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 Main {
    public void number()
    {
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt();
        for(int i=1;i<=n;i++)
        {
            int a=((i*(i+1))/2);
            if(a==n)
            {
                System.out.println("YES");
                return;
            }
        }
        System.out.println("NO");
    }
    public static void main(String[] args) {
       
        Main t1=new Main();
        t1.number();
       
          
    }
    
}
