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.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.util.Scanner;
import java.io.PrintWriter;
import java.lang.Math;

public class Main
{
	public static void main(String[] args)
	{
		DecimalFormatSymbols s = new DecimalFormatSymbols();
		s.setDecimalSeparator('.');
		DecimalFormat f = new DecimalFormat("#,######0.000000",s);
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		String a_x;
		String a_y;
		String b_x;
		String b_y;
		String c_x;
		String c_y;
		a_x = sc.next();
		a_y = sc.next();
		b_x = sc.next();
		b_y = sc.next();
		c_x = sc.next();
		c_y = sc.next();
		Point A = new Point(a_x, a_y);
		Point B = new Point(b_x, b_y);
		Point C = new Point(c_x, c_y);
		
		double k1 = -(A.x - B.x)/(A.y - B.y);
		double k2 = -(C.x - B.x)/(C.y - B.y);
		
		Point center1 = new Point((A.x + B.x)/2,(A.y + B.y)/2);
		Point center2 = new Point((C.x + B.x)/2,(C.y + B.y)/2);
		
		boolean flag1 = false;
		boolean flag2 = false;
		double b1 = center1.y - k1 * center1.x;
		if(A.x == B.x)b1 = center1.y;
		else if(A.y == B.y)
		{
			flag1 = true;
			b1 = center1.x;
			k1 = 0;
		}
		double b2 = center2.y - k2 * center2.x;
		if(C.x == B.x)b2 = center2.y;
		else if(C.y == B.y)
		{
			flag2 = true;
			b2 = center2.x;
			k2 = 0;
		}
		Point center = null;
		if(flag1)
		{
			center = new Point(b1, b1 * k2 + b2);
		}
		else if(flag2)
		{
			center = new Point(b2, b2 * k1 + b1);
		}
		else
		{
			center = new Point((b1 - b2)/(k2 - k1),(k2 * b1 - k1 * b2)/(k2 - k1));
		}
		double radius = (Math.pow(center.x - A.x,2) + Math.pow(center.y - A.y,2));
		
		double angle1 = Math.acos(((A.x - center.x) * (B.x - center.x) + (A.y - center.y) * (B.y - center.y))/radius);
		double angle2 = Math.acos(Double.valueOf(f.format(((C.x - center.x) * (B.x - center.x) + (C.y - center.y) * (B.y - center.y))))/Double.valueOf(f.format(radius)));
		double angle3 = Math.acos(((A.x - center.x) * (C.x - center.x) + (A.y - center.y) * (C.y - center.y))/radius);
		
		int i;
		double checkangle = 0;
		for(i = 3; i <= 100; i++)
		{
			checkangle = Double.valueOf(f.format(2 * Math.PI / i));
			float checkangle1 = Float.valueOf(f.format(angle1 / checkangle));
			float checkangle2 = Float.valueOf(f.format(angle2 / checkangle));
			float checkangle3 = Float.valueOf(f.format(angle3 / checkangle));
			while(checkangle1 > 1) checkangle1--;
			while(checkangle2 > 1) checkangle2--;
			while(checkangle3 > 1) checkangle3--;
			checkangle1 = Float.valueOf(f.format(checkangle1));
			checkangle2 = Float.valueOf(f.format(checkangle2));
			checkangle3 = Float.valueOf(f.format(checkangle3));
			if(checkangle1 <= 0.01 || checkangle1 >= 0.99)
				if(checkangle2 <= 0.01 || checkangle2 >= 0.99)
					if(checkangle3 <= 0.01 || checkangle3 >= 0.99)
						break;
		}
		pw.println(Math.sin(2 * Math.PI / i) * radius * i / 2);
		sc.close();
		pw.close();
	}
	public static class Point
	{
		public double x;
		public double y;
		public Point(double x, double y)
		{
			this.x = x;
			this.y = y;
		}
		public Point(String x, String y)
		{
			this.x = Double.parseDouble(x);
			this.y = Double.parseDouble(y);
		}
	}
}