$6.$ N queens problem: $(20$ Points$)$

Write a tail$-$recursive prolog program for the n queens problem. The objective is to place n queens

on a chessboard of size $(\backslash$times $)$ so that no two queens are attacking each other; i$.$e$.,$ no two queens

are in the same row, the same column, or on the same diagonal.

Note: All the recursive predicates in this program must be tail$-$recursive. Represent the positions

of the queens as a list of numbers $1..$N$.$ For example: When N $=8,$ the list $($Qs$)$ with the positions

would be $[4,2,7,3,6,8,5,1].$ This means that the queen in the first column is in row $4,$ the queen in

the second column is in row $2,$ etc. The goal predicate will take the form:

queens$($N$,$ Qs$).$

where N $=$ the number of queens

Qs $=$ solution to the problem

Sample Run:

$?-$ queens$(8,$ Qs$).$

Qs $=[4,2,7,3,6,8,5,1]$;

Qs $=[5,2,4,7,3,8,6,1]$;

Qs $=[3,5,2,8,6,4,7,1]$;

$...$

$...$