\problem{Funhouse}

\parpic[r]{\includegraphics[width=0.2\linewidth]{FunHouse/hhouse2.png}}

An amusement park is building a new walk-through funhouse. It is being
built in a large space: 1000ft x 1000ft. The park will build walls in
the space, separating it into rooms. Some walls will have doors so
that guests can move between rooms. Guests will enter through
specially marked entrances, and exit through specially marked
exits. They can move through the space as they wish -– in fact, there
may be many different ways of moving from the entrance to the exit. Of
course, there will be many amusing things along the way.

The park designers want to install {\em shakerboards}, which are
moving floors, to surprise the guests. To enhance the surprise factor,
wherever they install shakerboards, they'll fill the whole room with
them. That way, the boards won't stand out. 

The designers want every guest in the funhouse to experience
shakerboards, but, as you can imagine, shakerboards are expensive, so
the park wants to cover as little space with them as possible.

Given a description of a funhouse design, what's the smallest area
that must be covered with shakerboards to assure that every guest
experiences them?

\subsection*{Input}

There will be several data sets. Each data set will begin with a line with one integer $n$ ($3\leq n\leq 1,000$), which is the number of walls. 

Each of the next $n$ lines will describe a wall, like this:
\[ x_1 \; y_1 \; x_2 \; y_2 \; \mbox{EXDW} \]
where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints of the wall, and
$\mbox{EXDW}$ is a single capital letter: `E' for an entrance, `X' for
an exit, `D' for an interior wall with a door, and `W' for any wall
without a door. `E' and `X' are guaranteed to only appear on exterior
walls, and `D' is guaranteed to only appear on interior walls. `W' may
appear on either.

The endpoint coordinates will be integers, with values between $0$ and
$1,000$ inclusive. Walls will never intersect each other in any way or
be coincident, except for sharing endpoints. Every endpoint will be
coincident with another wall's endpoint. No wall will have zero
length. There is guaranteed to be at least one way to get from every
entrance to some exit and to every exit from some entrance. The
funhouse will consist of a single building. In order to provide power
throughout the building, every interior wall is connected to an
exterior wall either directly or indirectly via a series of other
walls.

End of input will be marked by a line with a single 0.


\subsection*{Output}

For each test case, print a single line containing the smallest area that the park owners must cover with shakerboards so that every guest in the funhouse will experience them. This should be printed as a floating point number to one decimal digit precision.

\subsection*{Example}

Given the input
\verbfile{FunHouse/sample.judge}

the output would be
\verbfile{FunHouse/sample.out}
