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;
const int MAX = 600;
int t[MAX];
int main() {
  memset(t, 0, sizeof(t));
  int i = 0, n;
  while (1) {
    n = i * (i + 1) / 2;
    if (n >= MAX) break;
    t[n] = 1;
    i++;
  }
  scanf("%d", &n);
  if (t[n])
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}
