There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.

Write a program which prints "YES" if a point $P$ $(x_p, y_p)$ is in the triangle and "NO" if not.

Constraints

You can assume that:

* $ -100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p \leq 100$
* 1.0 $\leq$ Length of each side of a tringle
* 0.001 $\leq$ Distance between $P$ and each side of a triangle

Input

Input consists of several datasets. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$


All the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.

Output

For each dataset, print "YES" or "NO" in a line.

Example

Input

0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5
0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0


Output

YES
NO
import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner stdIn = new Scanner(System.in);

		while(stdIn.hasNext()) {
			double x1, y1, x2, y2, x3, y3, px, py;
			x1 = stdIn.nextDouble();
			y1 = stdIn.nextDouble();
			x2 = stdIn.nextDouble();
			y2 = stdIn.nextDouble();
			x3 = stdIn.nextDouble();
			y3 = stdIn.nextDouble();
			px = stdIn.nextDouble();
			py = stdIn.nextDouble();

			double a = (x3 - x2) * (py - y2) - (y3 - y2) * (px - x2);
			double b = (x1 - x3) * (py - y3) - (y1 - y3) * (px - x3);
			double c = (x2 - x1) * (py - y1) - (y2 - y1) * (px - x1);

			if((a > 0 && b > 0 && c > 0) || (a < 0 && b < 0 && c < 0)) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
		}
	}
}