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 Codeforce 
{
  
 
    public static void main(String[] args)
    {
        Scanner s=new Scanner(System.in);
         int n=0;
         int T=s.nextInt();
         for(int i=1;(i*i)+i<=2*T;i++)
         {
             if(((i*i)+i)==2*T)
             {
                 n=i;
                 break;
             }
         }
         int count=0;
         
         for(int i=n;i>0;i--)
         {
             T-=i;
             count++;
             
         }
         if(count==n&&T==0)
             System.out.println("YES");
         else 
             System.out.println("NO");
       
    }
    
}
