Cliques
-------

Given an undirected graph G (a set of vertices and
edges), a clique C in G is a set of vertices each pair
of which is joined by an edge of G.

Given a graph G, you are asked to find all the cliques
of G with at least 3 vertices.

We restrict ourselves to graphs with at most 26 nodes
that are labeled A through Z.  We represent edges by
words consisting of two letters, where the letters are
in alphabetical order.  For example, AX represents an
edge, but XA does not.  We represent cliques by words
that list all the vertices in a clique in alphabetical
order.  For example, AXZ might represent a clique in
some graph, but AZX could NOT be a legal clique
representative.

To represent a graph or a set of cliques, we list repre-
sentatives of edges of the graph, or of the cliques in
the set, lexicographically: that is, in dictionary
order.  See the examples below.


Input
-----

For each of several cases, a specification of a
graph G as follows:

   A line containing the name of the graph.

   A line containing the number n of edges.

   n lines each containing nothing but a two letter word
     representing an edge.  No edge will be repeated,
     and the edge representatives will be sorted
     lexicographically.

Only the graph name line may contain any spaces.  The
input terminates with an end of file.


Output
------

For each case, a single line containing the name of the
graph exactly as input, followed by one line for each
clique with 3 or more vertices.  The line for a clique
contains just the representative of the clique, and all
the clique lines for one graph are sorted lexicographic-
ally.


Example Input
------- -----

TEST 1
6
AB
AC
AD
BC
BD
CD
TEST 2
10
AE
AF
BE
BF
BX
EF
EX
FX
XY
YZ


Example Output
------- ------

TEST 1
ABC
ABCD
ABD
ACD
BCD
TEST 2
AEF
BEF
BEFX
BEX
BFX
EFX


File:	   cliques.txt
Author:	   Bob Walton <walton@deas.harvard.edu>
Date:	   Wed Oct 10 07:18:28 EDT 2007

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2007/10/10 11:28:01 $
    $RCSfile: cliques.txt,v $
    $Revision: 1.3 $