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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main{
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        try {
            Double x1, x2, x3, y1, y2, y3, xp, yp;
            String line = br.readLine();
            while(line!=null) {
                StringTokenizer st = new StringTokenizer(line);
                x1 = Double.parseDouble(st.nextToken());
                y1 = Double.parseDouble(st.nextToken());
                x2 = Double.parseDouble(st.nextToken());
                y2 = Double.parseDouble(st.nextToken());
                x3 = Double.parseDouble(st.nextToken());
                y3 = Double.parseDouble(st.nextToken());
                xp = Double.parseDouble(st.nextToken());
                yp = Double.parseDouble(st.nextToken());
                Triangle tri = new Triangle(new Point(x1, y1), new Point(x2, y2), new Point(x3, y3));
                if(tri.hasPoint(xp,yp)){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
                line = br.readLine();
            }
        } catch (Exception e) {
            System.err.println();
        }
    }
}

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

class Triangle{
    Point A;
    Point B;
    Point C;
    double a,b,c;
    Triangle(Point A, Point B, Point C){
        this.A = A;
        this.B = B;
        this.C = C;
    }

    boolean hasPoint(double xp,double yp){
        double elementA,elementB,elementC,elementD,elementP,elementQ,s,t,detA;
        elementA = A.x-B.x;
        elementB = C.x-B.x;
        elementC = A.y-B.y;
        elementD = C.y-B.y;
        elementP = xp - B.x;
        elementQ = yp - B.y;
        detA = elementA*elementD - elementB*elementC;
        s=(elementD*elementP-elementB*elementQ)/detA;
        if(s <= 0 || 1 <= s){
            return false;
        }
        t=(-elementC*elementP+elementA*elementQ)/detA;
        if(t <= 0 || 1 <= t){
            return false;
        }
        if(0<s+t && s+t<1){
            return true;
        }
        return false;
    }
}