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Sabbir noticed one day that everyone in the city of BdMO has a distinct word of length
, where each letter is either
or
. Sabbir saw that two citizens are friends if one of their words can be altered a few times using a special rule and transformed into the other ones word. The rule is, if somewhere in the word
is located consecutively, then these letters can be changed to
or if
is located somewhere in the word consecutively, then these letters can be changed to
(if wanted, the word can be kept as it is, without making this change.) For example
can be transformed into
(the opposite is also possible.) Now Sabbir made a team of
citizens where no one is friends with anyone. What is the highest value of 










