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 Ten {

    
    public static void main(String[] args) {
        Scanner sc=new Scanner (System.in);
        int n=sc.nextInt();
        
        int i=0;
        boolean found=false;
        int x=0;
        while(n>=x){
            x=(int)((i*(i+1))/2);
            if(n==x){
                System.out.println("YES");
                found=true;
                break;
            }
            i++;    
        }
        
        if(!found)
            System.out.println("NO");
        
    }
}