Hmm, now why would someone break into a mundane software company?

After looking at the building blueprints (to place cameras), you've
noticed the suspicious room at the top.

Investigating a little, you find no visible entrance – but there's a
strange humming noise emanating from the room.

Upon asking your manager you are ushered into the conference room where
a confidential meeting seems to be taking place.

It seems that this secret room holds a certain treasure: the
thishasbeencensored

Now, they want to secure this room with lethal green laser beams.

The lasers are very thin, but they have the ability to burn a hole
through an intruder instantly.

The company engineers have built several laser designs, and they'd like
to choose the best one.

To make a laser design effective, they want to minimize the freedom a
thief would have while in the room.

As an estimate, they'd like to find the largest circle that could fit
anywhere without hitting a laser.

Now, doing this by hand would be quite tedious – so write a program to
do it for them!

#### Input Specification

Two positive integers, and representing the width and
height of the room.

Then, an integer , representing the number of laser beams.

For each laser beam:

integers, representing one laser beam.

A laser beam will travel between those two points (they are guaranteed
to be on the wall).

The room will be modeled as a 2D grid – being the lower left and
the upper right.

#### Output Specification

The radius of the largest circle that could fit without being cut by
lasers.

Your answer should be correct to decimal places.

#### Sample Input

```
7 7
5
0 0 7 7
0 7 7 0
0 6 7 2
2 0 2 7
5 0 5 7
```

#### Sample Output

`1.4497`

The exact answer is

(Try calculating it! Please don't try coordinate geometry :P)

## Comments