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;
using System.Threading.Tasks;

namespace _0012
{
    class Program
    {
        static void Main(string[] args)
        {
            string str;
            while ((str = Console.ReadLine()) != null)
            {
                string[] strList = str.Split(' ');
                double x1 = double.Parse(strList[0]);
                double y1 = double.Parse(strList[1]);
                double x2 = double.Parse(strList[2]);
                double y2 = double.Parse(strList[3]);
                double x3 = double.Parse(strList[4]);
                double y3 = double.Parse(strList[5]);
                double xp = double.Parse(strList[6]);
                double yp = double.Parse(strList[7]);
                double t = 0;
                double s = 0;
                if (x1 == x2)
                {
                    t = (((yp - y3) * (x2 - x3) - (xp - x3) * (y2 - y3)) / ((y1 - y3) * (x2 - x3) - (x1 - x3) * (y2 - y3)));
                    s = (((xp - x3) - t * (x1 - x3)) / (x2 - x3));
                }
                else
                {
                    t = (((yp - y1) * (x2 - x1) - (xp - x1) * (y2 - y1)) / ((y3 - y1) * (x2 - x1) - (x3 - x1) * (y2 - y1)));
                    s = (((xp - x1) - t * (x3 - x1)) / (x2 - x1));
                }
                if ((0 < s && s < 1) && (0 < t && t < 1) && (0 < 1 - s - t && 1 - s - t < 1))
                {
                    Console.WriteLine("YES");
                }
                else
                {
                    Console.WriteLine("NO");
                }

            }
        }
    }
}