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() {
  int n, sum = 0;
  cin >> n;
  int diff = 0;
  for (int i = 1; i <= 500; i++) {
    sum += i;
    if (sum == n) {
      diff = 1;
      break;
    }
  }
  if (diff == 1) {
    cout << "YES" << endl;
  } else {
    cout << "NO" << endl;
  }
  return 0;
}
