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;

class Main
{
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		
		while (true)
		{
			double x1, y1, x2, y2, x3, y3, xp, yp;
			try
			{
				x1 = sc.nextDouble();
				y1 = sc.nextDouble();
				x2 = sc.nextDouble();
				y2 = sc.nextDouble();
				x3 = sc.nextDouble();
				y3 = sc.nextDouble();
				xp = sc.nextDouble();
				yp = sc.nextDouble();
			}
			catch (Exception e)
			{
				break;
			}
			
			if (!((f(x1, y1, x2, y2, x3) < y3 && f(x1, y1, x2, y2, xp) < yp)
				|| (f(x1, y1, x2, y2, x3) > y3 && f(x1, y1, x2, y2, xp) > yp)
			)) {
				System.out.println("NO");
				continue;
			}
			if (!((f(x2, y2, x3, y3, x1) < y1 && f(x2, y2, x3, y3, xp) < yp)
				|| (f(x2, y2, x3, y3, x1) > y1 && f(x2, y2, x3, y3, xp) > yp)
			)) {
				System.out.println("NO");
				continue;
			}
			if (!((f(x3, y3, x1, y1, x2) < y2 && f(x3, y3, x1, y1, xp) < yp)
				|| (f(x3, y3, x1, y1, x2) > y2 && f(x3, y3, x1, y1, xp) > yp)
			)) {
				System.out.println("NO");
				continue;
			}
			System.out.println("YES");
		}
	}
	private static double f(double x1, double y1, double x2, double y2, double x)
	{
		return (y1 - y2) / (x1 - x2) * (x - x1) + y1;
	}
}