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 A47 {

    
    public static void main(String[] args) {
       Scanner input = new Scanner (System.in);
       int n;
       n=input.nextInt();
       int i=0;
       while(n > 0){
          
          n = n -i;
          
          if(n < 0){
              System.out.println("NO");
          }else if(n == 0){
              
              System.out.println("YES");
          }
          ++i;
      }
     
       
        
    }
    
}
