#1691 The Circumference of the Circle

12  1 s   128 MB  

Description

To calculate the circumference of a circle seems to be an easy task - provided you know its diameter. But what if you don't?

You are given the cartesian coordinates of three non-collinear points in the plane. Your job is to calculate the circumferencce of the unique circle that intersects all three points. The value of pi is approximately 3.141592653589793.

Input

The input will contain one or more test cases. Each test case consists of one line containing six real numbers x_1 y_1 x_2 y_2 x_3 y_3, representing the coordinates of the three points. The diameter of the circle determined by the three points will never exceed a million. Input is terminated by end of file.

Output

For each test case, print one line containing one real number telling the circumference of the circle determined by the three points. The circumference is to be printed accurately rounded to two decimals.

Sample Input

Sample Output

0.0 -0.5 0.5 0.0 0.0 0.5
0.0 0.0 0.0 1.0 1.0 1.0
5.0 5.0 5.0 7.0 4.0 6.0
0.0 0.0 -1.0 7.0 7.0 7.0
50.0 50.0 50.0 70.0 40.0 60.0
0.0 0.0 10.0 0.0 20.0 1.0
0.0 -500000.0 500000.0 0.0 0.0 500000.0
3.14
4.44
6.28
31.42
62.83
632.24
3141592.65

Source

Stanford Local 2000