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 binpow(long long int a, long long int b) {
  if (a == 0) return 0;
  if (b == 0) return 1;
  long long int ans = 1;
  while (b > 0) {
    if (b & 1) ans = ans * a;
    a = a * a;
    b = b >> 1;
  }
  return ans;
}
template <typename T>
T Min(T a, T b) {
  return a < b ? a : b;
}
template <typename T>
T Max(T a, T b) {
  return a > b ? a : b;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int e, f, g, h, i, j, k, l, n, o, p, q, r, x, y, z;
  cin >> n;
  map<int, int> m;
  for (int i = 0; i < (50); ++i) m[((i + 1) * (i + 2)) / 2] = 1;
  m[n] == 1 ? cout << "YES\n" : cout << "NO\n";
  return 0;
}
