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;

public class TriangularNumbers {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
        long num = in.nextLong();
        in.close();
        if(isTriangularNumber(num)){
        	System.out.println("YES");
        } else {
        	System.out.println("NO");
        }
        
	}
	
	public static boolean isTriangularNumber(long num) {
	     long calc_num = 8*num+1;
	     long t = (long) Math.sqrt(calc_num);
	     if (t*t==calc_num) {
	        return true;
	     }
	     return false;
	}

}