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
anuveshkothari:
20151214 08:59:17
really enjoyed solving it..O(n^2) TLE...O(nlogn) accepted...


Jaswanth:
20150814 04:13:42
check for case n=0 costed me 2 WA 

Sahil Dua:
20141104 09:19:30
Easier than what it looks like initially. O(nlogn) accepted :) 

renters_Land:
20140627 07:03:12
good 1 :)


****:
20140123 18:50:02
:) Last edit: 20140123 18:55:49 

Venkatesh Ganesan:
20131226 14:29:41
No need of long long. Constraints are right. I used only int and got AC. 

P_Quantum:
20131223 19:12:14
int> WA


J_P:
20131219 11:38:37
wrong data type costed me 6 WA... :(.. finally AC..:) 

Secret:
20121222 13:48:35
logical problem!! Last edit: 20121222 13:48:50 

saket diwakar:
20121129 22:38:58
cool one..:) 
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 