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;

/**
 *
 * @author a
 */
public class Test12 {


    public static void main(String[] args) {
        
      Scanner x=new Scanner (System.in);
      int n =x.nextInt();
      
      double  d=0;
       
      d=(Math.sqrt(8*n+1)-1)/2;
      
      if (d%1==0)
            System.out.println("YES");
      
      else 
            System.out.println("NO");
    }
    
}
