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 static java.lang.System.in;

import static java.lang.System.out;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import static java.lang.Math.*;
import java.util.*;


public class C1 {
	public static Scanner sc = new Scanner(in);
	StringBuilder sb = new StringBuilder();
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	double eps = 0.0001;
	public void run() throws IOException {
		String input;
		String[] inputArray;

		P [] ver = new P[3];
		for (int i=0; i<3; i++){
			input = br.readLine(); inputArray = input.split(" ");
			ver[i] = new P(Double.valueOf(inputArray[0]), Double.valueOf(inputArray[1]));
		}
		double [] angle = new double [3], len2 = new double[3];
		for (int i=0; i<3; i++){
			angle[i]=Math.abs(P.arg(ver[(i+1)%3],ver[i])-P.arg(ver[i],ver[(i+2)%3]));
			if (angle[i]>Math.PI) angle[i]-=Math.PI;
			len2[i] = ver[(i+1)%3].dist2(ver[(i+2)%3]);
		 
		}
		for (int n=3; n<10001; n++){
			double [] x = new double[3];
			for (int i=0; i<3; i++) x[i] = n*angle[i]/Math.PI;
			if ( (Math.abs(x[0]-Math.round(x[0]))<eps) && 
				 (Math.abs(x[1]-Math.round(x[1]))<eps) && 
				 (Math.abs(x[2]-Math.round(x[2]))<eps)) {
				//ln(angle[0]/Math.PI);
				//ln(len2[0]);
				double kaku = Math.sin((2*Math.PI)/(n));
				//ln(kaku);
				double R2 = len2[0]/(4*Math.sin(angle[0])*Math.sin(angle[0]));
				double S = R2*kaku/2;
				double ans = S*n;
				//ln("R2: " + R2);
				//ln("S: " + S);
				//ln("n: "+ n);

				ln(ans);
				break;
			}
			
		}
		 
		ln(sb);
	}

	public static void main(String[] args) throws IOException {
		new C1().run();
	}
	public static void ln(Object obj) {
		out.println(obj);
	}
	 
	static class P{
		 
			static final double EPS=1e-10;
			static int signum(double x){
				return x<-EPS?-1:x>EPS?1:0;
			}
		static Comparator<P> comp=new Comparator<P>(){
			public int compare(P p1, P p2) {
				return signum(p1.x-p2.x)!=0?signum(p1.x-p2.x):signum(p1.y-p2.y);
			}
		};
		public static  final P O=new P(0,0);
		final double x,y;
		P(double _x,double _y){
			x=_x;y=_y;
		}
		 
		P add(P a){
			return new P(x+a.x,y+a.y);
		}
		P sub(P a){
			return new P(x-a.x,y-a.y);
		}
		P mul(P a){
			return new P(x*a.x-y*a.y,x*a.y+y*a.x);
		}
		P div(P a){
			double d2=a.dist2(O);
			return new P(dot(a,this)/d2,cross(a,this)/d2);
		}
		 
		P conj(){
			return new P(x,-y);
		}
		 
		static double dot(P a,P b){
			return  a.x*b.x+a.y*b.y;
		}
		 
		static double cross(P a,P b){
			return  a.x*b.y-a.y*b.x;
		}
		 
		double dist2(P p){
			return (x-p.x)*(x-p.x)+(y-p.y)*(y-p.y);
		}
		 
		double dist(P p){
			return sqrt(dist2(p));
		}
		public double norm(){
			return dist(O);
		}
		 
		static int ccw(P a,P b,P c){
			b=b.sub(a);c=c.sub(a);
			if(cross(b,c)>EPS)return 1; 
			if(cross(b,c)<-EPS)return -1; 
			if(dot(b,c)<-EPS)return 2; 
			if(b.norm()<c.norm()-EPS)return -2; 
			return 0; 
		}
		 
		static double arg(P a,P o){
			P dir=a.sub(o);
			double s=acos(dir.x/dir.norm());
			return dir.y>0?s:2*PI-s;
		}
		 
		P rotate(P o,double arg){
			return this.add(this.sub(o).mul(new P(cos(arg),sin(arg))));
		}
		 
		static double S2(P a,P b,P o){
			return cross(a.sub(o),b.sub(o));
		}
		static double S(P a,P b,P o){
			return S2(a,b,o)/2;
		}
		 
		static P polar(double abs,double arg){
			return new P(abs*cos(arg),abs*sin(arg));
		}
		 
		static P proj(P p,P o){
			return o.mul(new P(dot(p,o)/o.norm(),0));
		}
		public boolean equals(Object obj) {
			if(obj instanceof P){
				P p=(P)obj;
				return signum(x-p.x)==0 && signum(y-p.y)==0;
			}
			return false;
		}
		public String toString(){
			return "("+x+","+y+")";
		}
	}

}