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;
inline long long read() {
  char c = getchar();
  long long f = 1, d = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    d = (d << 3) + (d << 1) + (c ^ 48);
    c = getchar();
  }
  return d * f;
}
int main() {
  long long n = read();
  long long ans = 0;
  for (register long long i = 1; i <= 999; ++i) {
    ans += i;
    if (ans == n) {
      cout << "YES";
      return 0;
    }
    if (ans > n) {
      cout << "NO";
      return 0;
    }
  }
  return 0;
}
