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 trio[500];
void tri() {
  trio[1] = 1;
  for (int i = 2; i <= 500; i++) trio[i] = trio[i - 1] + i;
}
int main() {
  int n;
  cin >> n;
  tri();
  int i = 1;
  while (trio[i] <= n) {
    if (trio[i] == n) {
      cout << "YES";
      return 0;
    }
    i++;
  }
  cout << "NO";
  return 0;
}
