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.io.PrintWriter;
import java.util.Scanner;

public class Main {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub

        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int a = in.nextInt();
        int b=1;
        for (int i=0;i<a+1;i++)
        {
            b=1;
            b*=i*(i+1)/2;
            if (a==b)
                {out.print("YES"); break;
                
                }
            if (b>a)
            {
                out.print("NO"); break;
            }
                
        }
            out.close();

    }

}
