Problem: Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.

In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.

Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.

You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.

Input

The input file consists of three lines, each of them contains a pair of numbers –– coordinates of the pillar. Any coordinate doesn't exceed 1000 by absolute value, and is given with at most six digits after decimal point.

Output

Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It's guaranteed that the number of angles in the optimal polygon is not larger than 100.

Examples

Input

0.000000 0.000000
1.000000 1.000000
0.000000 1.000000


Output

1.00000000

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class Main4 {
    
    static class Main {
        
        public Scanner sc;
        public final double EPS = 1e-5;
        
        class Vec2 {
            public double x, y;
            public Vec2(double _x, double _y) { x = _x; y = _y; }
            public Vec2() { x = y = 0.0; }
            public Vec2(Vec2 o) { x = o.x; y = o.y; }
            public Vec2 add(Vec2 o) { return new Vec2(x + o.x, y + o.y); }
            public Vec2 sub(Vec2 o) { return new Vec2(x - o.x, y - o.y); }
            public Vec2 mul(double k) { return new Vec2(x * k, y * k); }
            public Vec2 div(double k) { return new Vec2(x / k, y / k); }
            public double dot(Vec2 o) { return x * o.x + y * o.y; }
            public double cross(Vec2 o) { return x * o.y - o.x * y; }
            public double norm() { return x * x + y * y; }
            public double abs() { return Math.sqrt(norm()); }
            public void normalize() { double a = abs(); x /= a; y /= a; }
            public String toString() { return "(" + x + ", " + y + ")"; }
        }
        
        public Vec2 crosspoint(Vec2 p1, Vec2 p2, Vec2 q1, Vec2 q2) {
            double a = p2.sub(p1).cross(q2.sub(q1));
            double b = p2.sub(p1).cross(p2.sub(q1));
            return q1.add(q2.sub(q1).mul(b/a));
        }
        
        public Vec2 circumcenter2(Vec2 a, Vec2 b, Vec2 c) {
            Vec2 p1 = new Vec2(a.add(b).mul(0.5));
            Vec2 p2 = new Vec2(b.add(c).mul(0.5));
            Vec2 ab = b.sub(a), bc = c.sub(b);
            Vec2 abv = new Vec2(-ab.y, ab.x), bcv = new Vec2(-bc.y, bc.x);
            return crosspoint(p1, p1.add(abv), p2, p2.add(bcv));
        }
        
        public double arg(Vec2 p, Vec2 q) {
            return Math.acos(p.dot(q) / p.abs() / q.abs());
        }
        
        public boolean integer(double v) {
            return Math.abs(v - Math.floor(v + EPS)) < EPS;
        }
        
        public void run() {
            Vec2[] p = new Vec2[3];
            for (int i = 0; i < 3; i++)
                p[i] = new Vec2(sc.nextDouble(), sc.nextDouble());
            Vec2 c = circumcenter2(p[0], p[1], p[2]);
            for (int i = 0; i < 3; i++)
                p[i] = p[i].sub(c);
            double a1 = Math.abs(arg(p[0], p[1])), a2 = Math.abs(arg(p[2], p[1]));
            //System.err.println(a1 + " " + a2);
            for (int i = 3; i <= 100; i++) {
                double u = 2*Math.PI/(double)i;
                if (integer(a1/u) && integer(a2/u)) {
                    System.out.println(i * p[0].norm() * Math.sin(u) * 0.5);
                    break;
                }
            }
        }
        
    }
    
    public static void main(String[] args) {
        Main main = new Main();
        try { main.sc = new Scanner(new FileInputStream("test.in")); }
        catch (FileNotFoundException e) { main.sc = new Scanner(System.in); }
        main.run();
    }
    
}