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;
const long long infll = powl(2, 62) - 1;
const long double pi = 4.0 * atanl(1.0);
const long long mod = powl(10, 9) + 7;
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  long long i = 0;
  while (true) {
    long long temp = i * (i + 1) / 2;
    if (temp == n) {
      cout << "YES\n";
      return 0;
    }
    if (temp > n) {
      cout << "NO\n";
      return 0;
    }
    i++;
  }
}
