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.Scanner;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author Ura
 */
public class _47A {

    public static void main(String... arg) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();

        Double d = -0.5 + 0.5 * Math.sqrt(1 + 8 * n);

        int jj = (int) Math.round(d);

        if (d - jj == 0) {
            System.out.print("YES");
        } else {
        System.out.print("NO");
        }


    }
}
