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: Accepted)

import java.util.*;
import java.io.*;
import static java.lang.Math.*;

class Point {

    double x;
    double y;

    Point( double x, double y ) {
	this.x = x;
	this.y = y;
    }
}

class Main {

    public static void main( final String[] args ) {

	final Scanner stdin = new Scanner( System.in );

	while ( stdin.hasNextDouble() ) {
	    Point[] in = new Point[4];
	    for ( int i = 0; i < 4; i++ ) {
		in[i] = new Point( stdin.nextDouble(), stdin.nextDouble() );
	    }
	    final double deg1 = degree( in[3], in[0], in[1] );
	    final double deg2 = degree( in[3], in[1], in[2] );
	    final double deg3 = degree( in[3], in[2], in[0] );
	    if ( abs( deg1 + deg2 + deg3 - 2 * PI ) < 1.0e-8 ) {
		System.out.println( "YES" );
	    } else {
		System.out.println( "NO" );
	    }
	}	
    }

    static double degree( Point p1, Point p2, Point p3 ) {
	double d12 = distance( p1, p2 );
	double d13 = distance( p1, p3 );
	double d23 = distance( p2, p3 );

	return acos( ( d12 * d12 + d13 * d13 - d23 *d23 ) / ( 2 * d12 * d13 ) );
    }
    
    static double distance( Point p1, Point p2 ) {
	return sqrt( pow( p1.x - p2.x, 2.0 ) + pow( p1.y - p2.y, 2.0 ) );
    }
}