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
/**
 * @(#)Triang.java
 *
 *
 * @author Joshua P. Rarama
 * @version 1.00 2012/1/20
 */

import java.util.Scanner;

public class Triang {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int x=sc.nextInt();
        int ctr=0;
        int i=0;
        while(i<x){
        	i+= ++ctr;
        }
        
        System.out.println( x==i?"YES":"NO");
    }
}
