Problem A - Cosmic Cabbages
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Scientists from the planet Zeelich have figured out a way to grow
cabbages in space. They have constructed a huge 3-dimensional steel grid
upon which they plant said cabbages. Each cabbage is attached to a
corner in the grid, where 6 steel cables meet and is assigned Cartesian
coordinates. A cosmic ant wants to crawl from cabbage X to cabbage Y
along the cables that make the grid. The cosmic ant always chooses the
shortest possible path along the grid lines while going from cabbage X
to cabbage Y. This distance is called the cosmic distance between two
cabbages. Given a collection of cabbages what is the maximum distance
between any two of the cabbages?

Input
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The first line of input gives the number of cases, N (0<N<21). N test
cases follow. Each one starts with a line containing n (2<=n<=105). The
next n lines will each give the 3-dimensional coordinates of a cosmic
cabbage (integers in the range [-10^8, 10^8]).
 
Output
------

For each test case, output one line containing "Case #x: " followed by
the largest cosmic distance between cabbages X and Y, out of all
possible choices of X and Y.

Sample Input
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4
2
1 1 1
2 2 2
3
0 0 0
0 0 1
1 1 0
4
0 1 2
3 4 5
6 7 8
9 10 11
6
0 0 0
1 1 1
2 2 2
0 0 1
1 0 0
0 1 0

Output for Sample Input
-----------------------

Case #1: 3
Case #2: 3
Case #3: 27
Case #4: 6