Problem Description
There are n points in three dimensional space.
Consider the convex hull of n points.
Given a plane, you should work out the area of section of convex hull by the plane.
Input
First line contains T(T <= 10), a number of test cases.
For each test case, there are two integer n and m, number of points and number of queries.
Next n lines contains three integers x, y, z, coordinate of point.
Next m lines contains four integers a, b, c, d, specifying the equation of plane: ax + by + cz + d = 0.
1 <= n <= 1000
1 <= q <= 1000
Absolute values of x, y, z, a, b, c and d are not greater than 2000.
Output
For each test case, first line contains “Case #x:”, x is the number of the case.
For each query, you should print one float number in three decimal places in one line.
Sample Input
1
6 1
0 0 1
1 0 1
0 1 1
0 0 -1
1 0 -1
0 1 -1
0 0 1 0
Sample Output
Case #1:
0.500
