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() {
  string k, p;
  long long a, b, c[100000], d = 0, e = 0, f = 0, g, h, i, j, l, m, n, o, q, r,
                             s, t, u, v, w, x, y, z;
  cin >> a;
  b = sqrt(2 * a);
  for (i = 1; i <= b; i++) {
    d = d + i;
  }
  if (a == d) {
    cout << "YES";
  } else {
    cout << "NO";
  }
}
