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, ~W~ and ~H~ ~(W,H \le 10\,000)~ representing the width and height of the room.
Then, an integer ~N \le 50~, representing the number of laser beams.
For each laser beam:
~4~ integers, ~(x_1,y_1),(x_2,y_2)~ 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 – ~(0,0)~ being the lower left and ~(W,H)~ 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 ~4~ 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 ~3.5 \times (\sqrt{2} - 1) = 1.449747\dots~
(Try calculating it! Please don't try coordinate geometry :P)

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