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 tamrini {
public static void main(String[] args) {
	Scanner scanner = new Scanner (System.in);
	int n = scanner.nextInt(),sum=0;
	boolean dool=false;
	for (int i=1;i<=n;i++) {
		sum+=i;
		if (n==sum) {
			System.out.println("YES");
			dool=true;
			break;
		}
	}
	if (dool==false) System.out.println("NO");
	scanner.close();
}
}