After finishing his job involving the bulb panel, engineer Smith came home, exhausted after all this work. He's been resting for no more than 10 minutes, when his son, Maurice, came in and showed him his math homework on which he's been working for three extensive hours, asking him for help. As tired as he was, Smith decided to help little Maurice finish his homework after seeing how much time he's already spent on it. Maurice told him the problem's statement and he listened carefully:
You are given a right-angled triangle ABC embedded in a 2D cartesian metric system with the right angle in A; you construct 3 discs: the one having AB as a diameter (call it disc A), the one having AC as a diameter (call it disc B) and respectively the disc having BC as a diameter (call it disc C) and you are to find the area of (A∪B)\C.
Not knowing how to find the area of this curved region, Smith's only hope is you writing him a program which gets as input the points' coordinates and outputs the area of the curved surface represented by (A∪B)\C.
Input
The input consists of 3 lines. The first line contains the x and y coordinates of point A, separated by a single space. The same goes for lines 2 and 3 similarly for points B and C.Output
The only line of the output contains the required area.Sample
| Input | Output |
|---|---|
| -0.922680593509094 9.33078117765018 3.51455226267666 13.3888293896188 -6.02543595601116 14.9103387799459 | 22.7325 |
Constraints
The x and y coordinates of any point given in the input are so that both|x| ≤ 2000 and |y| ≤ 2000 hold. The outputed result is considered correct if and only if the diference between your result and the correct one is strictly less than 0.0001.
