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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		List<Integer> list = new ArrayList<Integer>();
		int arr[] = new int[502];
		arr[0] = 0;
		int x;
		for (int i = 1; i < arr.length; i++) {
			arr[i] = arr[i - 1] + i;
			list.add(arr[i]);

		}

		x = s.nextInt();
		if (list.contains(x))
			System.out.println("YES");
		else
			System.out.println("NO");

	}// main
}// class
