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
from __future__ import division
poids =  input().split(" ")
a = int(poids[0])
b="NO"
n=1
if(a==0):
    b="NO"
    n=555

while n<=500:
    c=n*(n+1)/2
    if(c==a):
        print("YES")
        b="YES"
        break
    else:
        n=n+1
    
if(b=="NO"):
    print("NO")
        
        

        
