Implement Max Pooling Algorithm
In Neural Networks used for Visual Recognition some layers perform a Max Pooling operation on an image represented as an NxM matrix of intensities (most often it is
squared but we do not make this assumption in this task). Max Pooling consists of the following: given a window of size KxL, “slide” the window through the array
without overlapping and return the maximum values for each window.

It’s best explained with an example:

Given a 4x4 matrix

1 1 2 4
5 6 7 8
3 2 1 0
1 2 3 4
and a square window of size 2x2, the subregions are:

1 1 | 2 4
5 6 | 7 8
--------
3 2 | 1 0
1 2 | 3 4
The corresponding Max Pooled values for each subregions are:

6 8
3 4
A square window of size 1x1 will return the original matrix.

For this task we will make the following assumptions:

Matrices will only contain integers in the range (-1000, 1000)
Matrices are always 2 dimensional (but not always square) and non-empty
We will always use a square window (so we’ll provide only 1 size)
The output should be the sum of Max Pooled values (e.g., 21 for the example above)
If the window cannot fit into the matrix without overlapping, the output should be the string “NONE”

Input:
The rows of the matrix each on a separate line, followed by a blank line, and then a single number for the Max Pooling window size.

Output:
Print to standard output the sum of the Max Pooled values, or the string “NONE” if assumptions are not fulfilled.

Test 1
Input
20 200
-13 134
120 32
-120 124

Expected Output:
NONE

Test 2
Test Input
20 200
-13 134
120 32
-120 12

Expected Output
Output:
320

Test 3
Test Input:
1 1 2 4
5 6 7 8
3 2 1 0
1 2 3 4

Expected Output
21

Question

Implement Max Pooling Algorithm
In Neural Networks used for Visual Recognition some layers perform a Max Pooling operation on an image represented as an NxM matrix of intensities (most often it is
 squared but we do not make this assumption in this task). Max Pooling consists of the following: given a window of size KxL, “slide” the window through the array 
 without overlapping and return the maximum values for each window.

It’s best explained with an example:

Given a 4x4 matrix

1 1 2 4
5 6 7 8
3 2 1 0
1 2 3 4
and a square window of size 2x2, the subregions are:

1 1 | 2 4
5 6 | 7 8
--------
3 2 | 1 0
1 2 | 3 4
The corresponding Max Pooled values for each subregions are:

6 8
3 4 
A square window of size 1x1 will return the original matrix.

For this task we will make the following assumptions:

Matrices will only contain integers in the range (-1000, 1000)
Matrices are always 2 dimensional (but not always square) and non-empty
We will always use a square window (so we’ll provide only 1 size)
The output should be the sum of Max Pooled values (e.g., 21 for the example above)
If the window cannot fit into the matrix without overlapping, the output should be the string “NONE”

Input:
The rows of the matrix each on a separate line, followed by a blank line, and then a single number for the Max Pooling window size.


Output:
Print to standard output the sum of the Max Pooled values, or the string “NONE” if assumptions are not fulfilled.


Test 1
Input
20 200
-13 134
120 32
-120 124

Expected Output:
NONE

Test 2
Test Input 
20 200
-13 134
120 32
-120 12

Expected Output 
Output:
320

Test 3
Test Input:
1 1 2 4
5 6 7 8
3 2 1 0
1 2 3 4 

Expected Output 
21

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