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.IOException;
import java.util.Scanner;

public class Solutions {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		
		int d = 1 + 8*n;
		
		double x1 = (-1 + Math.sqrt(d))/2;
		if(Math.abs(x1 - Math.floor(x1))< 1E-10){
			System.out.println("YES");
		}else {
			System.out.println("NO");
		}
		
		
		sc.close();
	}
}
