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.Scanner;


public class main{

    
    public static void main(String[] args) {
       int n,k=0,m=1,p,q,r,t;
       Scanner in=new Scanner(System.in);
       t=in.nextInt();
       for(int i=1;i<=t;i++)
       {
           if(t>=k)
           {
               k=k+i;
               if(k==t)
               {
                   System.out.println("YES");
                    System.exit(0);
               }
               else if(k>t)
               {
                   System.out.println("NO");
                   System.exit(0);
               }
           }
       }
    }
    
}
