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;
bool isPrime(long long int n) {
  if (n <= 1) return false;
  for (long long int i = 2; i * i < n; i++)
    if (n % i == 0) return false;
  return true;
}
signed main() {
  long long int t;
  cin >> t;
  vector<long long int> v;
  v.push_back(0);
  for (long long int i = 1; i < 40; i++) v.push_back(v[i - 1] + i);
  if (binary_search(v.begin(), v.end(), t))
    cout << "YES";
  else
    cout << "NO";
}
