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.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
	
	public class CF {
		public static void main(String[] args) {
			FasterScanner sc = new FasterScanner();
			PrintWriter out = new PrintWriter(System.out);
			double[] x = new double[3];
			double[] y = new double[3];
			for(int a=0;a<3;a++){
				x[a]=sc.nextDouble();
				y[a]=sc.nextDouble();
			}
			Vector A = new Vector(x[0],y[0]);
			Vector B = new Vector(x[1],y[1]);
			Vector C = new Vector(x[2],y[2]);
			
			Vector AB = B.sub(A);
			Vector AC = C.sub(A);
			Vector BA = A.sub(B);
			Vector BC = C.sub(B);
			Vector CA = A.sub(C);
			Vector CB = B.sub(C);
			
			double[] angs = new double[3];
			angs[0] = AB.angBetween(AC);
			angs[1] = BA.angBetween(BC);
			angs[2] = CA.angBetween(CB);
		
			double triarea = triangleAreaFromThreePoints(x[0],y[0],x[1],y[1],x[2],y[2]);
			double area = 0;
			double radius = AC.mag()*CB.mag()*BA.mag()/ (4*triarea);
			
			double n =Math.PI/GCD(GCD(angs[0],angs[1]),angs[2]);
//			search: for(double n=3;n<=1000;n++){
//				double total = (n-2)*180.0;
//				for(int a=0;a<3;a++){
//					if(total%angs[a]!=0)continue search;
//				}
//				System.out.println(n);
				area =  n/2.0*radius*radius*Math.sin(2.0*Math.PI/n);
//				break;
//			}
			out.println(area);
			out.close();
		}
		
		static double GCD(double x, double y) {
		    while (Math.abs(x) >  1e-4 && Math.abs(y) > 1e-4) {
		        if (x > y)
		                x -= Math.floor(x / y) * y;
		        else
		                y -= Math.floor(y / x) * x;
		    }
		    return x + y;
		}
		static class Vector implements Comparable<Vector> {
			double x, y;

			public Vector(double _x, double _y) {
				x = _x;
				y = _y;
			}

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

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

			public Vector scale(double s) {
				return new Vector(x * s, y * s);
			}

			public Vector rot(double t) { // Rotate t radians counter-clockwise
				double c = Math.cos(t);
				double s = Math.sin(t);
				return new Vector(x * c - y * s, x * s + y * c);
			}

			public Vector orthoCCW() { // Rotate 90 degrees counter-clockwise
				return new Vector(-y, x);
			}

			public Vector norm() { // Return a vector with same angle and magnitude
									// 1
				return new Vector(x / mag(), y / mag());
			}

			public Vector project(Vector p) { // Return projection of this onto p
				return p.scale(dot(p) / p.dot(p));
			}

			public double dot(Vector p) {
				return x * p.x + y * p.y;
			}

			public double cross(Vector p) {
				return x * p.y - y * p.x;
			}

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

			public double mag2() {
				return x * x + y * y;
			}

			public double dis(Vector p) {
				return sub(p).mag();
			}

			public double ang() {
				return (Math.atan2(y, x) + 2 * Math.PI) % (2 * Math.PI);
			}

			public double angBetween(Vector p) { // Returns inner angle between two
													// vectors
				double d = Math.abs(ang() - p.ang());
				return Math.min(d, 2 * Math.PI - d);
			}

			public int compareTo(Vector p) {
				if (p.x == x)
					return (int) Math.signum(y - p.y);
				return (int) Math.signum(x - p.x);
			}

			public String toString() {
				return String.format("(%.3f, %.3f)", x, y);
			}
		}
		
		private static double triangleAreaFromThreePoints(double x1, double y1, double x2, double y2,
				double x3, double y3) {
			return Math.abs((x1-x3)*(y2-y3)-(x2-x3)*(y1-y3))/2.0;
		}

		static class FasterScanner {
			private InputStream stream;
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
	
			public FasterScanner() {
				stream = System.in;
				// stream = new FileInputStream(new File("dec.in"));
	
			}
	
			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++];
			}
	
			boolean isSpaceChar(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	
			boolean isEndline(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
	
			int nextInt() {
				return Integer.parseInt(next());
			}
	
			long nextLong() {
				return Long.parseLong(next());
			}
	
			double nextDouble() {
				return Double.parseDouble(next());
			}
	
			String next() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	
			String nextLine() {
				int c = read();
				while (isEndline(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndline(c));
				return res.toString();
			}
	
		}
	
	}