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 Triangle {

    /**
     * @param args
     */
    Scanner sc;
    int res;
    String c;
    public void go() {
        sc = new Scanner(System.in);
        c = "NO";
        int Th = sc.nextInt();
        for(int n = 1; n <= Th; n++) {
            if (n * (n + 1) / 2 == Th) {
                c = "YES";
                break;
            }
        }
        System.out.print(c);
    }
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Triangle start = new Triangle();
        start.go();
    }

}