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;
void faster() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
int q, n, ar[456789], br[456789], d, k, sum;
string s, t;
void dii() {
  cin >> n;
  int i = 0, k = 1;
  while (i < n) {
    i += k;
    k++;
    if (i == n) {
      cout << "YES";
      return;
    }
  }
  cout << "NO";
}
int main() {
  faster();
  q = 1;
  while (q--) {
    dii();
  }
  return 0;
}
