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>
int main() {
  int n, i, m = 1;
  scanf("%d", &n);
  if (n == 1) {
    printf("YES");
  } else {
    for (i = 2;; i++) {
      m = m + i;
      if (n == m) {
        printf("YES");
        break;
      } else if (m < n) {
        continue;
      } else if (m > n) {
        printf("NO");
        break;
      }
    }
  }
}
