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

def triangle(n):
	return (n * (n + 1)) / 2

k = int(raw_input())

numbers = [False] * 600

i = 0
while triangle(i) <= 500:
	numbers[triangle(i)] = True
	i += 1

if numbers[k]:
	print 'YES'
else:
	print 'NO'
