#3037. H. Laser Alarm

H. Laser Alarm

Description

The museum in Byteland has plenty of jewels on display, secured by n laser alarms. Each laser alarm
can be considered as a segment in the 3D space. In this task, your job is to test the quality of the laser
alarm system. You need to find a plane such that it touches the most laser alarms. Note that if the plane
touches the endpoint of a segment, it should also be counted.

Input Format

The first line contains a single integer T (1 T 10), the number of test cases. For each test case:
The first line contains a single integer n (1 n 50), denoting the number of laser alarms.
Each of the following n lines contains six integers xi, yi, zi, x
i, y
i and z
i (1 xi, yi, zi, x
i, y
i, z
i 100),
describing a segment that connects (xi, yi, zi) and (x
i, y
i, z
i). It is guaranteed that the two endpoints of
each segment do not coincide.

Output Format

For each test case, output a single line containing an integer, denoting the maximum possible number of
laser alarms that can be touched
1
4
1 1 1 1 1 2
1 1 10 1 1 11
1 10 1 1 10 2
10 1 1 10 1 2
3