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;
map<int, int> d;
int n;
void solve() {
  if (d[n] == 1)
    printf("YES\n");
  else
    printf("NO\n");
}
int main() {
  int i, tong;
  tong = 0;
  for (i = 0; tong <= 5000; i++) {
    tong += i;
    d[tong] = 1;
  }
  while (scanf("%d", &n) > 0) {
    solve();
  }
  return 0;
}
