
"""simple docstring"""



import heapq
import sys

import numpy as np

UpperCAmelCase__          = tuple[int, int]

class       lowerCAmelCase__				:







     def __init__(							self			:			Union[str, Any]			):
       _snake_case					     =       []
       _snake_case					     =       set()







     def      lowercase	(							self			:			Union[str, Any]			):
       if not self.empty():
         return self.elements[0][0]
       else:
         return float('''inf'''			)







     def      lowercase	(							self			:			Optional[int]			):
       return len(self.elements			) == 0







     def      lowercase	(							self			:			Optional[Any]    ,      _lowerCamelCase			:			List[Any]    ,      _lowerCamelCase			:			Optional[int]			):
       if item not in self.set:
         heapq.heappush(self.elements    ,      (priority, item)			)
         self.set.add(_lowerCamelCase			)
       else:
         # update
         # print("update", item)
         _snake_case					     =       []
         ((_snake_case)     ,					(_snake_case))					     =       heapq.heappop(self.elements			)
         while x != item:
           temp.append((pri, x)			)
           ((_snake_case)     ,					(_snake_case))					     =       heapq.heappop(self.elements			)
         temp.append((priority, item)			)
         for pro, xxx in temp:
           heapq.heappush(self.elements    ,      (pro, xxx)			)







     def      lowercase	(							self			:			Dict    ,      _lowerCamelCase			:			Union[str, Any]			):
       if item in self.set:
         self.set.remove(_lowerCamelCase			)
         _snake_case					     =       []
         ((_snake_case)     ,					(_snake_case))					     =       heapq.heappop(self.elements			)
         while x != item:
           temp.append((pro, x)			)
           ((_snake_case)     ,					(_snake_case))					     =       heapq.heappop(self.elements			)
         for prito, yyy in temp:
           heapq.heappush(self.elements    ,      (prito, yyy)			)







     def      lowercase	(							self			:			int			):
       return self.elements[0][1]







     def      lowercase	(							self			:			Optional[Any]			):
       ((_snake_case)     ,					(_snake_case))					     =       heapq.heappop(self.elements			)
       self.set.remove(_lowerCamelCase			)
       return (priority, item)






def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos ,					__lowerCamelCase   :       TPos		)     ->					Tuple:
  # euclidean distance
  _snake_case					     =       np.array(__lowerCamelCase		)
  _snake_case					     =       np.array(__lowerCamelCase		)
  return np.linalg.norm(a - b		)
def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos ,					__lowerCamelCase   :       TPos		)     ->					Dict:
  # integer division by time variable
  return consistent_heuristic(__lowerCamelCase ,					__lowerCamelCase		) // t
def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos ,					__lowerCamelCase   :       TPos		)     ->					List[Any]:
  # manhattan distance
  return abs(p[0] - goal[0]		) + abs(p[1] - goal[1]		)
def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       TPos ,					__lowerCamelCase   :       dict[TPos, float]		)     ->					Optional[int]:
  _snake_case					     =       g_function[start] + Wa * heuristics[i](__lowerCamelCase ,					__lowerCamelCase		)
  return ans
def 					_UpperCAmelCase      ( __lowerCamelCase   :       Union[str, Any] ,					__lowerCamelCase   :       List[str] ,					__lowerCamelCase   :       Optional[int]		)     ->					Optional[Any]:
  _snake_case					     =       np.chararray((n, n)		)
  for i in range(__lowerCamelCase		):
    for j in range(__lowerCamelCase		):
      _snake_case					     =       '''*'''

  for i in range(__lowerCamelCase		):
    for j in range(__lowerCamelCase		):
      if (j, (n - 1) - i) in blocks:
        _snake_case					     =       '''#'''

  _snake_case					     =       '''-'''
  _snake_case					     =       back_pointer[goal]
  while x != start:
    ((_snake_case)     ,					(_snake_case))					     =       x
    # print(x)
    _snake_case					     =       '''-'''
    _snake_case					     =       back_pointer[x]
  _snake_case					     =       '''-'''

  for i in range(__lowerCamelCase		):
    for j in range(__lowerCamelCase		):
      if (i, j) == (0, n - 1):
        print(grid[i][j] ,					end=''' '''		)
        print('''<-- End position''' ,					end=''' '''		)
      else:
        print(grid[i][j] ,					end=''' '''		)
    print()
  print('''^'''		)
  print('''Start position'''		)
  print()
  print('''# is an obstacle'''		)
  print('''- is the path taken by algorithm'''		)
  print('''PATH TAKEN BY THE ALGORITHM IS:-'''		)
  _snake_case					     =       back_pointer[goal]
  while x != start:
    print(__lowerCamelCase ,					end=''' '''		)
    _snake_case					     =       back_pointer[x]
  print(__lowerCamelCase		)
  sys.exit()
def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos		)     ->					int:
  if p[0] < 0 or p[0] > n - 1:
    return False
  if p[1] < 0 or p[1] > n - 1:
    return False
  return True
def 					_UpperCAmelCase      ( __lowerCamelCase   :       Tuple ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       List[Any] ,					__lowerCamelCase   :       int ,					__lowerCamelCase   :       Any ,					__lowerCamelCase   :       Optional[Any] ,					__lowerCamelCase   :       str ,					__lowerCamelCase   :       Tuple ,					)     ->					Tuple:
  for itera in range(__lowerCamelCase		):
    open_list[itera].remove_element(__lowerCamelCase		)
  # print("s", s)
  # print("j", j)
  ((_snake_case)     ,					(_snake_case))					     =       s
  _snake_case					     =       (x - 1, y)
  _snake_case					     =       (x + 1, y)
  _snake_case					     =       (x, y + 1)
  _snake_case					     =       (x, y - 1)

  for neighbours in [left, right, up, down]:
    if neighbours not in blocks:
      if valid(__lowerCamelCase		) and neighbours not in visited:
        # print("neighbour", neighbours)
        visited.add(__lowerCamelCase		)
        _snake_case					     =       -1
        _snake_case					     =       float('''inf'''		)

      if valid(__lowerCamelCase		) and g_function[neighbours] > g_function[s] + 1:
        _snake_case					     =       g_function[s] + 1
        _snake_case					     =       s
        if neighbours not in close_list_anchor:
          open_list[0].put(__lowerCamelCase ,					key(__lowerCamelCase ,					0 ,					__lowerCamelCase ,					__lowerCamelCase		)		)
          if neighbours not in close_list_inad:
            for var in range(1 ,					__lowerCamelCase		):
              if key(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		) <= Wa * key(
                  __lowerCamelCase ,					0 ,					__lowerCamelCase ,					__lowerCamelCase		):
                open_list[j].put(
                    __lowerCamelCase ,					key(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		)		)
def 					_UpperCAmelCase      ( )     ->					Tuple:
  _snake_case					     =       []
  for x in range(1 ,					5		):
    for y in range(1 ,					6		):
      some_list.append((x, y)		)

  for x in range(15 ,					20		):
    some_list.append((x, 17)		)

  for x in range(10 ,					19		):
    for y in range(1 ,					15		):
      some_list.append((x, y)		)

    # L block
  for x in range(1 ,					4		):
    for y in range(12 ,					19		):
      some_list.append((x, y)		)
  for x in range(3 ,					13		):
    for y in range(16 ,					19		):
      some_list.append((x, y)		)
  return some_list


UpperCAmelCase__          = {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

UpperCAmelCase__          = [
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
UpperCAmelCase__          = make_common_ground()


UpperCAmelCase__          = blocks_blk
# hyper parameters
UpperCAmelCase__          = 1
UpperCAmelCase__          = 1
UpperCAmelCase__          = 20
UpperCAmelCase__          = 3  # one consistent and two other inconsistent

# start and end destination
UpperCAmelCase__          = (0, 0)
UpperCAmelCase__          = (n - 1, n - 1)

UpperCAmelCase__          = 1
def 					_UpperCAmelCase      ( __lowerCamelCase   :       TPos ,					__lowerCamelCase   :       TPos ,					__lowerCamelCase   :       int		)     ->					List[Any]:
  _snake_case					     =       {start: 0, goal: float('''inf'''		)}
  _snake_case					     =       {start: -1, goal: -1}
  _snake_case					     =       []
  _snake_case					     =       set()

  for i in range(__lowerCamelCase		):
    open_list.append(PriorityQueue()		)
    open_list[i].put(__lowerCamelCase ,					key(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		)		)

  _snake_case					     =       []
  _snake_case					     =       []
  while open_list[0].minkey() < float('''inf'''		):
    for i in range(1 ,					__lowerCamelCase		):
      # print(open_list[0].minkey(), open_list[i].minkey())
      if open_list[i].minkey() <= Wa * open_list[0].minkey():
        global t
        t += 1
        if g_function[goal] <= open_list[i].minkey():
          if g_function[goal] < float('''inf'''		):
            do_something(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		)
        else:
          _snake_case     ,					_snake_case					     =       open_list[i].top_show()
          visited.add(__lowerCamelCase		)
          expand_state(
              __lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					)
          close_list_inad.append(__lowerCamelCase		)
      else:
        if g_function[goal] <= open_list[0].minkey():
          if g_function[goal] < float('''inf'''		):
            do_something(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		)
        else:
          _snake_case					     =       open_list[0].top_show()
          visited.add(__lowerCamelCase		)
          expand_state(
              __lowerCamelCase ,					0 ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase ,					)
          close_list_anchor.append(__lowerCamelCase		)
  print('''No path found to goal'''		)
  print()
  for i in range(n - 1 ,					-1 ,					-1		):
    for j in range(__lowerCamelCase		):
      if (j, i) in blocks:
        print('''#''' ,					end=''' '''		)
      elif (j, i) in back_pointer:
        if (j, i) == (n - 1, n - 1):
          print('''*''' ,					end=''' '''		)
        else:
          print('''-''' ,					end=''' '''		)
      else:
        print('''*''' ,					end=''' '''		)
      if (j, i) == (n - 1, n - 1):
        print('''<-- End position''' ,					end=''' '''		)
    print()
  print('''^'''		)
  print('''Start position'''		)
  print()
  print('''# is an obstacle'''		)
  print('''- is the path taken by algorithm'''		)


if __name__ == "__main__":
 multi_a_star(start, goal, n_heuristic)





"""simple docstring"""



from math import sqrt
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int = 1_00_00_00		)     ->					int:
  _snake_case					     =       0
  _snake_case					     =       0
  _snake_case					     =       42

  while num_cuboids <= limit:
    max_cuboid_size += 1
    for sum_shortest_sides in range(2 ,					2 * max_cuboid_size + 1		):
      if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
        num_cuboids += (
            min(__lowerCamelCase ,					sum_shortest_sides // 2		)
            - max(1 ,					sum_shortest_sides - max_cuboid_size		)
            + 1
        )

  return max_cuboid_size


if __name__ == "__main__":
 print(F"{solution() = }")



