In the $2020$ grid far below, four numbers along a diagonal line have been marked in

red. The product of these numbers is $26637814=1788696.$ Write a program to

answer the question: what is the greatest product of $"z"$ adjacent numbers in the same

direction $($up$,$ down, left, right or diagonally$)$ in the grid?

grid$20.$txt

$2020$

$0802229738150040007504050778521250779108$

$4949994017811857608717409843694804566200$

$8149317355791429937140675388300349133665$

$5270952304601142692468560132567137023691$

$2231167151676389419236542240402866331380$

$2447326099034502447533537836842035171250$

$3298812864236710263840675954706618386470$

$6726206802621220956394396308409166499421$

$2455580566739926971778789683148834896372$

$2136230975007644204535140061339734313395$

$7817532822753167159403800462161409535692$

$1639054296353147555888240017542436298557$

$8656004835718907054444374460215851541758$

$1980816805944769287392138652177704895540$

$0452088397359916079757321626267933279866$

$8836688757622072034633674655123263935369$

$0442167338253911249472180846293240627636$

$2069364172302388346299698267598574043616$

$2073352978319001743149714886811623570554$

$0170547183515469169233486143520189196748$

Your program must accept the parameter $"z"$ from command line along with the name of

the grid file. It must output the positions of the numbers in the greatest product, the

actual numbers and the product. For example, to indicate the above four red numbers,

your program must print the following:

Example $1$ output $($input in bold$)$:

Enter filename: $2$ grid$20.$txt

Enter the adjacent number: $4$

Maximum $4-$product in file "grid.txt$"$

Row $7$ col $9$: $26$

Row $8$col$10$:$63$

Row $9$ col $11$:$78$

Row $10$col$12$:$14$

Max Product: $1788696$

Note that the grid may be smaller or larger than $2020$ but must always be a square

grid. If your program detects something other than a square grid, it should output an

error message. Also note that the user may request a $"z"$ larger than the grid, in which

case your program should also output an error message.

grid$3.$txt

$33$

$080222$

$494999$

$814931$

Example $2$ output $($input in bold$)$:

Enter filename: grid$3.$txt

Enter the adjacent number: $2$

Maximum $2-$product in file "grid.txt$"$

Row $1$ col $1$: $49$

Row $1$col$2$:$99$

Max Product: $4851$

Please use "grid$20.$txt$"$ and "grid$3.$txt$"$ to test your program.

Submission detail:

Implement the program use both recursive and non$-$recursive method $(100$pt as

starting point$)$