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>
double sqrt2(int m) {
  double sqrts = (10 + m / 10) / 2;
  for (int i = 0; i < 25; i++) {
    sqrts = (sqrts + m / sqrts) / 2;
  }
  return sqrts;
}
int main() {
  int t;
  scanf("%d", &t);
  int det = 1 - 4 * 1 * (-2 * t);
  double x1 = (-1 + sqrt2(det)) / 2;
  double x2 = (-1 - sqrt2(det)) / 2;
  if ((x1 == (int)x1 || x2 == (int)x2) && (x1 > 0 || x2 > 0)) {
    printf("YES");
  } else
    printf("NO");
}
