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_TriangularNumbers {

	public static void main(String[] args) {
		
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		String res = "";
		
		for (int i = 1 ; i <= n ; i++){
			if (n == i * (i+1) / 2 ) {
			res = "YES";
					break;
			}else{
				res = "NO";
			}

		}
		
		System.out.println(res);

	}

}
