Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Roger Wilco is in charge of the design of a low orbiting space station for the
planet Mars. To simplify construction, the station is made up of a series of Airtight
Cubical Modules (ACM's), which are connected together once in space. One problem
that concerns Roger is that of (potentially) lethal bacteria that may reside in
the upper atmosphere of Mars. Since the station will occasionally fly through
the upper atmosphere, it is imperative that extra shielding be used on all faces
of the ACM's touch, either edge to edge or face to face, that joint is sealed
so no bacteria can sneak through. Any face of an ACM shared by another ACM will
not need shielding, of course, nor will a face which cannot be reached from the
outside. Roger could just put extra shielding on all of the faces of every ACM,
but the cost would be prohibitive. Therefore, he wants to know the exact number
of ACM faces which need the extra shielding.

Input consists of multiple problem instances. Each instance consists of a specification
of a space station. We assume that each space station can fit into an n x m
x k grid (1 <= n, m, k <= 60), where each grid cube may or may not contain
an ACM. We number the grid cubes 0, 1, 2, ��, kmn-1 as shown in the diagram below.
Each space station specification then consists of the following: the first line
contains four positive integers n m k l, where n, m and k are as described above
and l is the number of ACM's in the station. This is followed by a set of lines
which specify the l grid locations of the ACM's. Each of these lines contain
10 integers (except possibly the last). Each space station is fully connected
(i.e., an astronaut can move from one ACM to any other ACM in the station without
leaving the station). Values of n = m = k = l = 0 terminate input.

For each problem instance, you should output one line of the form

The number of faces needing shielding is s.

2 2 1 3 0 1 3 3 3 3 26 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 0 0 0 0

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