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
# Codeforces Round 44 (Division 2)
# Problem A: Triangular Numbers

def isTriangular(n):
    t = 0
    for i in xrange(1,100):
        t += i
        if (t == n):
            return "YES"
        if (t > n):
            break
    return "NO"

n = raw_input("")
n = int(n)
print isTriangular(n)
