Problem:
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A Point in a Triangle

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.

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.

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

Output

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

Sample 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 for the Sample Input

YES
NO

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.Scanner;


public class Main {
	Scanner sc;
	
	boolean solve(double[][] point){
		double[][] v=new double[3][2];
		for(int i=0;i<3;++i){
			for(int j=0;j<2;++j){
				v[i][j]=point[i][j]-point[3][j];
			}
		}
		double theta=0;
		for(int i=0;i<3;++i){
			double ip=(v[i][0]*v[(i+1)%3][0]+v[i][1]*v[(i+1)%3][1]);
			theta+=Math.acos(ip/Math.hypot(v[i][0],v[i][1])/Math.hypot(v[(i+1)%3][0],v[(i+1)%3][1]));
		}
		return theta>=Math.PI*2;
	}
	
	double nd(){
		return sc.nextDouble();
	}
	
	void io(){
		sc=new Scanner(System.in);
		double[][] point=new double[4][2];
		while(sc.hasNext()){
			for(int i=0;i<4;++i){
				for(int j=0;j<2;++j){
					point[i][j]=nd();
				}
			}
			System.out.println(solve(point)?"YES":"NO");
		}
	}
	
	public static void main(String[] args){
		new Main().io();
	}
}