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 ConsoleApplication1
{
    class Program
    {
        struct Point
        {
            internal double x, y;
        }

        static void Main(string[] args)
        {
            StringBuilder sb = new StringBuilder();

            string input;

            while (!string.IsNullOrEmpty(input = Console.ReadLine()))
            {
                double[] nums = Array.ConvertAll(input.Split(' '), double.Parse);

                Point a, b, c, p;
                a.x = nums[0]; a.y = nums[1];
                b.x = nums[2]; b.y = nums[3];
                c.x = nums[4]; c.y = nums[5];
                p.x = nums[6]; p.y = nums[7];

                sb.AppendLine(IsContain(a, b, c, p) ? "YES" : "NO");
            }
            Console.Write(sb);
        }

        static bool IsContain(Point a, Point b, Point c, Point p)
        {
            Point ab = Sub(b, a), bp = Sub(p, b);
            Point bc = Sub(c, b), cp = Sub(p, c);
            Point ca = Sub(a, c), ap = Sub(p, a);

            double c1 = Cross(ab, bp);
            double c2 = Cross(bc, cp);
            double c3 = Cross(ca, ap);

            if (c1 > 0 && c2 > 0 && c3 > 0) return true;
            if (c1 < 0 && c2 < 0 && c3 < 0) return true;

            return false;
        }

        static Point Sub(Point a, Point b)
        {
            Point ret;
            ret.x = a.x - b.x;
            ret.y = a.y - b.y;
            return ret;
        }

        static double Cross(Point a, Point b)
        {
            return a.x * b.y - a.y * b.x;
        }
    }
}