inserting(A,B,C):-deleting-one(A,C,B).
deleting-one(A,[A|B],B).
deleting-one(A,[B|C],[B|D]):-
    deleting-one(A,C,D).

%deleting-all(B,[B],[]).
%deleting-all(A,[A|LIST1],LIST1).
%deleting-all(B,[B|LIST],[A|LIST1]):-deleting-all(A,LIST,LIST1).
deleting-all(B,A,Result):-delete(A,B,Result).
range(A,B,X):-numlist(A,B,X).
 last(X,[X]).
 last(X,[_|Z]) :- last(X,Z).
 rotate(A,N,Result):-
    length(Tail,N),
    append(Head,Tail,A),
    append(Tail,Head,Result).
%append(last(_,A),Result).


duplicate([],[]).
duplicate([H|T],[[H,H]|NT]):-
duplicate(T,NT).