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 mm887
 */
public class TriangularNumbers {

    public static void main(String[] args) {
        
        Scanner input = new Scanner(System.in);
        long num = input.nextLong();
        for(int x=1; x<=500; x++){
            long remain = x*(x+1) / 2;
        if(remain == num){ 
            System.out.println("YES");
            return;
        }
        }
        System.out.println("NO");    
    }
}