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 long long MXN = 1e5 + 1;
const long long MNN = 1e3 + 1;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
const long double EPS = 1e-9;
const long double PI = 3.1415926536;
const string TIME = "rovno_ushten_push_ketti";
long long n, road_to_respa_bronze;
long long dp[MXN];
string ans[5] = {
    "NO",
    "YES",
};
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (long long i = 1; i <= 100; i++) {
    dp[road_to_respa_bronze + i] = 1;
    road_to_respa_bronze += i;
  }
  cout << ans[dp[n]];
  return 0;
}
