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 Main
{
    static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
	    int k=sc.nextInt();
	    int n=1;
	    int tn=0;
	    boolean is=false;
	    while(tn<=k)
	    {
	        tn=(n*(n+1))/2;
	        if(tn==k)
	        {
	            is=true;
	            break;
	        }
	        n++;
	    }
	    if(is)
	    System.out.println("YES");
	    else
	    System.out.println("NO");
	}
	    
}