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
import java.util.*;

public class Code {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int t = n * (n + 1) / 2;
        int d = 0;
        int v = 1;
        while (true) {
            d = n - v;
            if (d >= 0) {
                n -= v;
                if(n==0){
                    break;
                }
            } else {
                d = n + v;
                break;
            }
            v++;
        }
         
        if (n == d) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }

    }
}
