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 TriangularNumber {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n=scan.nextInt();
		int c=1;
		int i=1;
		while(c<n) {
			i+=1;
			c+=i;
		}
		if(c==n) System.out.println("YES");
		else System.out.println("NO");
	}

}
