Serval and Brain Power

### 题目描述 定义一个字符串 $T$ 是好的，当且仅当存在字符串 $T'$ 和整数 $k(k\geq2)$，使得 $T$ 可以由 $k$ 个 $T'$ 首尾相接得到。 例如，字符串 $\texttt{gogogo}$ 就是好的，因为它可以由 $3$ 个字符串 $\texttt{go}$ 首尾相接得到；而 $\texttt{power}$ 就不是好的。 给定仅包含小写英文字母的字符串 $S$。 你需要求出 $S$ 最长的好的子序列（不一定连续）的长度，特别的如果 $S$ 没有好的子序列，答案为 $0$。 ### 输入格式 输入一行一个小写英文字母字符串表示 $S(|S|\leq80)$。 ### 输出格式 输出一行一个整数表示 $S$ 中最长的好的子序列的长度。 如果 $S$ 没有好的子序列，输出 $0$。

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 $ .

buaa

2

codeforcesround

6

oooooooooooaaaaeaaiaujooooooooooooo

24

zero

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 $ .