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:
//package main;

import java.io.*;
import java.util.StringTokenizer;

public class Main{
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        StringBuffer outBuffer = new StringBuffer();
        
        double Ax, Ay, Bx, By, Cx, Cy;
        Ax = Reader.nextDouble();
        Ay = Reader.nextDouble();
        Bx = Reader.nextDouble();
        By = Reader.nextDouble();
        Cx = Reader.nextDouble();
        Cy = Reader.nextDouble();
        
        //Translate coordinates such that A is at the origin (for simpler formula)
        Bx -= Ax;
        By -= Ay;
        Cx -= Ax;
        Cy -= Ay;
        Ax = 0;
        Ay = 0;
        
        double D, Ux, Uy;
                 
        //Find circum center of the circle using handi Wiki formula
        D = 2*(Bx*Cy - By*Cx);
        Ux = (Cy*(Bx*Bx + By*By) - By*(Cx*Cx + Cy*Cy))/D;
        Uy = (Bx*(Cx*Cx + Cy*Cy) - Cx*(Bx*Bx + By*By))/D;
        
        //Use circum center to find radius
        double radius = Math.sqrt((Ux*Ux)+(Uy*Uy));
        //Get the relative angle from the center to A
        //TODO: Fix initial angle calculation
        double initialAngle = Math.atan2(-Uy, -Ux);
        
        //Use Circum center, a point, and diameter to circumscribe every regular
            //polygon up to 100 on the circle.
        for(int n = 3; n < 101; n++) {
            //
            boolean matB = false, matC = false;
            //Calculate the next point on the regular N-gon
            for(int p = 1; p < n && (!matB || !matC); p++) {
                double Px = Ux + radius * Math.cos(initialAngle + p*2*Math.PI/n);
                double Py = Uy + radius * Math.sin(initialAngle + p*2*Math.PI/n);
                
                //Check if the calculated position is within 10^-7 of B or C
                if(Math.abs(Px - Bx) < 0.00001 && Math.abs(Py - By) < 0.00001) {
                    //Mark as found
                    matB = true;
                }
                if(Math.abs(Px - Cx) < 0.00001 && Math.abs(Py - Cy) < 0.00001) {
                    //Mark as found
                    matC = true;
                }
            }
            //Check if both pillars are on this regular N-gon
            if(matB && matC) {
                //Calculate area
                double area = radius*radius * n * Math.sin(2*Math.PI/n)/2;
                //Output formatted result
                outBuffer.append(String.format("%1$.6f", area));
                break;
            }
        }
        
        System.out.println(outBuffer);
    }
}

// Class for buffered reading int and double values 
//Mad props go out to: http://www.cpe.ku.ac.th/~jim/java-io.html
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    //call this method to initialize reader for InputStream
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    //get next word
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}