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.*;
public class S
{
    public static void main(String args[])
    {
        Scanner scan =new Scanner(System.in);
        int n=scan.nextInt();
       int temp=1+(8*n);
          double u=Math.sqrt(temp);
          if(Math.ceil(u)==Math.floor(u))
          {
              if(((int)u+1)%2==0)
              System.out.println("YES");
              else
              System.out.println("NO");
          }
          else
          System.out.println("NO");
       
        
    }
}