Perhaps you have heard of the legend of the Tower of Babylon. Nowadays many details of this tale have been forgotten. So now, in line with the educational nature of this contest, we will tell you the whole story:

The babylonians had *n* types of blocks, and an unlimited supply of
blocks of each type. Each type-*i* block was a rectangular solid with
linear dimensions . A block could be
reoriented so that any two of its three dimensions determined the dimensions of
the base and the other dimension was the height. They wanted to construct the
tallest tower possible by stacking blocks. The problem was that, in building a
tower, one block could only be placed on top of another block as long as the two
base dimensions of the upper block were both strictly smaller than the
corresponding base dimensions of the lower block. This meant, for example, that
blocks oriented to have equal-sized bases couldn't be stacked.

Your job is to write a program that determines the height of the tallest tower the babylonians can build with a given set of blocks.

The input file will contain one or more test cases. The first line of each
test case contains an integer *n*, representing the number of different
blocks in the following data set. The maximum value for *n* is 30. Each of
the next *n* lines contains three integers representing the values , and .

Input is terminated by a value of zero (0) for *n*.

For each test case, print one line containing the case number (they are
numbered sequentially starting from 1) and the height of the tallest possible
tower in the format "`Case` *case*`: maximum height =`
*height*"

1 10 20 30 2 6 8 10 5 5 5 7 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 5 31 41 59 26 53 58 97 93 23 84 62 64 33 83 27 0

Case 1: maximum height = 40 Case 2: maximum height = 21 Case 3: maximum height = 28 Case 4: maximum height = 342