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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class ProbC implements Runnable {
	private boolean _ReadFromFile = false;
	private boolean _WriteToFile = false;
	static final String TASK_ID = "in";
	static final String IN_FILE = TASK_ID + ".in";
	static final String OUT_FILE = TASK_ID + ".out";
	private static final double eps = 1e-5;
	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter writer;

	class Point {
		private static final double eps = 1e-4;
		double x, y;
		public Point(double x, double y) {
			this.x = x;
			this.y = y;
		}
		public double len() {
			return Math.sqrt(x*x + y*y);
		}
		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 Point mul(double k) {
			return new Point(k*x, k*y);
		}
		public double cross(Point p) {
			return x*p.y - y*p.x;
		}
		public double dot(Point p) {
			return x*p.x + y*p.y;
		}
		public double angleCCW(Point p) {
			double res = Math.acos(this.dot(p)/this.len()/p.len());
			if (this.cross(p) > eps)
				return res;
			else
				return -res;
		}
		public String toString() {
			return x + " " + y;
		}
	}
	private void core() throws Exception {
		Point a = new Point(nextDouble(), nextDouble());
		Point b = new Point(nextDouble(), nextDouble());
		Point c = new Point(nextDouble(), nextDouble());
		Point centerPoint = getCenter(a,b,c);
		
		a = a.sub(centerPoint);
		b = b.sub(centerPoint);
		c = c.sub(centerPoint);
		double alpha = Math.abs(a.angleCCW(b));
		double beta = Math.abs(b.angleCCW(c));
		for (int nAngle = 1;; nAngle++) {
			double u = Math.sin(alpha * nAngle / 2);
			double v = Math.sin(beta * nAngle / 2);
			if (Math.abs(u) < eps && Math.abs(v) < eps) {
				double r = 0.5 * a.len() * b.len() * Math.sin(2*Math.PI/nAngle);
				r *= nAngle;
				writer.println(r);
				break;
			}
		}
	}
	private Point getCenter(Point a, Point b, Point c) {
		ArrayList<Point> l1 = findNormal(a, b);
		ArrayList<Point> l2 = findNormal(b, c);
		return intersection(l1.get(0), l1.get(1), l2.get(0), l2.get(1));
	}
	private Point intersection(Point a, Point b, Point c,
			Point d) {
		double num = - (a.sub(d)).cross(c.sub(d));
		double den = b.sub(a).cross(c.sub(d));
		if (Math.abs(den) < 1e-7)
			return null;
		else
			return a.add(b.sub(a).mul(num/den));
	}
	private ArrayList<Point> findNormal(Point a, Point b) {
		Point v = b.sub(a).mul(0.5);
		Point i = a.add(v);
		Point u = new Point(a.y-b.y, b.x-a.x);
		Point j = i.add(u);
		
		ArrayList<Point> res = new ArrayList<Point>();
		res.add(i); 
		res.add(j);
		return res;
	}
	void debug(Object...os) {
		System.out.println(Arrays.deepToString(os));
	}
	//--------------------- IO stuffs ---------------------
    public static void main(String[] args) throws InterruptedException {
        Thread thread = new Thread(new ProbC());
        thread.start();
        thread.join();
    }
	public void run() {
        try {
        	reader = _ReadFromFile ? new BufferedReader(new FileReader(IN_FILE)) : new BufferedReader(new InputStreamReader(System.in));
        	writer = _WriteToFile ? new PrintWriter(OUT_FILE) : new PrintWriter(new BufferedOutputStream(System.out));
            tokenizer = null;
            core();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
    int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
    long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
    double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
    String nextToken() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}