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;
vector<int> triangu;
int bBinaria(int mini, int maxi, int buscar) {
  if (maxi < mini) return false;
  int mitad = (maxi + mini) / 2;
  if (triangu[mitad] == buscar) return true;
  if (triangu[mitad] > buscar)
    return bBinaria(mini, mitad - 1, buscar);
  else
    return bBinaria(mitad + 1, maxi, buscar);
}
int main() {
  int n2;
  while (cin >> n2) {
    triangu.push_back(1);
    for (int i = 1; triangu[i - 1] < n2; i++) {
      triangu.push_back(triangu[i - 1] + i + 1);
    }
    if (bBinaria(0, triangu.size() - 1, n2)) {
      cout << "YES";
    } else {
      cout << "NO";
    }
    cout << endl;
  }
}
