\n17 1",
"3\n1 5\n9 19\n17 1",
"3\n1 5\n16 19\n17 1",
"3\n1 8\n16 19\n17 1",
"3\n1 2\n16 19\n17 1",
"3\n2 2\n16 19\n17 1",
"3\n2 2\n12 19\n17 1",
"3\n2 2\n12 34\n17 1",
"3\n2 2\n19 34\n17 1",
"3\n2 2\n19 34\n17 0",
"3\n2 2\n19 32\n17 0",
"3\n2 2\n5 32\n17 0",
"3\n3 2\n5 32\n17 0",
"3\n3 2\n5 13\n17 0",
"3\n1 2\n5 13\n17 0",
"3\n1 2\n2 13\n17 0",
"3\n1 2\n2 21\n17 0",
"3\n1 2\n2 21\n3 0",
"3\n1 1\n2 21\n3 0",
"3\n1 1\n2 21\n5 0",
"4\n24 99\n15 68\n12 155\n95 79",
"3\n2 46\n94 12\n46 57",
"4\n24 99\n15 68\n0 90\n95 79",
"3\n2 46\n94 5\n46 57",
"4\n24 99\n15 68\n0 90\n95 33",
"3\n2 46\n94 5\n56 57",
"4\n24 99\n24 68\n0 90\n95 33",
"3\n0 46\n94 5\n56 57",
"3\n0 46\n94 5\n56 105",
"3\n0 46\n94 5\n27 105",
"3\n0 46\n94 5\n25 105",
"3\n0 46\n15 5\n25 105",
"4\n24 99\n15 97\n12 90\n95 79",
"3\n2 46\n94 8\n5 57",
"4\n24 99\n15 68\n0 90\n95 87",
"3\n2 26\n94 5\n46 57",
"4\n24 99\n15 68\n0 78\n95 33",
"3\n2 46\n94 5\n56 110",
"4\n24 99\n24 68\n0 90\n95 64",
"3\n0 46\n94 5\n56 41",
"3\n0 46\n94 3\n27 105",
"3\n0 46\n60 5\n25 105",
"3\n0 46\n15 5\n30 105",
"4\n24 99\n15 97\n12 149\n95 79",
"3\n2 72\n94 8\n5 57",
"4\n24 99\n15 34\n0 90\n95 87",
"3\n2 26\n94 5\n69 57",
"3\n2 90\n94 5\n56 110",
"4\n24 99\n24 68\n0 90\n95 31",
"3\n0 46\n94 5\n27 41",
"3\n0 46\n23 5\n25 105",
"3\n0 46\n15 1\n30 105",
"4\n39 99\n15 97\n12 149\n95 79",
"3\n2 72\n94 8\n8 57",
"3\n2 26\n78 5\n69 57",
"3\n2 90\n94 5\n56 100",
"4\n24 99\n24 127\n0 90\n95 31",
"3\n0 46\n54 5\n27 41",
"3\n0 46\n23 5\n28 105",
"3\n0 46\n8 1\n30 105",
"3\n2 72\n94 13\n8 57",
"3\n2 26\n78 5\n132 57"
],
"output": [
"0",
"1",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
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]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Playing with Stones
Koshiro and Ukiko are playing a game with black and white stones. The rules of the game are as follows:
1. Before starting the game, they define some small areas and place "one or more black stones and one or more white stones" in each of the areas.
2. Koshiro and Ukiko alternately select an area and perform one of the following operations.
(a) Remove a white stone from the area
(b) Remove one or more black stones from the area. Note, however, that the number of the black stones must be less than or equal to white ones in the area.
(c) Pick up a white stone from the stone pod and replace it with a black stone. There are plenty of white stones in the pod so that there will be no shortage during the game.
3. If either Koshiro or Ukiko cannot perform 2 anymore, he/she loses.
They played the game several times, with Koshiro’s first move and Ukiko’s second move, and felt the winner was determined at the onset of the game. So, they tried to calculate the winner assuming both players take optimum actions.
Given the initial allocation of black and white stones in each area, make a program to determine which will win assuming both players take optimum actions.
Input
The input is given in the following format.
$N$
$w_1$ $b_1$
$w_2$ $b_2$
:
$w_N$ $b_N$
The first line provides the number of areas $N$ ($1 \leq N \leq 10000$). Each of the subsequent $N$ lines provides the number of white stones $w_i$ and black stones $b_i$ ($1 \leq w_i, b_i \leq 100$) in the $i$-th area.
Output
Output 0 if Koshiro wins and 1 if Ukiko wins.
Examples
Input
4
24 99
15 68
12 90
95 79
Output
0
Input
3
2 46
94 8
46 57
Output
1
### Input:
4
24 99
15 68
12 90
95 79
### Output:
0
### Input:
3
2 46
94 8
46 57
### Output:
1
### Code:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
g = defaultdict(lambda : None)
g[(0,0)] = 0
def grundy(w,b):
if g[(w,b)] != None:
return g[(w,b)]
s = set()
if w:
s.add(grundy(w-1,b))
if b:
s.add(grundy(w+1,b-1))
for i in range(1,min(w,b)+1):
s.add(grundy(w,b-i))
i = 0
while i in s:
i += 1
g[(w,b)] = i
return i
n = I()
ans = 0
for _ in range(n):
w,b = LI()
ans ^= grundy(w,b)
print(0 if ans else 1)
return
#Solve
if __name__ == "__main__":
solve()
|
p00749 Off Balance_3274 | You are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building.
Submitted designs will look like a screenshot of a well known game as shown below.
<image>
This is because the center specifies that the building should be constructed by stacking regular units called pieces, each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions.
* All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position.
* All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse.
* The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces.
* The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below.
<image>
It will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows.
Assume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy-coordinates of its left-bottom corner. The unit length is the edge length of a block.
Among the blocks of the piece that touch another piece or the ground on their bottom faces, let xL be the leftmost x-coordinate of the leftmost block, and let xR be the rightmost x-coordinate of the rightmost block. Let the x-coordinate of its accumulated center of mass of the piece be M, where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P, in addition to P itself. Then the piece is stable, if and only if xL < M < xR. Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable.
Note that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable.
<image> | | <image>
---|---|---
Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.
Write a program that judges stability of each design based on the above quick check rules.
Input
The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset, which represents a front view of a building, is formatted as follows.
> w h
> p0(h-1)p1(h-1)...p(w-1)(h-1)
> ...
> p01p11...p(w-1)1
> p00p10...p(w-1)0
>
The integers w and h separated by a space are the numbers of columns and rows of the layout, respectively. You may assume 1 ≤ w ≤ 10 and 1 ≤ h ≤ 60. The next h lines specify the placement of the pieces. The character pxy indicates the status of a block at (x,y), either ``.`', meaning empty, or one digit character between ``1`' and ``9`', inclusive, meaning a block of a piece. (As mentioned earlier, we denote a location of a block by xy-coordinates of its left-bottom corner.)
When two blocks with the same number touch each other by any of their top, bottom, left or right face, those blocks are of the same piece. (Note that there might be two different pieces that are denoted by the same number.) The bottom of a block at (x,0) touches the ground.
You may assume that the pieces in each dataset are stacked in a tree-like form.
Output
For each dataset, output a line containing a word `STABLE` when the design is stable with respect to the above quick check rules. Otherwise, output `UNSTABLE`. The output should be written with uppercase letters, and should not contain any other extra characters.
Sample Input
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2.
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
Output for the Sample Input
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE
Example
Input
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2.
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
Output
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE | while True:
w, h = map(int, input().split())
if w == 0:
break
mp = [[0] + list(input()) + [0] for _ in range(h)]
mp.insert(0, [0] * (w + 2))
mp.append([0] * (w + 2))
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y][x] == ".":
mp[y][x] = 0
else:
mp[y][x] = int(mp[y][x])
last_id = 10
vec = ((0, 1), (0, -1), (1, 0), (-1, 0))
def update(last_id, target, x, y):
if mp[y][x] != target:
return
mp[y][x] = last_id
for dx, dy in vec:
update(last_id, target, x + dx, y + dy)
for y in range(1, h + 1):
for x in range(1, w + 1):
if 1 <= mp[y][x] <= 9:
update(last_id, mp[y][x], x, y)
last_id += 1
node_num = last_id - 10
edges = [set() for _ in range(node_num)]
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y - 1][x] != mp[y][x] and mp[y - 1][x] != 0 and mp[y][x] != 0:
edges[mp[y][x] - 10].add(mp[y - 1][x] - 10)
for x in range(1, w + 1):
if mp[h][x] != 0:
root = mp[h][x] - 10
break
center = [0] * node_num
ground = [None] * node_num
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y][x] != 0:
target = mp[y][x] - 10
center[target] += (x + 0.5) / 4
if mp[y + 1][x] in (0, target + 10):
continue
if ground[target] == None:
ground[target] = [x, x + 1]
else:
ground[target][0] = min(ground[target][0], x)
ground[target][1] = max(ground[target][1], x + 1)
for x in range(1, w + 1):
if mp[h][x] == root + 10:
if ground[root] == None:
ground[root] = [x, x + 1]
else:
ground[root][0] = min(ground[root][0], x)
ground[root][1] = max(ground[root][1], x + 1)
total_center = [None] * node_num
def get_total_center(node):
mom = center[node]
wei = 1
for to in edges[node]:
to_wei, to_pos = get_total_center(to)
mom += to_wei * to_pos
wei += to_wei
total_center[node] = mom / wei
return wei, total_center[node]
get_total_center(root)
for gr, cen in zip(ground, total_center):
l, r = gr
if not (l < cen < r):
print("UNSTABLE")
break
else:
print("STABLE")
| {
"input": [
"4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n..33\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n..33\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n..33\n2222\n.1..\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n33..\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n..33\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n33..\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1..1\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n..33\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n1.0304765877571223\n0 0",
"4 5\n..33\n33..\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n1..1.\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n..33\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2/\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n1.5938270010912552\n0 0",
"4 5\n..33\n..32\n2222\n..1.\n.111\n5 7\n....1\n.1..1\n.1.1.\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n..32\n2222\n..1.\n.111\n5 7\n./..1\n.1..1\n.1.1.\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n..11\n..11\n4 5\n.3..\n33..\n322.\n3944\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n21\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
"4 5\n..33\n..32\n2222\n..1.\n.111\n5 7\n.-..1\n.1..1\n.1.1.\n11..1\n.2222\n..111\n...1.\n3 6\n.3.\n233\n23.\n22.\n.11\n.11\n4 3\n2222\n.11.\n..11\n4 5\n.3..\n33..\n322.\n2211\n.11.\n3 3\n222\n2.1\n111\n3 4\n11.\n11.\n.2.\n222\n3 4\n.11\n.11\n.2.\n222\n2 7\n11\n.1\n32\n22\n23\n.3\n33\n2 3\n1.\n11\n.1\n0 0",
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],
"output": [
"STABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE",
"STABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"UNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
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"UNSTABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
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"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n",
"STABLE\nUNSTABLE\nSTABLE\nUNSTABLE\nSTABLE\nSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\nUNSTABLE\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are working for an administration office of the International Center for Picassonian Cubism (ICPC), which plans to build a new art gallery for young artists. The center is organizing an architectural design competition to find the best design for the new building.
Submitted designs will look like a screenshot of a well known game as shown below.
<image>
This is because the center specifies that the building should be constructed by stacking regular units called pieces, each of which consists of four cubic blocks. In addition, the center requires the competitors to submit designs that satisfy the following restrictions.
* All the pieces are aligned. When two pieces touch each other, the faces of the touching blocks must be placed exactly at the same position.
* All the pieces are stable. Since pieces are merely stacked, their centers of masses must be carefully positioned so as not to collapse.
* The pieces are stacked in a tree-like form in order to symbolize boundless potentiality of young artists. In other words, one and only one piece touches the ground, and each of other pieces touches one and only one piece on its bottom faces.
* The building has a flat shape. This is because the construction site is a narrow area located between a straight moat and an expressway where no more than one block can be placed between the moat and the expressway as illustrated below.
<image>
It will take many days to fully check stability of designs as it requires complicated structural calculation. Therefore, you are asked to quickly check obviously unstable designs by focusing on centers of masses. The rules of your quick check are as follows.
Assume the center of mass of a block is located at the center of the block, and all blocks have the same weight. We denote a location of a block by xy-coordinates of its left-bottom corner. The unit length is the edge length of a block.
Among the blocks of the piece that touch another piece or the ground on their bottom faces, let xL be the leftmost x-coordinate of the leftmost block, and let xR be the rightmost x-coordinate of the rightmost block. Let the x-coordinate of its accumulated center of mass of the piece be M, where the accumulated center of mass of a piece P is the center of the mass of the pieces that are directly and indirectly supported by P, in addition to P itself. Then the piece is stable, if and only if xL < M < xR. Otherwise, it is unstable. A design of a building is unstable if any of its pieces is unstable.
Note that the above rules could judge some designs to be unstable even if it would not collapse in reality. For example, the left one of the following designs shall be judged to be unstable.
<image> | | <image>
---|---|---
Also note that the rules judge boundary cases to be unstable. For example, the top piece in the above right design has its center of mass exactly above the right end of the bottom piece. This shall be judged to be unstable.
Write a program that judges stability of each design based on the above quick check rules.
Input
The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset, which represents a front view of a building, is formatted as follows.
> w h
> p0(h-1)p1(h-1)...p(w-1)(h-1)
> ...
> p01p11...p(w-1)1
> p00p10...p(w-1)0
>
The integers w and h separated by a space are the numbers of columns and rows of the layout, respectively. You may assume 1 ≤ w ≤ 10 and 1 ≤ h ≤ 60. The next h lines specify the placement of the pieces. The character pxy indicates the status of a block at (x,y), either ``.`', meaning empty, or one digit character between ``1`' and ``9`', inclusive, meaning a block of a piece. (As mentioned earlier, we denote a location of a block by xy-coordinates of its left-bottom corner.)
When two blocks with the same number touch each other by any of their top, bottom, left or right face, those blocks are of the same piece. (Note that there might be two different pieces that are denoted by the same number.) The bottom of a block at (x,0) touches the ground.
You may assume that the pieces in each dataset are stacked in a tree-like form.
Output
For each dataset, output a line containing a word `STABLE` when the design is stable with respect to the above quick check rules. Otherwise, output `UNSTABLE`. The output should be written with uppercase letters, and should not contain any other extra characters.
Sample Input
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2.
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
Output for the Sample Input
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE
Example
Input
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2.
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
Output
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE
### Input:
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2.
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
### Output:
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE
### Input:
4 5
..33
..33
2222
..1.
.111
5 7
....1
.1..1
.1..1
11..1
.2222
..111
...1.
3 6
.3.
233
23.
22.
.11
.11
4 3
2222
..11
..11
4 5
.3..
33..
322.
2211
.11.
3 3
222
2.1
111
3 4
11.
11.
.2/
222
3 4
.11
.11
.2.
222
2 7
11
.1
21
22
23
.3
33
2 3
1.
11
.1
0 0
### Output:
STABLE
STABLE
STABLE
UNSTABLE
STABLE
STABLE
UNSTABLE
UNSTABLE
UNSTABLE
UNSTABLE
### Code:
while True:
w, h = map(int, input().split())
if w == 0:
break
mp = [[0] + list(input()) + [0] for _ in range(h)]
mp.insert(0, [0] * (w + 2))
mp.append([0] * (w + 2))
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y][x] == ".":
mp[y][x] = 0
else:
mp[y][x] = int(mp[y][x])
last_id = 10
vec = ((0, 1), (0, -1), (1, 0), (-1, 0))
def update(last_id, target, x, y):
if mp[y][x] != target:
return
mp[y][x] = last_id
for dx, dy in vec:
update(last_id, target, x + dx, y + dy)
for y in range(1, h + 1):
for x in range(1, w + 1):
if 1 <= mp[y][x] <= 9:
update(last_id, mp[y][x], x, y)
last_id += 1
node_num = last_id - 10
edges = [set() for _ in range(node_num)]
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y - 1][x] != mp[y][x] and mp[y - 1][x] != 0 and mp[y][x] != 0:
edges[mp[y][x] - 10].add(mp[y - 1][x] - 10)
for x in range(1, w + 1):
if mp[h][x] != 0:
root = mp[h][x] - 10
break
center = [0] * node_num
ground = [None] * node_num
for y in range(1, h + 1):
for x in range(1, w + 1):
if mp[y][x] != 0:
target = mp[y][x] - 10
center[target] += (x + 0.5) / 4
if mp[y + 1][x] in (0, target + 10):
continue
if ground[target] == None:
ground[target] = [x, x + 1]
else:
ground[target][0] = min(ground[target][0], x)
ground[target][1] = max(ground[target][1], x + 1)
for x in range(1, w + 1):
if mp[h][x] == root + 10:
if ground[root] == None:
ground[root] = [x, x + 1]
else:
ground[root][0] = min(ground[root][0], x)
ground[root][1] = max(ground[root][1], x + 1)
total_center = [None] * node_num
def get_total_center(node):
mom = center[node]
wei = 1
for to in edges[node]:
to_wei, to_pos = get_total_center(to)
mom += to_wei * to_pos
wei += to_wei
total_center[node] = mom / wei
return wei, total_center[node]
get_total_center(root)
for gr, cen in zip(ground, total_center):
l, r = gr
if not (l < cen < r):
print("UNSTABLE")
break
else:
print("STABLE")
|
p00887 Awkward Lights_3277 | You are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.
Each floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x1, y1) of a grid of rooms and the room at (x2, y2) is given by |x1 - x2| + |y1 - y2|. For example, if the position of the toggle switch of the room at (2, 2) of a 4 × 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1, 1), (1, 3), (2, 4), (3, 1), (3, 3), and (4, 2) as well as at (2, 2) are reversed as shown in Figure D.1, where black and white squares represent the ON/OFF states of the lights.
<image>
Figure D.1: An example behavior of the lighting system
Your mission is to write a program that answer whether all the lights on a floor can be turned off.
Input
The input is a sequence of datasets. Each dataset is formatted as follows.
m n d
S11 S12 S13 ... S1m
S21 S22 S23 ... S2m
...
Sn1 Sn2 Sn3 ... Snm
The first line of a dataset contains three integers. m and n (1 ≤ m ≤ 25, 1 ≤ n ≤ 25) are the numbers of columns and rows of the grid, respectively. d (1 ≤ d ≤ m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each Sij (1 ≤ i ≤ n, 1 ≤ j ≤ m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.
The end of the input is indicated by a line containing three zeros.
Output
For each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case, print it in one line for each input dataset.
Example
Input
1 1 1
1
2 2 1
1 1
1 1
3 2 1
1 0 1
0 1 0
3 3 1
1 0 1
0 1 0
1 0 1
4 4 2
1 1 0 1
0 0 0 1
1 0 1 1
1 0 0 0
5 5 1
1 1 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
5 5 2
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
13 13 7
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0
Output
1
1
0
1
0
0
1
1
0
1 | import sys,queue,math,copy,itertools
LI = lambda : [int(x) for x in sys.stdin.readline().split()]
while True:
M,N,D = LI()
if N == 0 : break
S = []
for _ in range(N):
S.extend(LI())
x = []
for i in range(N):
for j in range(M):
y = [0 for _ in range(N*M)]
for p in range(-D,D+1):
q1 = j + (D - abs(p))
q2 = j - (D - abs(p))
if 0 <= i + p < N and 0 <= q1 < M:
y[(i+p) * M + q1] = 1
if 0 <= i+ p < N and 0 <= q2 < M:
y[(i+p) * M + q2] = 1
y[i * M + j] = 1
x.append(y)
x.append(S)
z = []
for i in range(N*M):
b = 0
for j in range(N*M+1):
b <<= 1
b += x[j][i]
z.append(b)
c = [True for _ in range(N*M)]
b = 1 << (N * M)
for i in range(N*M):
for j in range(N*M):
if z[j] & b and c[j]:
for k in range(N*M):
if k == j or z[k] & b == 0: continue
z[k] ^= z[j]
c[j] = False
break
b >>= 1
if z.count(1):
print (0)
else:
print (1)
| {
"input": [
"1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0",
"1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 -1 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0",
"1 1 1\n1\n2 2 1\n1 1\n1 1\n3 2 1\n1 0 1\n0 1 0\n3 3 1\n1 0 1\n0 1 0\n1 0 1\n4 4 2\n1 1 0 1\n0 0 0 1\n1 0 1 1\n1 0 0 0\n5 5 1\n1 1 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n0 1 0 1 0\n1 0 1 0 1\n5 5 2\n0 0 0 0 0\n0 0 0 0 0\n0 0 1 0 0\n0 0 0 0 0\n0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n11 11 3\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 1 1 0 0 0 0\n0 0 0 0 0 0 0 0 -1 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 -1 0\n13 13 7\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 1 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 -1 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0 0 0 0\n0 0 0",
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"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n",
"1\n1\n0\n1\n0\n0\n0\n0\n",
"1\n1\n0\n1\n0\n0\n1\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are working as a night watchman in an office building. Your task is to check whether all the lights in the building are turned off after all the office workers in the building have left the office. If there are lights that are turned on, you must turn off those lights. This task is not as easy as it sounds to be because of the strange behavior of the lighting system of the building as described below. Although an electrical engineer checked the lighting system carefully, he could not determine the cause of this behavior. So you have no option but to continue to rely on this system for the time being.
Each floor in the building consists of a grid of square rooms. Every room is equipped with one light and one toggle switch. A toggle switch has two positions but they do not mean fixed ON/OFF. When the position of the toggle switch of a room is changed to the other position, in addition to that room, the ON/OFF states of the lights of the rooms at a certain Manhattan distance from that room are reversed. The Manhattan distance between the room at (x1, y1) of a grid of rooms and the room at (x2, y2) is given by |x1 - x2| + |y1 - y2|. For example, if the position of the toggle switch of the room at (2, 2) of a 4 × 4 grid of rooms is changed and the given Manhattan distance is two, the ON/OFF states of the lights of the rooms at (1, 1), (1, 3), (2, 4), (3, 1), (3, 3), and (4, 2) as well as at (2, 2) are reversed as shown in Figure D.1, where black and white squares represent the ON/OFF states of the lights.
<image>
Figure D.1: An example behavior of the lighting system
Your mission is to write a program that answer whether all the lights on a floor can be turned off.
Input
The input is a sequence of datasets. Each dataset is formatted as follows.
m n d
S11 S12 S13 ... S1m
S21 S22 S23 ... S2m
...
Sn1 Sn2 Sn3 ... Snm
The first line of a dataset contains three integers. m and n (1 ≤ m ≤ 25, 1 ≤ n ≤ 25) are the numbers of columns and rows of the grid, respectively. d (1 ≤ d ≤ m + n) indicates the Manhattan distance. Subsequent n lines of m integers are the initial ON/OFF states. Each Sij (1 ≤ i ≤ n, 1 ≤ j ≤ m) indicates the initial ON/OFF state of the light of the room at (i, j): '0' for OFF and '1' for ON.
The end of the input is indicated by a line containing three zeros.
Output
For each dataset, output '1' if all the lights can be turned off. If not, output '0'. In either case, print it in one line for each input dataset.
Example
Input
1 1 1
1
2 2 1
1 1
1 1
3 2 1
1 0 1
0 1 0
3 3 1
1 0 1
0 1 0
1 0 1
4 4 2
1 1 0 1
0 0 0 1
1 0 1 1
1 0 0 0
5 5 1
1 1 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
5 5 2
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
13 13 7
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0
Output
1
1
0
1
0
0
1
1
0
1
### Input:
1 1 1
1
2 2 1
1 1
1 1
3 2 1
1 0 1
0 1 0
3 3 1
1 0 1
0 1 0
1 0 1
4 4 2
1 1 0 1
0 0 0 1
1 0 1 1
1 0 0 0
5 5 1
1 1 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
5 5 2
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
13 13 7
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0
### Output:
1
1
0
1
0
0
1
1
0
1
### Input:
1 1 1
1
2 2 1
1 1
1 1
3 2 1
1 0 1
0 1 0
3 3 1
1 0 1
0 1 0
1 0 1
4 4 2
1 1 0 1
0 0 0 1
1 0 1 1
1 0 0 0
5 5 1
1 1 1 0 1
0 1 0 1 0
1 0 1 0 1
0 1 0 1 0
1 0 1 0 1
5 5 2
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
11 11 3
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 -1 0
13 13 7
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0
### Output:
1
1
0
1
0
0
1
1
0
1
### Code:
import sys,queue,math,copy,itertools
LI = lambda : [int(x) for x in sys.stdin.readline().split()]
while True:
M,N,D = LI()
if N == 0 : break
S = []
for _ in range(N):
S.extend(LI())
x = []
for i in range(N):
for j in range(M):
y = [0 for _ in range(N*M)]
for p in range(-D,D+1):
q1 = j + (D - abs(p))
q2 = j - (D - abs(p))
if 0 <= i + p < N and 0 <= q1 < M:
y[(i+p) * M + q1] = 1
if 0 <= i+ p < N and 0 <= q2 < M:
y[(i+p) * M + q2] = 1
y[i * M + j] = 1
x.append(y)
x.append(S)
z = []
for i in range(N*M):
b = 0
for j in range(N*M+1):
b <<= 1
b += x[j][i]
z.append(b)
c = [True for _ in range(N*M)]
b = 1 << (N * M)
for i in range(N*M):
for j in range(N*M):
if z[j] & b and c[j]:
for k in range(N*M):
if k == j or z[k] & b == 0: continue
z[k] ^= z[j]
c[j] = False
break
b >>= 1
if z.count(1):
print (0)
else:
print (1)
|
p01018 Warping Girl_3280 | Problem
Aizu Magic School is a school where people who can use magic gather. Haruka, one of the students of that school, can use the magic of warp on the magic team.
From her house to the school, there is a straight road of length L. There are also magic circles on this road.
She uses this road every day to go to school, so she wants to get to school in the shortest possible time.
So as a programmer, you decided to teach her the minimum amount of time it would take to get to school.
Haruka can walk forward by a distance of 1 in 1 minute (* cannot go back). Also, by casting magic at the position Pi where the magic circle of the warp is written, you can move in Ti minutes to the place just Di from Pi. Even if there is a magic circle at the destination, it will be continuous. You can use warp magic.
The location of her house is 0 and the location of her school is L.
Constraints
The input meets the following conditions.
* All numbers given are integers
* 1 ≤ L ≤ 109
* 0 ≤ n ≤ min (103, L) (min represents the smaller of A and B)
* 0 ≤ Pi ≤ L -1
* 0 ≤ Di ≤ L --Pi
* 0 ≤ Ti ≤ 103
* Pi ≠ Pj
Input
L n
P1 D1 T1
P2 D2 T2
..
..
Pn Dn Tn
The first line is given the length of the road L, the number of magic circles n. Next, the state of n magic circles is given. Pi is the position where the i-th magic circle is, and Di is the i-th magic circle. Distance to warp from, Ti represents the time it takes to warp using the i-th magic circle.
Output
Output the minimum time to get to school in one line.
Examples
Input
10 3
2 2 1
4 2 1
8 1 1
Output
8
Input
10 2
2 3 1
3 5 1
Output
6
Input
1 0
Output
1 | INF = 10 ** 20
l, n = map(int, input().split())
lst = [list(map(int, input().split())) for _ in range(n)] + [[l, 0, INF]]
lst.sort()
score = {}
for p, _, _ in lst:
score[p] = p
for i in range(n + 1):
p, d, t = lst[i]
for j in range(i + 1, n + 1):
to_p, _, _ = lst[j]
if to_p >= p + d:
score[to_p] = min(score[to_p], score[p] + t + to_p - p - d, score[p] + to_p - p)
else:
score[to_p] = min(score[to_p], score[p] + to_p - p)
print(score[l])
| {
"input": [
"10 2\n2 3 1\n3 5 1",
"1 0",
"10 3\n2 2 1\n4 2 1\n8 1 1",
"10 2\n2 3 1\n1 5 1",
"10 2\n2 3 1\n1 5 0",
"10 0\n2 3 1\n1 5 1",
"18 0\n2 3 1\n1 5 1",
"0 0\n2 -1 1\n0 1 1",
"1 0\n2 0 2\n1 2 1",
"2 1\n1 0 7\n4 -1 0",
"10 3\n2 0 1\n4 2 1\n8 1 1",
"34 0\n2 3 1\n1 5 1",
"8 0\n2 0 1\n0 3 1",
"10 2\n2 6 1\n1 5 -1",
"30 0\n2 0 1\n-1 2 1",
"20 2\n2 6 1\n1 5 -1",
"20 2\n2 6 1\n1 5 0",
"23 0\n2 2 1\n-1 1 1",
"7 0\n2 1 1\n-1 0 1",
"27 0\n3 1 1\n0 1 1",
"43 0\n1 2 2\n0 1 1",
"16 0\n2 -2 1\n2 2 1",
"19 1\n0 1 1\n-2 0 1",
"31 1\n2 2 2\n0 3 1",
"4 1\n0 2 1\n-2 0 1",
"16 1\n2 2 -1\n0 3 1",
"25 0\n3 3 1\n1 5 1",
"35 0\n2 0 2\n0 5 1",
"23 1\n1 2 1\n0 1 1",
"12 0\n1 1 7\n5 0 0",
"30 1\n2 1 0\n0 1 -1",
"24 0\n1 1 0\n0 1 -1",
"21 0\n2 3 1\n0 5 1",
"10 3\n2 3 1\n1 5 1",
"18 0\n2 0 1\n1 5 1",
"18 0\n2 0 1\n1 2 1",
"18 0\n2 0 1\n0 2 1",
"18 0\n2 0 1\n0 1 1",
"18 0\n2 0 1\n1 1 1",
"18 0\n2 0 1\n0 3 1",
"18 0\n2 -1 1\n0 3 1",
"18 0\n2 -1 1\n0 1 1",
"0 0\n2 -1 1\n0 2 1",
"0 0\n2 -1 1\n1 2 1",
"0 0\n2 0 1\n1 2 1",
"0 0\n2 0 2\n1 2 1",
"1 0\n2 0 2\n1 2 0",
"1 0\n0 0 2\n1 2 0",
"1 0\n0 0 2\n2 2 0",
"1 0\n0 0 2\n2 3 0",
"1 1\n0 0 2\n2 3 0",
"1 1\n1 0 2\n2 3 0",
"1 1\n1 0 4\n2 3 0",
"1 1\n1 0 4\n2 0 0",
"1 1\n1 0 4\n4 0 0",
"1 1\n1 0 4\n4 -1 0",
"1 1\n1 0 7\n4 -1 0",
"10 2\n2 3 2\n3 5 1",
"10 2\n2 3 1\n0 5 1",
"10 2\n2 6 1\n1 5 0",
"10 0\n2 2 1\n1 5 1",
"18 0\n2 0 2\n1 5 1",
"18 0\n2 0 1\n2 2 1",
"18 0\n2 0 1\n-1 2 1",
"18 0\n2 1 1\n0 1 1",
"18 1\n2 0 1\n1 1 1",
"18 0\n4 0 1\n0 1 1",
"0 0\n1 -1 1\n0 1 1",
"0 0\n2 -1 1\n0 2 2",
"0 0\n2 0 0\n1 2 1",
"0 0\n2 0 2\n1 2 0",
"0 0\n4 0 2\n1 2 1",
"2 0\n2 0 2\n1 2 0",
"2 0\n0 0 2\n2 2 0",
"1 0\n0 1 2\n2 2 0",
"1 0\n0 0 2\n4 3 0",
"1 1\n0 0 2\n4 3 0",
"1 1\n1 0 4\n2 3 -1",
"1 1\n1 0 4\n2 0 -1",
"1 1\n1 0 4\n0 0 0",
"1 1\n1 0 4\n0 -1 0",
"1 0\n1 0 7\n4 -1 0",
"2 1\n1 0 7\n4 0 0",
"10 3\n2 3 2\n3 5 1",
"10 0\n2 2 1\n1 6 1",
"34 0\n3 3 1\n1 5 1",
"18 0\n2 0 2\n0 5 1",
"18 0\n2 0 1\n2 2 0",
"18 1\n2 1 1\n0 1 1",
"18 1\n2 0 2\n1 1 1",
"8 0\n2 1 1\n0 3 1",
"18 0\n4 0 2\n0 1 1",
"0 0\n1 -1 1\n-1 1 1",
"0 0\n2 0 1\n0 2 1",
"0 0\n2 0 0\n1 3 1",
"1 0\n4 0 2\n1 2 0",
"0 0\n4 0 3\n1 2 1",
"2 0\n2 0 2\n0 2 0",
"2 0\n0 0 2\n2 2 1",
"1 0\n0 0 2\n3 2 0",
"1 0\n0 0 2\n4 4 0",
"1 1\n0 0 2\n7 3 0",
"1 1\n1 0 0\n2 3 -1"
],
"output": [
"6",
"1",
"8",
"6\n",
"5\n",
"10\n",
"18\n",
"0\n",
"1\n",
"2\n",
"9\n",
"34\n",
"8\n",
"4\n",
"30\n",
"14\n",
"15\n",
"23\n",
"7\n",
"27\n",
"43\n",
"16\n",
"19\n",
"31\n",
"3\n",
"13\n",
"25\n",
"35\n",
"22\n",
"12\n",
"29\n",
"24\n",
"21\n",
"6\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"6\n",
"6\n",
"5\n",
"10\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"18\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"6\n",
"10\n",
"34\n",
"18\n",
"18\n",
"18\n",
"18\n",
"8\n",
"18\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem
Aizu Magic School is a school where people who can use magic gather. Haruka, one of the students of that school, can use the magic of warp on the magic team.
From her house to the school, there is a straight road of length L. There are also magic circles on this road.
She uses this road every day to go to school, so she wants to get to school in the shortest possible time.
So as a programmer, you decided to teach her the minimum amount of time it would take to get to school.
Haruka can walk forward by a distance of 1 in 1 minute (* cannot go back). Also, by casting magic at the position Pi where the magic circle of the warp is written, you can move in Ti minutes to the place just Di from Pi. Even if there is a magic circle at the destination, it will be continuous. You can use warp magic.
The location of her house is 0 and the location of her school is L.
Constraints
The input meets the following conditions.
* All numbers given are integers
* 1 ≤ L ≤ 109
* 0 ≤ n ≤ min (103, L) (min represents the smaller of A and B)
* 0 ≤ Pi ≤ L -1
* 0 ≤ Di ≤ L --Pi
* 0 ≤ Ti ≤ 103
* Pi ≠ Pj
Input
L n
P1 D1 T1
P2 D2 T2
..
..
Pn Dn Tn
The first line is given the length of the road L, the number of magic circles n. Next, the state of n magic circles is given. Pi is the position where the i-th magic circle is, and Di is the i-th magic circle. Distance to warp from, Ti represents the time it takes to warp using the i-th magic circle.
Output
Output the minimum time to get to school in one line.
Examples
Input
10 3
2 2 1
4 2 1
8 1 1
Output
8
Input
10 2
2 3 1
3 5 1
Output
6
Input
1 0
Output
1
### Input:
10 2
2 3 1
3 5 1
### Output:
6
### Input:
1 0
### Output:
1
### Code:
INF = 10 ** 20
l, n = map(int, input().split())
lst = [list(map(int, input().split())) for _ in range(n)] + [[l, 0, INF]]
lst.sort()
score = {}
for p, _, _ in lst:
score[p] = p
for i in range(n + 1):
p, d, t = lst[i]
for j in range(i + 1, n + 1):
to_p, _, _ = lst[j]
if to_p >= p + d:
score[to_p] = min(score[to_p], score[p] + t + to_p - p - d, score[p] + to_p - p)
else:
score[to_p] = min(score[to_p], score[p] + to_p - p)
print(score[l])
|
p01290 Queen's Case_3284 | A small country called Maltius was governed by a queen. The queen was known as an oppressive ruler. People in the country suffered from heavy taxes and forced labor. So some young people decided to form a revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into the entrance.
Your task is to write a program to determine whether the queen can escape or will be caught by the army.
Here is detailed description.
* The palace can be considered as grid squares.
* The queen and the army move alternately. The queen moves first.
* At each of their turns, they either move to an adjacent cell or stay at the same cell.
* Each of them must follow the optimal strategy.
* If the queen and the army are at the same cell, the queen will be caught by the army immediately.
* If the queen is at any of exit cells alone after the army’s turn, the queen can escape from the army.
* There may be cases in which the queen cannot escape but won’t be caught by the army forever, under their optimal strategies.
Hint
On the first sample input, the queen can move to exit cells, but either way the queen will be caught at the next army’s turn. So the optimal strategy for the queen is staying at the same cell. Then the army can move to exit cells as well, but again either way the army will miss the queen from the other exit. So the optimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won’t be caught.
Input
The input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 ≤ W ≤ 30) and H (1 ≤ H ≤ 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. "Q" indicates the queen, "A" the army,"E" an exit,"#" a wall and "." a floor.
The map contains exactly one "Q", exactly one "A" and at least one "E". You can assume both the queen and the army can reach all the exits.
The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.
Output
For each dataset, output "Queen can escape.", "Army can catch Queen." or "Queen can not escape and Army can not catch Queen." in a line.
Examples
Input
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
####.
..E..
.####
....Q
0 0
Output
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen.
Input
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
.
..E..
.####
....Q
0 0
Output
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen. | from collections import deque, defaultdict
import sys
readline = sys.stdin.readline
write = sys.stdout.write
dd = ((-1, 0), (0, -1), (1, 0), (0, 1), (0, 0))
def solve():
W, H = map(int, readline().split())
if W == H == 0:
return False
S = [readline().strip() for i in range(H)]
px = py = qx = qy = 0
rs = []
pp = []
MP = [[0]*W for i in range(H)]
for i in range(H):
for j, c in enumerate(S[i]):
if c == "Q":
px = j; py = i
elif c == "A":
qx = j; qy = i
elif c == "E":
MP[i][j] = 1
rs.append((j, i))
elif c == "#":
MP[i][j] = 2
if c != "#":
pp.append((j, i))
mp = {}
L = 0
for ax, ay in pp:
for bx, by in pp:
mp[ax, ay, bx, by, 0] = L
L += 1
mp[ax, ay, bx, by, 1] = L
L += 1
que1 = deque()
ss = [-1]*L
cc = [0]*L
que = deque([(px, py, qx, qy, 0)])
used = [0]*L
used[mp[px, py, qx, qy, 0]] = 1
RG = [[] for i in range(L)]
deg = [0]*L
while que:
ax, ay, bx, by, t = key = que.popleft()
k0 = mp[key]
if ax == bx and ay == by:
que1.append(k0)
ss[k0] = 1
continue
if t == 0 and MP[ay][ax] == 1:
que1.append(k0)
ss[k0] = 0
continue
if t == 1:
for dx, dy in dd:
nx = bx + dx; ny = by + dy
if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:
continue
k1 = mp[ax, ay, nx, ny, t^1]
deg[k0] += 1
RG[k1].append(k0)
if not used[k1]:
used[k1] = 1
que.append((ax, ay, nx, ny, t^1))
else:
for dx, dy in dd:
nx = ax + dx; ny = ay + dy
if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:
continue
k1 = mp[nx, ny, bx, by, t^1]
deg[k0] += 1
RG[k1].append(k0)
if not used[k1]:
used[k1] = 1
que.append((nx, ny, bx, by, t^1))
while que1:
v = que1.popleft()
s = ss[v]; t = v % 2
if t == 0:
for w in RG[v]:
if ss[w] != -1:
continue
if s == 1:
que1.append(w)
ss[w] = 1
else:
deg[w] -= 1
if deg[w] == 0:
que1.append(w)
ss[w] = 0
else:
for w in RG[v]:
if ss[w] != -1:
continue
if s == 0:
que1.append(w)
ss[w] = 0
else:
deg[w] -= 1
if deg[w] == 0:
que1.append(w)
ss[w] = 1
k0 = mp[px, py, qx, qy, 0]
if ss[k0] == -1:
write("Queen can not escape and Army can not catch Queen.\n")
elif ss[k0] == 0:
write("Queen can escape.\n")
else:
write("Army can catch Queen.\n")
return True
while solve():
...
| {
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"2 2\nQE\nAD\n2 1\nQAE\n3 1\nAEQ\n10 5\n..E..\n.###.\nA#$#Q\n.###.\n..E..\n10 1\n..EQA\n5 5\nA....\n.\n.E...\n.####\n....Q\n0 0",
"2 2\nQE\nAD\n2 1\nQAE\n3 1\nAEQ\n10 5\n..E..\n.###.\nA#$#Q\n.###.\n..E..\n10 1\n..EQA\n5 5\nA....\n.\n.E...\n.####\nQ....\n0 0",
"4 2\nQE\nAD\n2 1\nQAE\n3 1\nAEQ\n10 5\n..E..\n.###.\nA#$#Q\n.###.\n..E..\n10 1\n..EQA\n5 5\nA....\n.\n.E...\n.####\n....Q\n0 0",
"4 2\nQE\nAD\n2 1\nQAE\n3 1\nQEA\n10 5\n..E..\n.###.\nA#$#Q\n.###.\n..E..\n10 1\n..EQA\n5 5\nA....\n.\n.E...\n.####\n....Q\n0 0",
"4 2\nQE\nAD\n2 1\nQAE\n3 1\nQEA\n10 5\n..E..\n.###.\nA#$#Q\n.###.\n..E..\n10 1\n..EQA\n5 5\n....A\n.\n.E...\n.####\n....Q\n0 0",
"4 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0",
"4 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA\"##Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nEQ\nEA\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n##A#Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n##A#Q\n.#.##\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n....E\n.####\n....Q\n0 0",
"2 2\nQE\nAE\n3 1\nQAE\n6 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA..-.\n.\nE....\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nAQE\n11 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nAQE\n10 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n..Q..\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nAQE\n10 5\n..E..\n.#$#.\nA###Q\n.###.\n..E..\n5 1\nQ.E.A\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nEQA\n5 5\n..E..\n.###.\nA\"##Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"3 2\nEQ\nEA\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n##A#Q\n.#.##\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nEQ\nAE\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nAE\n3 1\nQAE\n5 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA..-.\n.\nE....\n.####\n....Q\n0 0",
"2 2\nEQ\nEA\n3 1\nQAE\n3 1\nAQD\n5 5\n..E..\n.###.\nA##\"Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA/...\n.\nE....\n.####\n....Q\n0 0",
"2 2\nQE\nAE\n3 1\nEAQ\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA.--.\n.\nE....\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nEQA\n10 5\n..E-.\n###..\nA###Q\n###..\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"3 2\nQE\nAE\n3 1\nQAF\n3 1\nAQD\n5 5\n..E..\n.###.\nA###Q\n.###.\n.-.E.\n6 1\nA.E.Q\n5 5\nA....\n.\nE....\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n@###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA.-..\n.\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nAE\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n##A#Q\n.#.##\n..E..\n5 1\n..EAQ\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n6 1\nAQE\n10 5\n..E..\n.##\".\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n..E..\n.####\n....Q\n0 0",
"2 2\nEQ\nEA\n2 1\nQAE\n3 1\nAQE\n10 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nQ.E.A\n5 5\nA.-..\n.\n.E...\n.####\n....Q\n0 0",
"2 2\nEQ\nAE\n3 1\nQAE\n2 1\nAQD\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\nE./..\n.####\n....Q\n0 0",
"1 2\nQD\nAE\n3 1\nQAE\n3 1\nAQE\n5 5\nE....\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA../.\n.\nE....\n.####\n....Q\n0 0",
"2 2\nEQ\nEA\n3 1\nEAQ\n3 1\nDQA\n6 5\n....E\n.###.\nA##\"Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\nE....\n.####\n....Q\n0 0",
"7 2\nQE\nEA\n3 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA....\n.\n..E..\n.####\n....Q\n0 0",
"2 2\nQE\nEA\n2 1\nQAE\n3 1\nAQE\n5 5\n..E..\n.###.\n\"#A#Q\n.#.##\n..E..\n5 1\nA.E.Q\n5 5\nA....\n-\n....E\n.####\n....Q\n0 0",
"2 2\nQE\nAE\n3 1\nEAQ\n6 1\nAQE\n5 5\n..E..\n.###.\nA###Q\n.###.\n..E..\n5 1\nA.E.Q\n5 5\nA..-.\n.\nE....\n.####\n....Q\n0 0"
],
"output": [
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\n",
"Army can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nQueen can escape.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nQueen can escape.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\n",
"Queen can escape.\nQueen can escape.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nQueen can escape.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Army can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Army can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Army can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nQueen can escape.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Army can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nQueen can escape.\nQueen can escape.\nArmy can catch Queen.\nArmy can catch Queen.\n",
"Queen can escape.\nArmy can catch Queen.\nQueen can escape.\nQueen can not escape and Army can not catch Queen.\nArmy can catch Queen.\nArmy can catch Queen.\n"
]
} | 6AIZU
| Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A small country called Maltius was governed by a queen. The queen was known as an oppressive ruler. People in the country suffered from heavy taxes and forced labor. So some young people decided to form a revolutionary army and fight against the queen. Now, they besieged the palace and have just rushed into the entrance.
Your task is to write a program to determine whether the queen can escape or will be caught by the army.
Here is detailed description.
* The palace can be considered as grid squares.
* The queen and the army move alternately. The queen moves first.
* At each of their turns, they either move to an adjacent cell or stay at the same cell.
* Each of them must follow the optimal strategy.
* If the queen and the army are at the same cell, the queen will be caught by the army immediately.
* If the queen is at any of exit cells alone after the army’s turn, the queen can escape from the army.
* There may be cases in which the queen cannot escape but won’t be caught by the army forever, under their optimal strategies.
Hint
On the first sample input, the queen can move to exit cells, but either way the queen will be caught at the next army’s turn. So the optimal strategy for the queen is staying at the same cell. Then the army can move to exit cells as well, but again either way the army will miss the queen from the other exit. So the optimal strategy for the army is also staying at the same cell. Thus the queen cannot escape but won’t be caught.
Input
The input consists of multiple datasets. Each dataset describes a map of the palace. The first line of the input contains two integers W (1 ≤ W ≤ 30) and H (1 ≤ H ≤ 30), which indicate the width and height of the palace. The following H lines, each of which contains W characters, denote the map of the palace. "Q" indicates the queen, "A" the army,"E" an exit,"#" a wall and "." a floor.
The map contains exactly one "Q", exactly one "A" and at least one "E". You can assume both the queen and the army can reach all the exits.
The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.
Output
For each dataset, output "Queen can escape.", "Army can catch Queen." or "Queen can not escape and Army can not catch Queen." in a line.
Examples
Input
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
####.
..E..
.####
....Q
0 0
Output
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen.
Input
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
.
..E..
.####
....Q
0 0
Output
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen.
### Input:
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
.
..E..
.####
....Q
0 0
### Output:
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen.
### Input:
2 2
QE
EA
3 1
QAE
3 1
AQE
5 5
..E..
.###.
A###Q
.###.
..E..
5 1
A.E.Q
5 5
A....
####.
..E..
.####
....Q
0 0
### Output:
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Queen can escape.
Queen can not escape and Army can not catch Queen.
Army can catch Queen.
Army can catch Queen.
### Code:
from collections import deque, defaultdict
import sys
readline = sys.stdin.readline
write = sys.stdout.write
dd = ((-1, 0), (0, -1), (1, 0), (0, 1), (0, 0))
def solve():
W, H = map(int, readline().split())
if W == H == 0:
return False
S = [readline().strip() for i in range(H)]
px = py = qx = qy = 0
rs = []
pp = []
MP = [[0]*W for i in range(H)]
for i in range(H):
for j, c in enumerate(S[i]):
if c == "Q":
px = j; py = i
elif c == "A":
qx = j; qy = i
elif c == "E":
MP[i][j] = 1
rs.append((j, i))
elif c == "#":
MP[i][j] = 2
if c != "#":
pp.append((j, i))
mp = {}
L = 0
for ax, ay in pp:
for bx, by in pp:
mp[ax, ay, bx, by, 0] = L
L += 1
mp[ax, ay, bx, by, 1] = L
L += 1
que1 = deque()
ss = [-1]*L
cc = [0]*L
que = deque([(px, py, qx, qy, 0)])
used = [0]*L
used[mp[px, py, qx, qy, 0]] = 1
RG = [[] for i in range(L)]
deg = [0]*L
while que:
ax, ay, bx, by, t = key = que.popleft()
k0 = mp[key]
if ax == bx and ay == by:
que1.append(k0)
ss[k0] = 1
continue
if t == 0 and MP[ay][ax] == 1:
que1.append(k0)
ss[k0] = 0
continue
if t == 1:
for dx, dy in dd:
nx = bx + dx; ny = by + dy
if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:
continue
k1 = mp[ax, ay, nx, ny, t^1]
deg[k0] += 1
RG[k1].append(k0)
if not used[k1]:
used[k1] = 1
que.append((ax, ay, nx, ny, t^1))
else:
for dx, dy in dd:
nx = ax + dx; ny = ay + dy
if not 0 <= nx < W or not 0 <= ny < H or MP[ny][nx] == 2:
continue
k1 = mp[nx, ny, bx, by, t^1]
deg[k0] += 1
RG[k1].append(k0)
if not used[k1]:
used[k1] = 1
que.append((nx, ny, bx, by, t^1))
while que1:
v = que1.popleft()
s = ss[v]; t = v % 2
if t == 0:
for w in RG[v]:
if ss[w] != -1:
continue
if s == 1:
que1.append(w)
ss[w] = 1
else:
deg[w] -= 1
if deg[w] == 0:
que1.append(w)
ss[w] = 0
else:
for w in RG[v]:
if ss[w] != -1:
continue
if s == 0:
que1.append(w)
ss[w] = 0
else:
deg[w] -= 1
if deg[w] == 0:
que1.append(w)
ss[w] = 1
k0 = mp[px, py, qx, qy, 0]
if ss[k0] == -1:
write("Queen can not escape and Army can not catch Queen.\n")
elif ss[k0] == 0:
write("Queen can escape.\n")
else:
write("Army can catch Queen.\n")
return True
while solve():
...
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