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
#include <bits/stdc++.h>
using namespace std;
int n, num, x = 500;
bool isTriangular(int num) {
  if (num < 0) return false;
  int sum = 0;
  for (int n = 1; sum <= num; n++) {
    sum = sum + n;
    if (sum == num) return true;
  }
  return false;
}
int main() {
  cin >> n;
  if (isTriangular(n))
    cout << "YES";
  else
    cout << "NO";
  return 0;
}
