\problemname{Date Picker}

\newcommand{\hours}{24}
\newcommand{\days}{7}

\illustration{0.28}{agenda.jpg}{A filled agenda.}% Source: Jeroen's camera
The NWERC is coming up and your agenda is filling up with meetings.
One of your teammates wants to plan a meeting, and asks for your input.
However, instead of asking you for your exact agenda, you have to fill out two separate polls:
one for indicating which days you are available, and one for the hours!

As a computer scientist, you plan your meetings only on whole hours and each meeting takes an integer number of hours.
Therefore, your agenda can be modelled as a matrix of $\days$ rows (days), and $\hours$ columns (hours).
Each cell in this matrix is either `\texttt{.}' or `\texttt{x}',
meaning that hour of that day you are either free or have a meeting, respectively.

You have to pick at least $d$ days in the first poll and $h$ hours in the second poll,
and we assume the meeting will take place on any of your picked hour/day combinations with equal probability.
What is the probability that you can attend the meeting if you fill in the polls optimally?

\begin{Input}
    The input consists of:
    \begin{itemize}
        \item $\days$ lines with $\hours$ characters, each character being
            either `\texttt{.}' or `\texttt{x}', with `\texttt{.}' indicating the time
            slots you are available.
        \item One line with two integers $d$ and $h$ ($1 \leq d \leq \days$, $1 \leq h \leq \hours$),
            the minimum number of days and hours you have to fill in.
    \end{itemize}
\end{Input}

\begin{Output}
    Output the probability that you are available at the chosen meeting time.

    Your answer should have an absolute or relative error of at most $10^{-6}$.
\end{Output}
