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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace mondai0012
{
	class Program
	{
		static void Main(string[] args)
		{
			while( true ) {
				var	s	= Console.ReadLine();
				if( s == null ) {
					break;
				}
				//var	ss	= s.Split( new char[ 0 ], StringSplitOptions.RemoveEmptyEntries );
				var	ss	= s.Split();
				var	x1	= double.Parse( ss[ 0 ] );
				var	y1	= double.Parse( ss[ 1 ] );
				var	x2	= double.Parse( ss[ 2 ] );
				var	y2	= double.Parse( ss[ 3 ] );
				var	x3	= double.Parse( ss[ 4 ] );
				var	y3	= double.Parse( ss[ 5 ] );
				var	xp	= double.Parse( ss[ 6 ] );
				var	yp	= double.Parse( ss[ 7 ] );

				var	org_area	= area_calc( x1, y1, x2, y2, x3, y3 );
				
				var	test_area	= area_calc( x1, y1, x2, y2, xp, yp );
					test_area	+= area_calc( x2, y2, x3, y3, xp, yp );
					test_area	+= area_calc( x3, y3, x1, y1, xp, yp );
				
				if( Math.Round( test_area, 10 ) <= Math.Round( org_area, 10 ) ) {
					Console.WriteLine( "YES" );
				} else {
					Console.WriteLine( "NO" );
				}
			}
		}

		static double area_calc( double x1, double y1, double x2, double y2, double x3, double y3 )
		{
			var	a	= Math.Sqrt( ((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2)) );
			var	b	= Math.Sqrt( ((x2 - x3) * (x2 - x3)) + ((y2 - y3) * (y2 - y3)) );
			var	c	= Math.Sqrt( ((x3 - x1) * (x3 - x1)) + ((y3 - y1) * (y3 - y1)) );
			var	s	= (a + b + c) / 2.0;
			return( Math.Sqrt( s * (s - a) * (s - b) * (s - c) ) );
		}
	}
}