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Automatic Chemical Manufacturing is experimenting with a process called self-assembly. In this pro-
cess, molecules with natural affinity for each other are mixed together in a solution and allowed to spon-
taneously assemble themselves into larger structures. But there is one problem: sometimes molecules
assemble themselves into a structure of unbounded size, which gums up the machinery.
You must write a program to decide whether a given collection of molecules can be assembled into a
structure of unbounded size. You should make two simplifying assumptions: 1) the problem is restricted
to two dimensions, and 2) each molecule in the collection is represented as a square. The four edges of
the square represent the surfaces on which the molecule can connect to other compatible molecules.
In each test case, you will be given a set of molecule descriptions. Each type of molecule is described
by four two-character connector labels that indicate how its edges can connect to the edges of other
molecules. There are two types of connector labels:
• An uppercase letter (A, . . . , Z ) followed by + or −. Two edges are compatible if their labels have
the same letter but different signs. For example, A+ is compatible with A− but is not compatible
with A+ or B−.
• Two zero digits 00. An edge with this label is not compatible with any edge (not even with another
edge labeled 00).
Assume there is an unlimited supply of molecules of each type, which may be rotated and reflected. As
the molecules assemble themselves into larger structures, the edges of two molecules may be adjacent
to each other only if they are compatible. It is permitted for an edge, regardless of its connector label, to
be connected to nothing (no adjacent molecule on that edge).
Figure A.1 shows an example of three molecule types and a structure of bounded size that can be assem-
bled from them (other bounded structures are also possible with this set of molecules).