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 A_47 
{
    public static void main(String [] args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for(int i = 1; i <= n/2+1; i++)
        {
            if((i*(i+1))/2 == n)
            {
                System.out.println("YES");
                System.exit(0);
            }
        }
        System.out.println("NO");
    }
}