The Sultan of Sylvania loves throwing parties, because that gives him a reason
to decorate the palace. He particularly likes decorations called streamers made
up of different beads strung together on a string and hung from the ceiling. Now,
like most Sultans, he is very particular about everything, including these strung
decorations. Specifically, he only likes certain combinations of beads to be used
on the streamers. For example, if there are four different types of beads - A,
B, C and D - the Sultan might say "It pleases his highness that only the
combinations ABB, BCA, BCD, CAB, CDD and DDA appear in the streamers at tonight's
party". This, needless to say, puts a severe limit on the number of different
streamers possible. For example, if the length of the streamers was 5, then the
only possible streams of beads would be BCABB and BCDDA (strings such as ABBCA
could not be used because BBC is not an approved combination). Since the Sultan
likes variety, it is important to know the total number of streamers possible,
given a length and the current bead combinations which tickle the Sultan's fancy.
Input will consist of multiple test cases. Each case will consist of two lines.
The first line will contain three positive integers n, l and m, where n indicates
the number of bead types, l is the length of the streamers and m indicates the
number of bead combinations which the Sultan likes. The maximum values for n,
l and m will be 26, 100 and 600, respectively. The next line will contain the
m combinations. Each combination will be of the same length (between 1 and 10)
and will be separated using a single space. All combinations will make use of
only the uppercase letters of the alphabet. An input line of 0 0 0 will terminate
input and should not be processed.
For each test case, output a single line indicating the number of possible
streamers. All answers will be within the range of a 32-bit integer.
4 5 6
ABB BCA BCD CAB CDD DDA
5 4 5
E D C B A
4 8 3
AA BB CC
0 0 0