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
import math


class CodeforcesTask47ASolution:
    def __init__(self):
        self.result = ''
        self.n = 0

    def read_input(self):
        self.n = int(input())

    def process_task(self):
        x = (-1 + math.sqrt(1+8*self.n)) / 2
        if x.is_integer():
            self.result = "YES"
        else:
            self.result = "NO"

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask47ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
