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# Trapping Rain Water ll

Difficulty: HARD
Avg. time to solve
45 min
Success Rate
55%

Problem Statement

#### Given an M * N matrix, where the value at any cell denotes the height of that cell in a 2-D elevation map. You need to find the volume of water that can be trapped within it.

``````For a matrix =
[ 5, 5, 5 ]
[ 5, 2, 3 ]
[ 6, 9, 8 ]

2-D elevation map will look like this
`````` ``````After the rain, a total of 1 unit volume of water gets trapped, and this 2-D elevation map will look like this
`````` ##### Input Format:
``````The first line contains a single integer ‘T’ denoting the number of test cases.

The first line of each test case contains two space-separated integers ‘M’ and ‘N’ denoting the number of rows and columns in the matrix.

The next ‘M’ lines contain ‘N’ space-separated integers denoting the height of each cell.
``````
##### Output Format:
``````For each test case, print a single integer denoting the volume of water that can be trapped.

Print the output of each test case in a separated line.
``````
##### Note:
``````You don't need to print anything, it has already been taken care of. Just implement the given function.
``````
##### Constraints:
``````1 <= T <= 10
1 <= M,N <= 100
1 <= matrix[i][j] <= 10^3

Where ‘T’ is the number of test cases, ‘M’ and ‘N’ are the dimensions of the given matrix.
Matrix[i][j] is the height of the cell at the ‘i-th’ row and ‘j-th’ column.

Time Limit: 1 sec.
``````
##### Sample Input 1:
``````2
3 3
5 5 5
5 2 3
6 9 8
5 4
10 11 1 10
11 2 11 10
11 6 8 10
10 11 10 10
11 11 11 11
``````
##### Sample Output 1:
``````1
14
``````
##### Explanation For Sample Input 1:
``````Test Case 1: Only 1 unit volume of water can be trapped between cells with height ‘3’ and ‘2’.

Test Case 2: ‘2’ unit of volume will be stored between matrix [ 2 ][ 2 ] and matrix[ 2 ][ 3 ].
‘4’ unit of volume will be stored between matrix [ 2 ][ 1 ] and matrix[ 2 ][ 3 ].
‘8’ units of volume will be stored between matrix [ 1 ][ 1 ] and matrix[ 2 ][ 3 ].
Therefore a total of ‘14’ unit volume will be trapped.
``````
##### Sample Input 2:
``````2
2 4
3 8 9 2
2 5 7 1
4 4
4 12 8 6
2 1 5 13
2 1 12 7
2 2 10 5
``````
##### Sample Output 2:
``````0
2
``````
##### Explanation For Sample Input 2:
``````Test Case 1: They only have two sides. Thus, to accommodate any water it needs 4 edges. So, no units of water can be trapped between sides.

Test Case 2: ‘1’ unit of volume will be stored between matrix [ 2 ][ 1 ] and matrix[ 2 ][ 2 ].
‘2’ unit of volume will be stored between matrix [ 3 ][ 1 ] and matrix[ 3 ][ 3 ].
Therefore a total of ‘2’ unit volume will be trapped.
``````   Console