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>
const int MOD = 1e9 + 7;
const int MAX_VAL = 1e20 + 2;
const int INF = 0x3f3f3f3f;
using namespace std;
string s;
int t;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> t;
  for (int i = 1; i < 501; ++i)
    if (t == (i * (i + 1) / 2)) return cout << "YES\n", 0;
  cout << "NO\n";
  return 0;
}
