Andrew Stankevich (text), Elena Kryuchkova (original idea)

Time limit:

2 sec

Input file:

farmer.in

Memory limit:

200 Mb

Output file:

farmer.out

Statement

It is rumored that the planet Earth is often visited by Unidentified Flying
Objects (UFOs). Sometimes UFOs land and leave
burned out regions. Observations show that these regions
have the form of circles.

Recently farmer Bill has found such circles on his nice rectangular
wheat field.
Bill likes all mysterious things very much, so he has decided to
keep these circles on the field. However, although being an ufolog, first
of all Bill is the farmer, so he needs to harvest his wheat. Therefore
he has decided to keep some regions containing circles intact, and harvest
the rest of the field.

All regions that Bill keeps unharvested must be rectangles
that neither touch nor overlap each other.
The sides of the rectangles must be parallel to the sides of the field.
All circles left by UFOs must be inside these regions.
The total area of the regions must be minimal possible, so that Bill could
harvest the maximal possible part of his field.

Now Bill wants to know the total area of the field that he will be able
to harvest. Help him!

Input file format

The first line of the input file contains two integer numbers x and y
— the dimensions of Bill's field. Let Bill's field
be positioned on the plane in such a way that its corners are located
in points with coordinates (0, 0), (x, 0), (x, y) and (0, y).

The second line of the input file contains N — the number of circles
left by UFOs on Bill's field.
Next N lines describe circles: each line contains three positive integer numbers
x_{i}, y_{i} and r_{i} —
coordinates of the center and radius of the circle.
Circles may touch, overlap or contain each other.
All circles are completely located within the field bounds.

Output file format

Output a single integer number — the area of the part of the field that
Bill will be able to harvest.