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 JavaStudy {
        static Scanner input = new Scanner(System.in) ;
    public static void main(String[] args){

        int n = input.nextInt() ;
        boolean m = false ;
        if (n < 0 ){
            System.out.println("NO");
        }
        int sum = 0 ;
        for (int i = 1 ; sum <= n ; i++){
            sum = sum + i ;
            if(sum == n){
                m = true ;
            }

        }
        if(m==true){
            System.out.println("YES") ;

        }
        else {
            System.out.println("NO") ;
        }






    }

    }




    
