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.IOException;
import java.util.Locale;
import java.util.Scanner;

public class Main
{
	private static double greatestCommonDivider(double a, double b)
	{
		if (Math.abs(b) < 1e-4)
			return a;

		return greatestCommonDivider(b, a % b);
	}

	public static void main(String[] args) throws IOException
	{
		try (Scanner in = new Scanner(System.in))
		{
			in.useLocale(Locale.US);

			Point a = new Point(in.nextDouble(), in.nextDouble());
			Point b = new Point(in.nextDouble(), in.nextDouble());
			Point c = new Point(in.nextDouble(), in.nextDouble());

			Line ab = new Line(a, b);
			Line ac = new Line(a, c);

			Line abPerp = ab.perpendicularAt(a.midPoint(b));
			Line acPerp = ac.perpendicularAt(a.midPoint(c));

			Point midPoint = abPerp.intersection(acPerp);

			double radius = midPoint.distance(a);

			Line aSpoke = new Line(midPoint, a);
			Line bSpoke = new Line(midPoint, b);
			Line cSpoke = new Line(midPoint, c);

			double abAngle = aSpoke.angle(bSpoke);
			double acAngle = aSpoke.angle(cSpoke);
			double bcAngle = bSpoke.angle(cSpoke);

			double gcd = greatestCommonDivider(abAngle, greatestCommonDivider(acAngle, bcAngle));

			int bestN = 0;
			for (int n = 3; n <= 100; ++n)
			{
				double angle = 2 * Math.PI / n;

				if (Math.abs(greatestCommonDivider(gcd, angle) - angle) < 1e-4)
				{
					bestN = n;
					break;
				}
			}

			double area = 0.5d * bestN * radius * radius * Math.sin(2 * Math.PI / bestN);
			System.out.println(area);
		}
	}

	private static class Point
	{
		double x;
		double y;

		public Point(double x, double y)
		{
			this.x = x;
			this.y = y;
		}

		public Point midPoint(Point other)
		{
			double dx = other.x - x;
			double dy = other.y - y;

			return new Point(x + (dx / 2), y + (dy / 2));
		}

		public double distance(Point other)
		{
			double dx = other.x - x;
			double dy = other.y - y;

			return Math.sqrt(dx * dx + dy * dy);
		}

		@Override
		public String toString()
		{
			return "Point{" +
					"x=" + x +
					", y=" + y +
					'}';
		}
	}

	private static class Line
	{
		Point a;
		Point b;

		double dx;
		double dy;

		double slope;
		double yIntercept;

		public Line(Point a, Point b)
		{
			this.a = a;
			this.b = b;

			dx = a.x - b.x;
			dy = a.y - b.y;

			this.slope = dy / dx;
			this.yIntercept = (-slope * a.x) + a.y;
		}

		public Line perpendicularAt(Point point)
		{
			return new Line(point, new Point(point.x - (dy / 2), point.y + (dx / 2)));
		}

		public Point intersection(Line other)
		{
			double x = (yIntercept - other.yIntercept) / (other.slope - slope);
			double y = slope * x + yIntercept;

			return new Point(x, y);
		}

		public double angle(Line other)
		{
			double angle1 = Math.atan2(a.y - b.y, a.x - b.x);
			double angle2 = Math.atan2(other.a.y - other.b.y, other.a.x - other.b.x);

			return Math.abs(angle1 - angle2);
		}

		@Override public String toString()
		{
			return "Line{" +
					"a=" + a +
					", b=" + b +
					", dx=" + dx +
					", dy=" + dy +
					", slope=" + slope +
					", yIntercept=" + yIntercept +
					'}';
		}
	}
}