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;
import java.util.Set;
import java.util.HashSet;

public class Main {
	public static void main(String[] args) {
		try (Scanner in = new Scanner(System.in)) {
			Set<Integer> a = new HashSet<>();
     		for (int i = 0; i <= 1000; i++)
				a.add(i*(i+1)/2);

			int n = in.nextInt();

			if (a.contains(n)) 
				System.out.println("YES");
			else
				System.out.println("NO");
		} catch (Exception ex) {
			throw new RuntimeException(ex);
		}
	}
}
