chars_digits([], []).
chars_digits([C|Cs], [D|Ds]) :-
    char_type(C, digit(D)),
    chars_digits(Cs, Ds).

read_file(Stream, []) :-
    at_end_of_stream(Stream).
read_file(Stream, [X|L]) :-
    \+ at_end_of_stream(Stream),
    read_line_to_codes(Stream, C),
    chars_digits(C, X),
    read_file(Stream, L).

main :-
    open('../input/03', read, Stream),
    read_file(Stream, Lines), !,
    close(Stream),
    solve(Lines, A, B),
    bin_dec(A, A1),
    bin_dec(B, B1),
    X is A1 * B1,
    print([A1, B1, X]).

list_sum([], [], []).
list_sum([A|As], [B|Bs], [C|Cs]) :-
    list_sum(As, Bs, Cs),
    C is A + B.
listlist_sum([], C, C).
listlist_sum([A|As], I, C) :-
    list_sum(A, I, I1),
    listlist_sum(As, I1, C).

zerolist([], []).
zerolist([_|As], [0|Bs]) :-
    zerolist(As, Bs).

listlist_sum([A|As], Sum) :-
    zerolist(A, B),
    listlist_sum([A|As], B, Sum).

div([], _, []).
div([A|As], N, [B|Bs]) :-
    B is A // N,
    div(As, N, Bs).

neg([], []).
neg([A|As], [B|Bs]) :-
    B is 1 - A,
    neg(As, Bs).

solve(Lines, Res1, Res2) :-
    listlist_sum(Lines, Sum),
    length(Lines, Len),
    div(Sum, Len // 2, Res1),
    neg(Res1, Res2).

bin_dec(B, X) :-
    bin_dec(B, 0, X).
bin_dec([], X, X).
bin_dec([B|Bs], N, X) :-
    M is N * 2 + B,
    bin_dec(Bs, M, X).