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;
double PI = acos(-1);
int arr[10000005];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n, m, T, res;
  int maxi = -(1 << 30) - 1, mini = (1 << 30) - 1, count = 0;
  int i, j, k;
  bool flag;
  string s1, s2;
  char s[100000];
  int ara[100005], ara2[100005];
  cin >> n;
  int sum = 0;
  i = 0;
  while (sum <= n) {
    sum += i;
    i++;
    if (sum == n) cout << "YES" << endl, exit(0);
  }
  cout << "NO" << endl;
}
