CF1789F Serval and Brain Power

Serval loves Brain Power and his brain power problem. Serval defines that a string $ T $ is powerful iff $ T $ can be obtained by concatenating some string $ T' $ multiple times. Formally speaking, $ T $ is powerful iff there exist a string $ T' $ and an integer $ k\geq 2 $ such that $$ T=\underbrace{T'+T'+\dots+T'}_{k\text{ times}} $$ For example, $\texttt{gogogo}$ is powerful because it can be obtained by concatenating $\texttt{go}$ three times, but $\texttt{power}$ is not powerful. Serval has a string $ S $ consists of lowercase English letters. He is curious about the longest powerful subsequence of $ S $ , and he only needs you to find out the length of it. If all the non-empty subsequences of $ S $ is not powerful, the answer is considered to be $ 0 $ . A string $ a $ is a subsequence of a string $ b $ if $ a $ can be obtained from $ b$ by the deletion of several (possibly, zero or all) characters.

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For the first sample, all of the non-empty subsequences of buaa are listed below: - b - u - a (occurred twice, buaa and buaa) - bu - ba (occurred twice, buaa and buaa) - ua (occurred twice, buaa and buaa) - aa - bua (occurred twice, buaa and buaa ) - baa - uaa - buaa Since $ \texttt{aa} = \texttt{a} + \texttt{a} $ , aa is a powerful subsequence. It can be shown that aa is the only powerful subsequence among them. So the answer is $ 2 $ . For the second sample, the longest powerful subsequence is codcod from codeforcesround. So the answer is $ 6 $ .