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/python

__author__="Guillermo Candia Huerta"
__date__ ="$07-12-2010 01:05:53 PM$"

def resolver(e):
    menos = 1
    
    while e > 0:
        e = e - menos
        menos = menos + 1
    if e == 0:
        return "YES"
    else:
        return "NO"

#    return r

if __name__ == "__main__":
    e = int(raw_input())
    r = resolver(e)
    print r
