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.*;
import java.util.*;
import java.math.*;

public class C implements Runnable {

	static class Point {
		double x;
		double y;

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

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

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

		public Point setLength(double len) {
			double e = len();
			return new Point(x * len / e, y * len / e);
		}

		public Point rotate(double ang) {
			return new Point(x * Math.cos(ang) - y * Math.sin(ang), x
					* Math.sin(ang) + y * Math.cos(ang));
		}

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

		@Override
		public String toString() {
			return "Point [x=" + String.format("%.3f", x) + ", y="
					+ String.format("%.3f", y) + "]";
		}

		public Point multiply(double d) {
			return new Point(d * x, d * y);
		}

		@Override
		public boolean equals(Object obj) {
			if (!(obj instanceof Point)) {
				return false;
			}
			Point p = (Point) obj;
			return compare(x, p.x) == 0 && compare(y, p.y) == 0;
		}
	}

	static final double EPS = 5.41e-5;

	static int compare(double a, double b) {
		return Math.abs(a - b) < EPS ? 0 : Double.compare(a, b);
	}

	static double check(int n, Point[] p) {
		double ret = Double.POSITIVE_INFINITY;
		double angle = 0;
		double one = 2 * Math.PI / n;
		Point v = p[1].subtract(p[0]);
		double d = v.len();
		for (int i = 1; i < n; i++) {
			angle += one;
			double r = d / (2 * Math.sin(angle * .5));
			double angle2;
			if (angle >= Math.PI) {
				angle2 = -(Math.PI - (2 * Math.PI - angle)) * .5;
			} else {
				angle2 = (Math.PI - angle) * .5;
			}
			Point v2 = v.setLength(r).rotate(angle2);
			Point center = p[0].add(v2);
			v2 = v2.multiply(-1);
			for (int j = 0; j < n; j++) {
				// System.err.println(p[2] + " " + center.add(v2));
				if (p[2].equals(center.add(v2))) {
					ret = Math.min(ret, n * r * r * Math.sin(one) * .5);
					break;
				}
				v2 = v2.rotate(one);
			}
		}
		return ret;
	}

	void solve() {
		Point[] p = new Point[3];
		for (int i = 0; i < 3; i++) {
			p[i] = new Point(nextDouble(), nextDouble());
		}
		double ans = Double.POSITIVE_INFINITY;
		for (int i = 3; i <= 100; i++) {
			ans = Math.min(ans, check(i, p));
		}
		out.println(ans);
	}

	FastScanner sc;
	PrintWriter out;

	public void run() {
		Locale.setDefault(Locale.US);
		try {
			sc = new FastScanner(System.in);
			out = new PrintWriter(System.out);
			solve();
			sc.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() {
		return sc.nextInt();
	}

	String nextToken() {
		return sc.nextToken();
	}

	long nextLong() {
		return sc.nextLong();
	}

	double nextDouble() {
		return sc.nextDouble();
	}

	BigInteger nextBigInteger() {
		return sc.nextBigInteger();
	}

	class FastScanner extends BufferedReader {
		StringTokenizer st;
		boolean eof;
		String buf;
		String curLine;
		boolean createST;

		public FastScanner(String fileName) throws FileNotFoundException {
			this(fileName, true);
		}

		public FastScanner(String fileName, boolean createST)
				throws FileNotFoundException {
			super(new FileReader(fileName));
			this.createST = createST;
			nextToken();
		}

		public FastScanner(InputStream stream) {
			this(stream, true);
		}

		public FastScanner(InputStream stream, boolean createST) {
			super(new InputStreamReader(stream));
			this.createST = createST;
			nextToken();
		}

		String nextLine() {
			String ret = curLine;
			if (createST) {
				st = null;
			}
			nextToken();
			return ret;
		}

		String nextToken() {
			if (!createST) {
				try {
					curLine = readLine();
				} catch (Exception e) {
					eof = true;
				}
				return null;
			}
			while (st == null || !st.hasMoreTokens()) {
				try {
					curLine = readLine();
					st = new StringTokenizer(curLine);
				} catch (Exception e) {
					eof = true;
					break;
				}
			}
			String ret = buf;
			buf = eof ? "-1" : st.nextToken();
			return ret;
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}

		BigInteger nextBigInteger() {
			return new BigInteger(nextToken());
		}

		public void close() {
			try {
				buf = null;
				st = null;
				curLine = null;
				super.close();
			} catch (Exception e) {

			}
		}

		boolean isEOF() {
			return eof;
		}
	}

	public static void main(String[] args) {
		new C().run();
	}
}