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, gogogo is powerful because it can be obtained by concatenating go three times, but 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.

Serval 热爱“脑力值”（Brain Power），并且热衷于解决与之相关的题目。

Serval 定义：一个字符串 $T$ 是强字符串（powerful），当且仅当 $T$ 可以通过将某个字符串 $T'$ 重复拼接若干次得到。形式化地说，$T$ 是强字符串当且仅当存在某个字符串 $T'$ 和某个整数 $k\geq 2$，使得

$$T=\underbrace{T'+T'+\dots+T'}_{k\text{ times}}$$

例如，gogogo 是强字符串，因为它可以由 go 重复拼接三次得到；但 power 不是强字符串。

Serval 有一个仅由小写英文字母组成的字符串 $S$。他很好奇：$S$ 的最长强子序列的长度是多少？你只需输出该长度。若 $S$ 的所有非空子序列均不是强字符串，则答案为 $0$。

字符串 $a$ 是字符串 $b$ 的子序列（subsequence），当且仅当 $a$ 可通过从 $b$ 中删除若干个（可能为零个或全部）字符而得到。

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

第一行包含一个仅由小写英文字母组成的字符串 $S$（$|S|\leq 80$）。

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 $0$.

输出一个整数——字符串 $S$ 的最长强子序列的长度。如果 $S$ 的所有非空子序列均不为强子序列，则输出 $0$。

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 $6$.

对于第一个样例，字符串 buaa 的所有非空子序列如下所示：

• b
• u
• a（出现两次，分别来自 buaa 和 buaa）
• bu
• ba（出现两次，分别来自 buaa 和 buaa）
• ua（出现两次，分别来自 buaa 和 buaa）
• aa
• bua（出现两次，分别来自 buaa 和 buaa）
• baa
• uaa
• buaa

由于 $\texttt{aa} = \texttt{a} + \texttt{a}$，因此 aa 是一个强子序列。可以验证，aa 是其中唯一的强子序列。故答案为 $2$。

对于第二个样例，最长的强子序列是 codeforcesround 中的 codcod。因此答案为 $6$。