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.BufferedReader;
import java.io.InputStreamReader;

public class CF001C {
    public static class Point {
        public Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public final double x, y;

        private static final Point VERTEX = new Point(0, 0);

        public static Point vertex() {
            return VERTEX;
        }

        public Point add(Point p) {
            return new Point(x + p.x, y + p.y);
        }

        public Point sub(Point p) {
            return new Point(x - p.x, y - p.y);
        }

        public double abs() {
            return Math.sqrt(x * x + y * y);
        }

        public double rad() {
            return Math.atan2(y, x);
        }

        public double dist(Point p) {
            return Math.sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y));
        }

        public double rad(Point a, Point b) {
            Point a2 = a.sub(this);
            Point b2 = b.sub(this);
            return b2.rad() - a2.rad();
        }

        public Point rotate(Point c, double rad) {
            double sx = c.x - x;
            double sy = c.y - y;
            double cos = Math.cos(rad);
            double sin = Math.sin(rad);
            double rx = sx * cos - sy * sin;
            double ry = sx * sin + sy * cos;
            return new Point(rx + c.x, ry + c.y);
        }

        public static Point fromLine(String s) {
            String c[] = s.split(" ");
            return new Point(Double.valueOf(c[0]), Double.valueOf(c[1]));
        }

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

    public static class Circle {
        public Circle(Point c, double r) {
            this.c = c;
            this.r = r;
        }

        public final Point c;
        public final double r;

        public Circle(double cx, double cy, double r) {
            this(new Point(cx, cy), r);
        }

        @Override
        public String toString() {
            return "Circle[" + c + "," + r + "]";
        }

        public static Circle circumscribed(Point a, Point b, Point c) {
            double d =
                    2 * (a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x
                            * (a.y - b.y));
            double ux =
                    ((a.x * a.x + a.y * a.y) * (b.y - c.y)
                            + (b.x * b.x + b.y * b.y) * (c.y - a.y) + (c.x
                            * c.x + c.y * c.y)
                            * (a.y - b.y))
                            / d;
            double uy =
                    ((a.x * a.x + a.y * a.y) * (c.x - b.x)
                            + (b.x * b.x + b.y * b.y) * (a.x - c.x) + (c.x
                            * c.x + c.y * c.y)
                            * (b.x - a.x))
                            / d;
            Point u = new Point(ux, uy);
            double ra = u.dist(a);
            double rb = u.dist(b);
            double rc = u.dist(c);
            double r = (ra + rb + rc) / 3;
            return new Circle(u, r);
        }
    }

    public static final double RAD_THRESHOLD = Math.PI / 10000;

    public static double area(Point p1, Point p2, Point p3, Circle c, int n) {
        double rad1 = Math.PI * 2 / n;
        double rad_ab = c.c.rad(p1, p2);
        double rad_ac = c.c.rad(p1, p3);
        double r1 = rad_ab / rad1;
        long l1 = Math.round(r1);
        double e1 = rad_ab - l1 * rad1;
        double r2 = rad_ac / rad1;
        long l2 = Math.round(r2);
        double e2 = rad_ac - l2 * rad1;
        if (Math.abs(e1) > RAD_THRESHOLD || Math.abs(e2) > RAD_THRESHOLD) {
            return Double.NaN;
        }
        return n * c.r * c.r * Math.sin(rad1) / 2;
    }

    public static void main(String[] args) throws Exception {
        BufferedReader br =
                new BufferedReader(new InputStreamReader(System.in));
        Point p1 = Point.fromLine(br.readLine());
        Point p2 = Point.fromLine(br.readLine());
        Point p3 = Point.fromLine(br.readLine());
        Circle c = Circle.circumscribed(p1, p2, p3);
        for (int n = 3; n <= 100; n++) {
            double area = area(p1, p2, p3, c, n);
            if (!Double.isNaN(area)) {
                System.out.printf("%.8f", area);
                return;
            }
        }
    }

}