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 int a, b;
bool temp = false;
int main() {
  cin >> a;
  for (b = 1; b <= 500; b++)
    if ((b * (b + 1)) / 2 == a) {
      temp = true;
      break;
    }
  if (temp)
    cout << "YES";
  else
    cout << "NO";
  return 0;
}
