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 TriangularNumber {

	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int sum = 0;
		String output="NO";

		for (int i = 1; i <=n; i++) {
			sum+=i;
			//System.out.println("sum = "+sum);
			if(sum==n) {
				output="YES";
				break;
			}
		}
		System.out.println(output);
		sc.close();
	}
}
