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;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long long maxn = 3e5;
const long long mod = 1e9 + 7;
const long double PI = 4 * atan((long double)1);
long long pw(long long a, long long b, long long md = mod) {
  long long res = 1;
  while (b) {
    if (b & 1) {
      res = (a * res) % mod;
    }
    a = (a * a) % mod;
    b >>= 1;
  }
  return (res);
}
int n;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    if (i * (i + 1) == n * 2) {
      cout << "YES";
      return (0);
      ;
    }
  }
  cout << "NO";
  return (0);
}
