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 triangle
{
    public static void main(String args[])
    {
        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        int x=8*n+1; 
        double y=Math.floor(Math.sqrt(x));
        double z=Math.sqrt(x);; 
        if((z-y)==0)
        System.out.println("YES");
        else
        System.out.println("NO");
    }
}