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() {
  long long int t = 1;
  while (t > 0) {
    t--;
    long long int n, k = 0, max = LONG_MIN, min = LONG_MAX, flag = 0, cnte = 0,
                     cnto = 0, ans = 0, gcd = 1;
    cin >> n;
    for (long long int i = 1; i <= n; i++) {
      if (n == ((i + 1) * i) / 2) {
        cout << "YES\n";
        flag = 1;
        break;
      }
    }
    if (flag == 0) cout << "NO\n";
  }
}
