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.*;
import java.lang.*;

public class Main{
    public static void main(String [] args)
    {
        Scanner scan =new Scanner(System.in);
        int n=scan.nextInt();
        int sum=0;
        for (int i=1 ; i<= n ; i++ )
        {
            sum += i;
            if(sum==n)
            {
                System.out.println("YES");
                return ;
            }
        }
        System.out.println("NO");
    }
}