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.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		try {
		    Scanner sc = new Scanner(System.in);
	       int n,k;
	       double d;
	       n=sc.nextInt();
	       d=(Math.sqrt(1+8*n)-1)/2;
	       k=(int)(d);
	       if(d==k)
	        System.out.println("YES");
	        else
	        System.out.println("NO");
		 }catch(Exception e) {
		}
	}

}