codeforces#P1789F. Serval and Brain Power
Serval and Brain Power
Description
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.
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 $0$.
Input
The first line contains a single string $S$ ($|S|\leq 80$) consisting of lowercase English letters.
Output
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
codeforcesround
oooooooooooaaaaeaaiaujooooooooooooo
zero
2
6
24
0
Note
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 $6$.