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;
bool triangular[10000];
int formula(int n) { return (n * (n + 1)) / 2; }
int main() {
  for (int i = 0; i <= 100; i++) {
    triangular[formula(i)] = true;
  }
  int n;
  cin >> n;
  if (triangular[n]) {
    printf("YES\n");
  } else {
    printf("NO\n");
  }
  return 0;
}
