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
/**
 * Created with IntelliJ IDEA.
 * User: akashm
 * Date: 6/21/13
 * Time: 2:58 PM
 * To change this template use File | Settings | File Templates.
 */
import java.util.*;

public class A47 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int tn = in.nextInt();
        int a = 1;
        int b = 1;
        int c = 2 * tn * -1;
        double disc = Math.sqrt(Math.pow(b, 2) - 4 * a * c);
        if (disc - Math.floor(disc) != 0) {
            System.out.println("NO");
            return;
        }
        int d = (int) disc;
        System.out.println(d >= 0 ? "YES" : "NO");
    }
}
