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.math.BigDecimal;
import java.util.Scanner;

public class B2 {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub

        //System.out.println(getR(6,6,6));
        String input;
        Scanner scanner = new Scanner(System.in);
        Point a[] = new Point[3];
        
        for(int i = 0 ; i < 3 ; ++i)
        {
            input = scanner.nextLine();
            a[i] = processInput(input);
        }
        
        double[] lengts = new double[3];
        lengts[0] = Math.sqrt((a[1].x - a[2].x)*(a[1].x - a[2].x) + (a[1].y - a[2].y)*(a[1].y - a[2].y));
        lengts[1] = Math.sqrt((a[0].x - a[2].x)*(a[0].x - a[2].x) + (a[0].y - a[2].y)*(a[0].y - a[2].y));
        lengts[2] = Math.sqrt((a[1].x - a[0].x)*(a[1].x - a[0].x) + (a[1].y - a[0].y)*(a[1].y - a[0].y));
        //System.out.println(getAngle(5,4,3));
        
        double r = getR(lengts[0], lengts[1], lengts[2]);
        double angles[] = new double[3];
        angles[0] = getAngle(lengts[0], r, r);
        angles[1] = getAngle(lengts[1], r, r);
        angles[2] = getAngle(lengts[2], r, r);
        
        //System.out.println(angles[1]/Math.PI * 180);
        //System.out.println(Math.acos(Math.cos(180))/Math.PI * 180);
        
        
        double little = getDivisor(angles[0], getDivisor(angles[1],Math.PI * 2));
        //System.out.println(little);
        System.out.println(r * r * Math.sin(little)/2 * (2 * Math.PI /little));
    }
    
    private static double getDivisor(double a, double b) {
        // TODO Auto-generated method stub
        if(isOk(a))
            return b;
        if(isOk(b))
            return a;
        return getDivisor(b,a%b);
    }

    private static boolean isOk(double b) {
        // TODO Auto-generated method stub
        if(Math.abs(b) < 0.001)
            return true;
        return false;
    }

    private static Point processInput(String input) {
        // TODO Auto-generated method stub
        
        int index = input.indexOf(" ");
        double a = Double.parseDouble(input.substring(0, index));
        double b = Double.parseDouble(input.substring(index +1));
        return new Point(a,b);
    }

    private static double getR(double l1,double l2,double l3)
    {   
        double sin = getSin(l1, l2, l3);
        return l1/(2 * sin);
    }
    
    private static double getSin(double l1,double l2,double l3)
    {
        double cos = (l2 * l2 + l3*l3 - l1 *l1)/(2 * l2 * l3);
        double sin = Math.sqrt(1.0 - cos * cos);
        return sin;
    }
    
    private static double getAngle(double l1,double l2,double l3)
    {
        double cos = (l2 * l2 + l3*l3 - l1 *l1)/(2 * l2 * l3);  
        BigDecimal b = new BigDecimal(cos);
        double af  =  b.setScale(8,BigDecimal.ROUND_HALF_UP).doubleValue();
        double result = Math.acos(af); 
        return result;
    }
    
}

class Point
{
    Point(double x1,double y1)
    {
        this.x = x1;
        this.y = y1;
    }
    double x;
    double y;
}