In this problem, you will write a program $($filter$.$cc$)$ which performs some very simple image processing operations. You can find a template program in Moodle $($filter$-$template.cc$).$ The program, once compiled, can be run as follows:

filter image.pgm

where image.pgm is the file containing an image.

Write the allocate and deallocate functions $($see the template$)$ which allocates and deallocates two$-$dimensional arrays of integers.

You will also write three functions which are used to process images in different ways:

$($a$)$ int average$($int A$[5][5])$;

This function computes the average $($rounded to the nearest integer$)$ of the two$-$

dimensional array of $25$ integers.

$($b$)$ int median$($int A$[5][5])$;

This function computes the median of the two$-$dimensional array of $25$ integers, rounded to the nearest integer. You may reuse code you have written for the previous problems.

$($c$)$ int strange$($int A$[5][5])$;

This function should return the value:

$255\mathrm{.}0\backslash$times $($A$[1][1]2\backslash$times A$[2][1]$ A$[3][1]+$ A$[1][3]+2\backslash$times A$[2][3]+$ A$[3][3]+1020)2040$

rounded to the nearest integer.