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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class A {

	private void work() {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(
				System.in)));
		int n = sc.nextInt();
		int t = 1;
		while (t * (t + 1) / 2 < n)
			t++;
		System.out.println((t * (t + 1) / 2 == n) ? "YES" : "NO");
	}

	public static void main(String[] args) {
		new A().work();
	}

}
