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
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.
InputThe 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.
OutputThe only line of the output contains the required area.
ConstraintsThe x and y coordinates of any point given in the input are so that both
|x| ≤ 2000and
|y| ≤ 2000hold. 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.