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 python2
# -*- coding: utf-8 -*-
import sys
input = sys.stdin
output = sys.stdout

from math import sqrt

def is_triangle_number(x):
    D = 1+8*x
    d = int(sqrt(D))
    return d*d == D and (1+d) % 2 == 0

def solve(n):
    if is_triangle_number(n):
        return 'YES'
    else:
        return 'NO'

n = int(input.readline())
assert 1<=n and n<=500 

a = solve(n)
output.write('%s\n' % a)
