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;
import java.lang.Math;
public class TriangularNumbers{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int k;
        k=sc.nextInt();
        double z=2*(k)+0.25;
        double j=Math.sqrt(z);
        double h=j-0.5;
        if(h==(int)h){
            System.out.println("YES");
        }
        else{
           System.out.println("NO"); 
        }
}}