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;
using namespace chrono;
void solve() {
  long long n;
  cin >> n;
  long long st = 1;
  while ((st * (st + 1)) / 2 <= n) {
    if ((st * (st + 1)) / 2 == n) {
      cout << "YES" << endl;
      return;
    }
    ++st;
  }
  cout << "NO" << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto t1 = high_resolution_clock::now();
  long long test = 1;
  for (long long i = 0; i < test; i++) {
    solve();
  }
  auto t2 = high_resolution_clock::now();
  auto duration = duration_cast<milliseconds>(t2 - t1).count();
  return 0;
}
