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) {
		Scanner s=new Scanner(System.in);
		double x1,x2,x3,y1,y2,y3,xp,yp;
		double px[]=new double[2];
		double py[]=new double[2];
		double ans[]=new double[3];
		int i;
		while(s.hasNext()){
			x1=s.nextDouble();
			y1=s.nextDouble();
			x2=s.nextDouble();
			y2=s.nextDouble();
			x3=s.nextDouble();
			y3=s.nextDouble();
			xp=s.nextDouble();
			yp=s.nextDouble();

			px[0]=x2-x1;py[0]=y2-y1;
			px[1]=xp-x1;py[1]=yp-y1;
			ans[0]=px[0]*py[1]-py[0]*px[1];

			px[0]=x3-x2;py[0]=y3-y2;
			px[1]=xp-x2;py[1]=yp-y2;
			ans[1]=px[0]*py[1]-py[0]*px[1];

			px[0]=x1-x3;py[0]=y1-y3;
			px[1]=xp-x3;py[1]=yp-y3;
			ans[2]=px[0]*py[1]-py[0]*px[1];

			if(ans[0]>0 && ans[1]>0 && ans[2]>0)
				System.out.println("YES");
			else if(ans[0]<0 && ans[1]<0 && ans[2]<0)
				System.out.println("YES");
			else{
				System.out.println("NO");
			}
		}//while
	}//main
}