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 TriangularNo {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String tmp = String.format("%.2f", Math.sqrt(1 + 4 * 2 * n));
		boolean flag = true;
		if (Integer.valueOf(tmp.split("\\.")[1]) > 0) {
			flag = false;
		} else {
			int a = 0, b = 0;
			if (((Integer.valueOf(tmp.split("\\.")[0]) - 1) % 2 == 0) && ((Integer.valueOf(tmp.split("\\.")[0]) + 1) % 2 == 0)) {
				a = (Integer.valueOf(tmp.split("\\.")[0]) - 1) / 2;
				b = (Integer.valueOf(tmp.split("\\.")[0]) + 1) / 2;
				if (Math.abs(a-b)!=1){
					flag = false;
				}
			}else {
				flag = false;
			}
		}
		System.out.println(flag?"YES":"NO");
	}
}
