\problemname{Biking Duck}

\illustration{0.5}{duckonbike}{\href{https://commons.wikimedia.org/wiki/File:Unknown_Chinese_Maker_Tin_Monkey_and_Duck_on_Bike_Ha_Ha!!.jpg}{Picture} by D J Shin via Wikimedia Commons, cc by-sa}%
\noindent
Gladstone Gander is walking through Duckburg and needs to
get to his date with Daisy Duck as soon as possible. If
he doesn't get there in time, Donald might show up and
take his place instead.

Duckburg has recently started providing
a very eco-friendly way of public transport: bikes.
At many bike stations throughout the city, one
can pick up a free bike, ride it to another bike station,
and drop it there. This gives Gladstone two ways of 
transportion: on foot or by bike. Biking is faster, of
course, but he must pick up and leave the bikes at
the designated stations. Gladstone can walk or bike
between any two points in a straight line.

Gladstone possesses a map of the (rectangular) center of
Duckburg. His current position is on this map and so is
the meeting point with Daisy. The map also contains the
locations of all bike stations within the boundaries of
the map.

There can be way more bike stations though, that are not within
the boundaries of the map. Considering his luck,
you can assume that the moment Gladstone walks (or
bikes) off the map, he encounters a bike station if that
suits him well. The bike stations not on the map can be located
anywhere outside the map, they do not have to lie on integer coordinates.

That leaves Gladstone with the task of figuring out which
route to take. Can you help him out? Given the map and his
infinite amount of luck, what is the fastest time to his 
date with Daisy?

\section*{Input}

The input consists of:
\begin{itemize}
\item one line with two integers $v_{\text{walk}}$ and $v_{\text{bike}}$
($1\le v_{\text{walk}}< v_{\text{bike}} \le 1\,000$), the speeds of
walking and of biking;
\item one line with four integers $x_1, y_1, x_2$ and $y_2$
($-10^6\le x_1< x_2\le 10^6$; $-10^6\le y_1< y_2\le 10^6$),
the bounding coordinates of the map of the center of Duckburg;
\item one line with two integers $x_{\text{G}}$ and $y_{\text{G}}$,
Gladstone's position;
\item one line with two integers $x_{\text{D}}$ and $y_{\text{D}}$,
Daisy's position;
\item one line with one integer $n$ ($0\le n\le 1\,000$), the number of known
bike stations;
\item $n$ lines with two integers $x_{\text{station}}$ and $y_{\text{station}}$ each,
the coordinates of the known bike stations.
\end{itemize}
All coordinates are on the map of the center, i.e.,
$x_1\le x\le x_2$ and $y_1\le y\le y_2$.

\section*{Output}
Output one line with the shortest possible time for Gladstone to get to Daisy.
Your answer should have an absolute or relative error of at most $10^{-6}$.
