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
# n^2 + n - x = 0]
# 1 - 1
# 2 - 3
# 3 - 6
# 4 - 10
# 5 - 15
# 6 - 21
# 7 - 28
# 8 - 36

from math import *

n = int(input())
x = 0
i = 1
while(n > x):
    x+=i
    i+=1
if (x == n):
    print("YES")
else:
    print("NO")
