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;

/**
 *
 * @author MasterEx
 */
public class P47A {
    
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        boolean t = (Math.sqrt(8*n + 1) - 1) % 2 == 0;
        if(t) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
    }
    
}
