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
{
	public static void main(String[] args) {
	    Scanner obj = new Scanner (System.in);
	int arr [] = {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496};
	int n = obj.nextInt();
	boolean f=false;
	for (int i=0;i<arr.length ;i++ ){
	    if(n==arr[i]){
	       System.out.println("YES");
	        f=true;
	        break;
	        
	    }
	} 
	if(!f)
	 System.out.println("NO");
	    
	}
}