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.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 *
 * @author jimmy
 */
public class Problem47A {
     public static void main(String arguments[]) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        List<Integer> mas = new ArrayList<Integer>();
        for(int i = 1; i < 501; i++) {
            mas.add(i * (i + 1) / 2);
        }

        if(mas.contains(n)) System.out.println("YES");
        else System.out.println("NO");
     }
}
