A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The n-th triangular number is the number of dots in a triangle with n dots on a side. <image>. You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).

Your task is to find out if a given integer is a triangular number.

Input

The first line contains the single number n (1 ≤ n ≤ 500) — the given integer.

Output

If the given integer is a triangular number output YES, otherwise output NO.

Examples

Input

1


Output

YES


Input

2


Output

NO


Input

3


Output

YES
#!/usr/bin/env python
# -*- coding: UTF-8 -*-
import time
import sys,io
import re,math
#start,=,time.clock()
n=input()
chk=[1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,253,276,300,
325,351,378,406,435,465,496,528,561,595,630,666,703,741,780,820,861,903,946,990,
1035,1081,1128,1176,1225,1275,1326,1378,1431,1485,1540,1596,1653,1711,1770,1830,
1891,1953,2016,2080,2145,2211,2278,2346,2415,2485,2556,2628,2701,2775,2850,2926,
3003,3081,3160,3240,3321,3403,3486,3570,3655,3741,3828,3916,4005,4095,4186,4278,
4371,4465,4560,4656,4753,4851,4950,5050,5151,5253,5356,5460,5565,5671,5778,5886,
5995,6105,6216,6328,6441,6555,6670,6786,6903,7021,7140,7260,7381,7503,7626,7750,
7875,8001,8128,8256,8385,8515,8646,8778,8911,9045,9180,9316,9453,9591,9730,9870,
10011,10153,10296,10440,10585,10731,10878,11026,11175,11325,11476,11628,11781,
11935,12090,12246,12403,12561,12720,12880,13041,13203,13366,13530,13695,13861,
14028,14196,14365,14535,14706,14878,15051,15225,15400,15576,15753,15931,16110,
16290,16471,16653,16836,17020,17205,17391,17578,17766,17955,18145,18336,18528,
18721,18915,19110,19306,19503,19701,19900,20100,20301,20503,20706,20910,21115,
21321,21528,21736,21945,22155,22366,22578,22791,23005,23220,23436,23653,23871,
24090,24310,24531,24753,24976,25200,25425,25651,25878,26106,26335,26565,26796,
27028,27261,27495,27730,27966,28203,28441,28680,28920,29161,29403,29646,29890,
30135,30381,30628,30876,31125,31375,31626,31878,32131,32385,32640,32896,33153,
33411,33670,33930,34191,34453,34716,34980,35245,35511,35778,36046,36315,36585,
36856,37128,37401,37675,37950,38226,38503,38781,39060,39340,39621,39903,40186,
40470,40755,41041,41328,41616,41905,42195,42486,42778,43071,43365,43660,43956,
44253,44551,44850,45150,45451,45753,46056,46360,46665,46971,47278,47586,47895,
48205,48516,48828,49141,49455,49770,50086,50403,50721,51040,51360,51681,52003,
52326,52650,52975,53301,53628,53956,54285,54615,54946,55278,55611,55945,56280,
56616,56953,57291,57630,57970,58311,58653,58996,59340,59685,60031,60378,60726,
61075,61425,61776,62128,62481,62835,63190,63546,63903,64261,64620,64980,65341,
65703,66066,66430,66795,67161,67528,67896,68265,68635,69006,69378,69751,70125,
70500,70876,71253,71631,72010,72390,72771,73153,73536,73920,74305,74691,75078,
75466,75855,76245,76636,77028,77421,77815,78210,78606,79003,79401,79800,80200,
80601,81003,81406,81810,82215,82621,83028,83436,83845,84255,84666,85078,85491,
85905,86320,86736,87153,87571,87990,88410,88831,89253,89676,90100,90525,90951,
91378,91806,92235,92665,93096,93528,93961,94395,94830,95266,95703,96141,96580,
97020,97461,97903,98346,98790,99235,99681,100128,100576,101025,101475,101926,
102378,102831,103285,103740,104196,104653,105111,105570,106030,106491,106953,
107416,107880,108345,108811,109278,109746,110215,110685,111156,111628,112101,
112575,113050,113526,114003,114481,114960,115440,115921,116403,116886,117370,
117855,118341,118828,119316,119805,120295,120786,121278,121771,122265,122760,
123256,123753,124251,124750,125250]
print 'YES' if n in chk else'NO'