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.

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 $$$0$$$.

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 $$$6$$$.

Serval and Brain Power

Examples