Largest Villa

Time Limit: 10 Seconds    Memory Limit: 131072 KB

Having a grid based map, we would like to build a villa that its plan is in the shape of below or any rotation of it. (a three quarter of a square)

On the other hand, there are some trees on the map which we certainly don't want to cut down. Your task is to find the biggest area (which is like the shape above) that has no trees in it. 

 

Input

The input  consists  of  several  test  cases  (at most  30  test  cases).  Each  test  case  starts with  3 integers, M, N and T. The Airst two are the dimensions of the Aield, and the third integer is the number of the trees. 

This line is followed by T lines, each having 2 integers, the coordinates of a tree (indexed from zero). 

Caution: Huge input!

2 ≤ M,N ≤ 4000

T ≤ M.N/2 −1

Output

For each test case, output the maximum possible area for the desired villa.

 

 

Sample Input

15 14 5
10 0
11 2
7 3
11 6
14 11

Sample Output

147

Submit

Source: 12th Iran Nationwide Internet Contest III