Given an ~N \times N~ grid of letters, one can select four squares such that the first is a
the second is an
A, the third is an
L, and the last is an
I, and two adjacent squares in the pattern
share at least a corner.
This selection process is repeated as many times as possible, with the caveat that a given square can only be selected at most once.
Compute the maximum number of distinct sets of letters that can be selected.
~1 \le N \le 200~
In tests worth ~3~ marks, you may assume ~N \le 4~.
In tests worth an additional ~5~ marks, you may assume ~N \le 10~.
The first line of the input contains a single integer, ~N~.
The next ~N~ lines contain ~N~ characters, all of which appear in
Output, on a single line, the maximum number of sets that can be selected.
4 CALI ILAC CLLC IAAI