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Every sequence of small letters and (also the empty sequence) is called an ab-word. If is an ab-word and are integers such that then denotes the subword of consisting of the letters . We say that an ab-word is nice if it has as many letters as and for all the subword has at least as many letters as .
Now, we give the inductive definition of the similarity between nice ab-words:
A level of diversity of a non-empty set of nice ab-words is the maximal number of ab-words that can be chosen from in such a way that for each pair of chosen words, is not similar to .
Write a program that:
In the first line of the standard input there is a number of elements of the set , ; in the following lines there are elements of the set , i.e. nice ab-words (one word in each line); the first letter of every ab-word is the first symbol in line and there are no spaces between two consecutive letters in the word; the length of every ab-word is an integer from the range .
In the first and only line of the standard output there should be written one integer — the level of diversity of .
For the input data:
3 aabaabbbab abababaabb abaaabbabb
the correct result is:
Task author: Krzysztof Diks.