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<long long> invi(long long n) {
  int x;
  vector<long long> a;
  for (long long i = 0; i < n; i++) {
    cin >> x;
    a.push_back(x);
  }
  return a;
}
void solve();
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  while (t--) solve();
}
void solve() {
  long long n;
  cin >> n;
  for (long long i = 1; 1 < n + 1 ? i < n + 1 : i > n + 1;
       1 < n + 1 ? i += 1 : i -= 1) {
    if ((i * (i + 1) / 2) == n) {
      cout << "YES\n";
      return;
    }
  }
  cout << "NO\n";
}
