A15717. 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.

The first line contains a single string $S$ ( $|S|\leq 80$ ) consisting of lowercase English letters.

Print a single integer — the length of the longest powerful subsequence of $S$ . If all the non-empty subsequences of $S$ is not powerful, print $0$ .

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 $6$ .