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We call “word” every string, containing two or more capital letters A and B, starting with A. We define upon each word the following two actions, resulting in another word:
The N-time consecutive applying of actions of type R1 and R2 in some order, starting with a given word w is called “N- transformation” of w if:
Consider a positive integer N, greater than 1. Write a program abwords, which finds out one word with as few letters as possible, which can be a start of an N-transformation, or ascertains that such word does not exist.
One positive integer N > 1 is read from the standard input.
The program should write to the standard output:
There is no word shorter than 4 letters that can start a sequence of 6 actions which reproduce it without repeating words in the meantime. On the other hand, for example, the word AABB with four letters has such sequence of actions (i.e., a 6-transformation for it exists):
AABB --2-> ABAB --2-> AAAA --1-> AAAB --2-> ABBA --1-> ABBA --2-> ABBB --2-> AABB