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
"""(c) gorlum0 [at] gmail.com"""
from sys import stdin

for t in map(int, stdin):
    D = 1 + 8*t
    x = int((-1 + D**0.5) / 2)
    triangular = t == x*(x+1) // 2
    print 'YES' if triangular else 'NO'
