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() {
  long long int a, i, j, sum = 0, k = 0;
  ;
  scanf("%lld", &a);
  for (i = 1; i < 50; i++) {
    for (j = 1; j <= i; j++) {
      sum = sum + 1;
    }
    if (sum == a) {
      k = 2;
      break;
    }
  }
  if (k == 2)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
