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.Linq;

namespace _012_APointinaTriangle
{
	class Program
	{
		static void Main ( string[] args )
		{
			string inputStr;

			while ((inputStr = Console.ReadLine ()) != null)
			{
				double[] numArray = inputStr.Split (' ').Select (str => double.Parse (str)).ToArray ();

				Vector2[] trianglePoint = new Vector2[3];
				trianglePoint[0] = new Vector2 (numArray[0], numArray[1]);
				trianglePoint[1] = new Vector2 (numArray[2], numArray[3]);
				trianglePoint[2] = new Vector2 (numArray[4], numArray[5]);

				Vector2 point = new Vector2 (numArray[6], numArray[7]);

				double result1 = Vector2.CrossProduct (trianglePoint[0], trianglePoint[1], point);
				double result2 = Vector2.CrossProduct (trianglePoint[1], trianglePoint[2], point);
				double result3 = Vector2.CrossProduct (trianglePoint[2], trianglePoint[0], point);

				bool isSameDirect = Math.Sign (result1) == Math.Sign (result2) && Math.Sign (result1) == Math.Sign (result3);

				if (isSameDirect)
					Console.WriteLine ("YES");
				else
					Console.WriteLine ("NO");
			}
		}
	}

	class Vector2
	{
		public Vector2 ( double x, double y )
		{
			this.X = x;
			this.Y = y;
		}

		public double X { private set; get; }
		public double Y { private set; get; }

		public static double CrossProduct ( Vector2 trianglePoint, Vector2 trianglePoint2, Vector2 point )
		{
			Vector2 subVector = new Vector2 (trianglePoint.X - trianglePoint2.X, trianglePoint.Y - trianglePoint2.Y);
			Vector2 distance = new Vector2 (point.X - trianglePoint.X, point.Y - trianglePoint.Y);

			return distance.X * subVector.Y - distance.Y * subVector.X;
		}
	}
}