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 boolean loadValues(int n){
        if(n==0)
            return true;
        boolean found=false;
        int prev=0;
        for (int i=1;prev<=n;i++){
            if(prev==n){
                found=true;
                break;
            }
            int tp=prev+i;
            prev=tp;
        }
        return found;
    }
    public static void main(String q[]){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        if(loadValues(n))
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}
