Cow Pool

The cows have decided they must have a swimming pool for next summer. They have also chosen a shape: an "L"-shaped pool. The pool will go in a forest near their pastures, and the cows do not want to remove any trees. You are given the size of the forest, W wide by H high, and a set of N tree locations. Find the largest possible pool by area that can be built in the forest.

Here is an example grid and forest with the largest pool:

.  .  *  .  .  .  .      .  .  *  .  .  .  .
*  .  .  .  .  .  .      *  P  P  .  .  .  .
.  .  .  *  *  *  .      .  P  P  *  *  *  .
.  .  .  .  .  .  .      .  P  P  .  .  .  .
*  .  .  *  .  *  .  ->  *  P  P  *  .  *  .
.  .  .  .  .  .  .      .  P  P  P  P  P  .
.  .  .  .  .  .  .      .  P  P  P  P  P  .
*  .  .  .  .  .  *      *  P  P  P  P  P  *
.  .  *  .  *  .  .      .  .  *  .  *  .  .

The largest pool covers 23 gridpoints.

The pool has an "L" shape, formed by combining two rectangles that share the lower left corner. The lower bar of the "L" must be wider than the upper part. The upper part must be taller than the lower bar. The "L" is never rotated or reflected. A simple rectangle is not an "L" shape.

The first line has three integers, W (5 ≤ W ≤ 150), H (5 ≤ H ≤ 150), and N (1 ≤ N ≤ 20000).

Each of the next N lines has two integers, the row and column of a tree. The upper left corner of the tree map is Row 1, Column 1. In the example above, the top row contains a tree at Row 1, Column 3.

Print a single line with the number of gridpoints covered by the largest possible pool.