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;
long long int a, b, c, d, e, f, n, m, x, k, l;
long long int arr1[10000001];
long long int summ, subb, divv, timm;
long long int cnt, ans, cnt1, ans1, cnt2, cnt3;
long double d1, d2, d3, d4, d5;
string s, s1, s2, s3, s4;
string s5 = "ZohidMirzoyev";
char cr[] = {"MirzoyevZohidjon"};
vector<long long int> v, v1, v2;
int main() {
  ;
  ios_base::sync_with_stdio(0);
  cin >> a;
  for (int i = 1; i <= a; i++) {
    if (i * (i + 1) / 2 == a) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
}
