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 main() {
  ios::sync_with_stdio(0), ios_base::sync_with_stdio(0), cin.tie(0),
      cout.tie(0);
  ;
  int x = 1, l[35], f;
  l[0] = 0;
  for (int m = 1; m < 33; m++) {
    l[m] = (m * (m + 1)) / 2;
  }
  cin >> f;
  for (int z = 1; z < 34; z++) {
    if (l[z] == f) {
      cout << "YES";
      return 0;
    } else if (l[z] > f) {
      cout << "NO";
      return 0;
    }
  }
}
