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.ArrayList;
import java.util.Scanner;

/**
 *
 * @author percy
 */
public class tri {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        ArrayList<Integer> t=new ArrayList();
        for (int i = 1; i <=500; i++) {
            t.add((i*(i+1))/2);
        }
        int n=in.nextInt();       
        String ans="NO";
        for (int i = 0; i < t.size(); i++) {
            if (n==t.get(i)) {
                ans="YES";
            }
        }
        System.out.println(ans);
    }
}