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 CF2
{
	public static void main(String[] args) throws Exception
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int expected = (int)Math.round(Math.sqrt(2*n+0.25)-0.5);
		System.out.println(expected*(expected+1)/2 == n ? "YES" : "NO");
		
		scan.close();
	}
}