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;
long long i, j, n, a, b, c, d, l, ll, r, s, t, k, m, xh, x, x1, y, z;
string p, q;
int main() {
  cin >> t;
  n = sqrt(2 * t);
  if (t == n * (n + 1) / 2)
    cout << "YES";
  else
    cout << "NO";
}
