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
md_meraj1319:
20191013 10:48:23
just apply the greedy approach! 

aayush_b1999:
20190804 13:33:32
handle n=0 case. cost me 2 WA 

rishabh8485:
20180310 01:10:02
Long Long  WA


nadstratosfer:
20170826 00:12:38
Wasted an hour trying to think of a better solution than the one I designed as a test, then gave up and submitted for the hell of it; got the best time in Python. Listen to minhthai's advice =) 

hacker:
20160907 12:48:51
logical 

GAURAV CHANDEL:
20160823 19:30:13
1st implemented O(n*logn*logn) sol..(not worked for me)


vivu01:
20160308 23:24:02
can be done in O(max(h,w)) 

codercool:
20160201 21:10:14
width+1 and height+1 

minhthai:
20160130 11:38:59
be a simple coder :) Last edit: 20160130 11:39:17 

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

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 