Given two balls in 3D space, you are asked to calculate the volume of their union, ie the total volume.
Input
There multiple cases:
Each case contains two lines:
1st-line: x1, y1, z1, r1
2nd-line: x2, y2, z2, r2
Each line specifies the coordinate and the radius of a ball.
The input file termitates with EOF.
All the data in the input are integers in [-20, 20].
Output
A single number: the volume of the union with a precision of 3 numbers after the decimal point.