\problem{Periodic Strings}

Define a  \textit{k-periodic string} as follows:

\begin{quotation}
A string $s$ is k-periodic if $|s|$, the length of the string, is a
multiple of $k$ and, if you chop the string up into $|s|/k$ substrings
of length $k$, then each of those substrings (except the first) is the
same as the previous substring, but with its last character moved to
the front.
\end{quotation}

For example, the following string is 3-periodic:

\[ abccabbcaabc \]

The above string breaks up into substrings $abc$, $cab$, $bca$, and
$abc$, and each substring (except the first) is a rotation of the
previous substring ($abc \rightarrow cab$, $cab \rightarrow bca$, $bca
\rightarrow abc$).

Given a string, determine the smallest $k$ for which the string is
k-periodic.



\subsection*{Input}

Input will be a single line containing a string $s$, ($1 \leq |s| \leq
100$), consisting only of lower-case letters.


\subsection*{Output}

Print a single line containing an integer denoting the smallest value
of $k$ for which the input string is k-periodic.

\subsection*{Examples}


\begin{center}
  \begin{tabular}{|l|l|}
    \multicolumn{1}{l}{\textbf{Sample Input}} &
    \multicolumn{1}{l}{\textbf{Sample Output}} \\
    \hline
    aaaaaaaa & 1 \\ \hline
    abbaabbaabba & 2 \\ \hline
    abcdef & 6 \\ \hline
    abccabbcaabc & 3 \\ \hline
  \end{tabular}

\end{center}
