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

def triangular():
    # print ("Input the number")
    _n = input()
    n = int(_n)
    tris = 1
    nexttoadd = 2
    while (tris <= n):
        if (tris == n):
            print ("YES")
            return
        else:
            tris = tris + nexttoadd
            nexttoadd = nexttoadd + 1
    print ("NO")

triangular()
        
