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 Triangularnumbers
{
	public static void main(String[] args)
	{
		int n;
		boolean ok=false;
		Scanner input =new Scanner(System.in);
		n=input.nextInt();
		for(int i=1; i<=500; i++)
		{
			if((i*(i+1))/2==n)
				ok=true;
		}
		if(ok)
			System.out.print("YES");
		else
			System.out.print("NO");	
	}
}
