DEFKIN  Defense of a Kingdom
Theodore implements a new strategy game “Defense of a Kingdom”. On each level a player defends the Kingdom that is represented by a rectangular grid of cells. The player builds crossbow towers in some cells of the grid. The tower defends all the cells in the same row and the same column. No two towers share a row or a column.
The penalty of the position is the number of cells in the largest undefended rectangle. For example, the position shown on the picture has penalty 12.
Help Theodore write a program that calculates the penalty of the given position.
Input
The first line of the input file contains the number of test cases.
Each test case consists of a line with three integer numbers: w — width of the grid, h — height of the grid and n — number of crossbow towers (1 ≤ w, h ≤ 40 000; 0 ≤ n ≤ min(w, h)).
Each of the following n lines contains two integer numbers x_{i} and y_{i} — the coordinates of the cell occupied by a tower (1 ≤ x_{i} ≤ w; 1 ≤ y_{i} ≤ h).
Output
For each test case, output a single integer number — the number of cells in the largest rectangle that is not defended by the towers.
Example
Input: 1 15 8 3 3 8 11 2 8 6 Output: 12
hide comments
Bharath Reddy:
20120710 05:59:23
Can anyone tell me some corner cases?


Shashank Shekhar Mishra:
20120705 19:57:34
what could be possibly wrong in my code?? its giving wa !! subm id7266003 Last edit: 20120705 20:05:32 

BLANKRK:
20120704 12:01:59
simple logic!!! got AC!!! 

Santiago Zubieta:
20110429 15:38:40
I'm getting time limit exceeded, I don't know what it could be, my code is very short (37 lines, 606 chars) :(

Added by:  Fidel Schaposnik 
Date:  20101108 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  ACM ICPC 2010, NEERC, Northern Subregional Contest 