WATER  Water among Cubes
On a rectangular mesh comprising n*m fields, n*m cuboids were put, one cuboid on each field. A base of each cuboid covers one field and its surface equals to one square inch. Cuboids on adjacent fields adhere one to another so close that there are no gaps between them. A heavy rain pelted on a construction so that in some areas puddles of water appeared.
Task
Write a program which:
 reads from the standard input a size of the chessboard and heights of cuboids put on the fields,
 computes maximal water volume, which may gather in puddles after the rain,
 writes results in the standard output.
Input
The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case two positive integers 1 <= n <= 100, 1 <= m <= 100 are written. They are the size of the mesh. In each of the following n lines there are m integers from the interval [1..10000]; ith number in jth line denotes a height of a cuboid given in inches put on the field in the ith column and jth raw of the chessboard.
Output
Your program should write for each tes case one integer equal to the maximal volume of water (given in cubic inches), which may gather in puddles on the construction.
Example
Sample input: 1 3 6 3 3 4 4 4 2 3 1 3 2 1 4 7 3 1 6 4 1 Sample output: 5
The picture below shows the mesh after the rain (seen from above). Puddles are drawn in gray.
hide comments
sohit5012:
20200531 11:06:22
Commenting for the first time. AC in 1 go 

Artur Tadra³a:
20200511 10:24:44
"separated by an empty line"  cost me 8 NZEC... 

vcode11:
20190523 21:23:45
How to think about such problems? Any similar problems to try?


vjvjain0:
20190521 17:30:44
Java coders don't use FastReader : 

masterchef2209:
20190513 05:14:29
this problem is super awesome. got 1WA because I missed '\n' after each test case


cegprakash:
20181015 20:41:06
Test cases very weak. There are only 13 test cases in the worst test file. 7 Seconds is way too much for 13 test cases. Last edit: 20181015 20:41:47 

cegprakash:
20181015 01:23:19
What is the upper limit for number of test cases? 

megatron10599:
20180427 15:07:40
Dijkstra + BFS...0.12s Last edit: 20180427 15:49:23 

deadbrain:
20170330 08:59:52
well this is one of those problems which require basic knowledge with awesome logics... thanks for the problem. 

tni_mdixit:
20170226 23:18:02
a better explanation would be to seek the possible opening from where the water may leak... i. e. the least high column on the boundary!

Added by:  Piotr Łowiec 
Date:  20040913 
Time limit:  7s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  6th Polish Olympiad in Informatics, stage 3 