Uncle Tom's Inherited Land

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Your old uncle Tom inherited a piece of land from his great-great-uncle. Originally,
the property had been in the shape of a rectangle. A long time ago, however,
his great-great-uncle decided to divide the land into a grid of small squares.
He turned some of the squares into ponds, for he loved to hunt ducks and wanted
to attract them to his property. (You cannot be sure, for you have not been
to the place, but he may have made so many ponds that the land may now consist
of several disconnected islands.)

Your uncle Tom wants to sell the inherited land, but local rules now regulate
property sales. Your uncle has been informed that, at his great-great-uncle's
request, a law has been passed which establishes that property can only be sold
in rectangular lots the size of two squares of your uncle's property. Furthermore,
ponds are not salable property.

Your uncle asked your help to determine the largest number of properties he
could sell (the remaining squares will become recreational parks).

**Input**

Input will include several test cases. The first line of a test case contains
two integers N and M, representing, respectively, the number of rows and columns
of the land (1 <= N, M <= 100). The second line will contain an integer
K indicating the number of squares that have been turned into ponds ( (N x M)
- K <= 50). Each of the next K lines contains two integers X and Y describing
the position of a square which was turned into a pond (1 <= X <= N and
1 <= Y <= M). The end of input is indicated by N = M = 0.

**Output**

For each test case in the input your program should produce one line of output,
containing an integer value representing the maximum number of properties which
can be sold.

**Sample Input**

4 4

6

1 1

1 4

2 2

4 1

4 2

4 4

4 3

4

4 2

3 2

2 2

3 1

0 0

**Sample Output**

4

3

Source:

**South America 2002, Practice**
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