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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Alex
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
    static class TaskC {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
//        Random rand = new Random(System.currentTimeMillis());
            Point[] trip = new Point[3];
            for (int i = 0; i < trip.length; i++)
                trip[i] = Point.readPoint(in);
//        double randangle = (rand.nextDouble() % 90);
//        for(Point p : trip) p.rotate(randangle);
            Segment zerotofirst = new Segment(trip[0], trip[1]);
            Segment zerotosecond = new Segment(trip[0], trip[2]);
            Line zerotofirstperp = zerotofirst.line().perpendicular(zerotofirst.middle());
            Line zerotosecondperp = zerotosecond.line().perpendicular(zerotosecond.middle());
            Point center = zerotofirstperp.intersect(zerotosecondperp);
//        out.printLine(center);
            double firstangle = GeometryUtils.positiveAngle(new Angle(center, trip[0], trip[1]).value());
            double secondangle = GeometryUtils.positiveAngle(new Angle(center, trip[0], trip[2]).value());
            double otherangle = 2 * Math.PI - firstangle - secondangle;
            double[] angles = new double[] {
                    firstangle,
                    secondangle,
                    otherangle
            };
            Arrays.sort(angles);
            angles[1] /= angles[0];
            angles[2] /= angles[0];
            double twooverone = angles[2] / angles[1];
//        out.printLine(angles[2], angles[1]);
            int ratio = 1;
//        out.printLine(twooverone);
            while (Math.abs((double) Math.round(angles[2] * ratio) - angles[2] * ratio) > 1e-3 ||
                    Math.abs((double) Math.round(angles[1] * ratio) - angles[1] * ratio) > 1e-3)
                //Math.abs((double) Math.round(twooverone * ratio) - twooverone * ratio) > 1e-3
                ratio++;
//        out.printLine(((double) Math.round(twooverone * ratio) - twooverone * ratio));
            // 3 4 5 = 9
//        out.printLine("RATIO", ratio);
            int moarpoints = (int) (Math.round(angles[2] * ratio) + Math.round(angles[1] * ratio)) - 2;
//        out.printLine("MOAR", moarpoints);
            int totalpoint = moarpoints + 3;
            double maintrigdist = center.distance(trip[0]);
            double onearea = maintrigdist * maintrigdist * Math.sin(angles[0]) / 2;
//        double onearea = Polygon.triangleArea(center, trip[0], trip[1]);
//        out.printLine(center);
//        out.printLine(trip[0]);
//        out.printLine(trip[1]);
//        out.printLine(totalpoint * onearea);
            int first = (int) Math.round(ratio);
            int second = (int) Math.round(ratio * angles[1]);
            int third = (int) Math.round(ratio * angles[2]);
            int totpoint = first + second + third;
            double arrreea = maintrigdist * maintrigdist * Math.sin(angles[0] / ratio) / 2;
            out.printLine(totpoint * arrreea);
        }
    }
    static class GeometryUtils {
        public static double epsilon = 1e-8;
        public static double fastHypot(double x, double y) {
            return Math.sqrt(x * x + y * y);
        }
        public static double positiveAngle(double angle) {
            while (angle > 2 * Math.PI - GeometryUtils.epsilon)
                angle -= 2 * Math.PI;
            while (angle < -GeometryUtils.epsilon)
                angle += 2 * Math.PI;
            return angle;
        }
    }
    static class Point {
        public final double x;
        public final double y;
        public String toString() {
            return "(" + x + ", " + y + ")";
        }
        public Point(double x, double y) {
            this.x = x;
            this.y = y;
        }
        public Line line(Point other) {
            if (equals(other))
                return null;
            double a = other.y - y;
            double b = x - other.x;
            double c = -a * x - b * y;
            return new Line(a, b, c);
        }
        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Point point = (Point) o;
            return Math.abs(x - point.x) <= GeometryUtils.epsilon && Math.abs(y - point.y) <= GeometryUtils.epsilon;
        }
        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }
        public double distance(Point other) {
            return GeometryUtils.fastHypot(x - other.x, y - other.y);
        }
        public static Point readPoint(InputReader in) {
            double x = in.readDouble();
            double y = in.readDouble();
            return new Point(x, y);
        }
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    static class Line {
        public final double a;
        public final double b;
        public final double c;
        public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
        }
        public Line(double a, double b, double c) {
            double h = GeometryUtils.fastHypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
        }
        public Point intersect(Line other) {
            if (parallel(other))
                return null;
            double determinant = b * other.a - a * other.b;
            double x = (c * other.b - b * other.c) / determinant;
            double y = (a * other.c - c * other.a) / determinant;
            return new Point(x, y);
        }
        public boolean parallel(Line other) {
            return Math.abs(a * other.b - b * other.a) < GeometryUtils.epsilon;
        }
        public Line perpendicular(Point point) {
            return new Line(-b, a, b * point.x - a * point.y);
        }
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Line line = (Line) o;
            if (!parallel(line)) return false;
            if (Math.abs(a * line.c - c * line.a) > GeometryUtils.epsilon || Math.abs(b * line.c - c * line.b) > GeometryUtils.epsilon)
                return false;
            return true;
        }
    }
    static class OutputWriter {
        private final PrintWriter writer;
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }
        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }
        public void close() {
            writer.close();
        }
    }
    static class Angle {
        public final Point o;
        public final Point a;
        public final Point b;
        public Angle(Point o, Point a, Point b) {
            this.o = o;
            this.a = a;
            this.b = b;
        }
        public double value() {
            double ab = a.distance(b);
            double ao = a.distance(o);
            double bo = b.distance(o);
            return Math.acos((ao * ao + bo * bo - ab * ab) / (2 * ao * bo));
        }
    }
    static class Segment {
        public final Point a;
        public final Point b;
        private Line line = null;
        public Segment(Point a, Point b) {
            this.a = a;
            this.b = b;
        }
        public Line line() {
            if (line == null)
                line = a.line(b);
            return line;
        }
        public Point middle() {
            return new Point((a.x + b.x) / 2, (a.y + b.y) / 2);
        }
    }
}