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

split1([], [], []).
split1([""|As], [], As). % starts with "" -> [], seq end
split1([A|As], [A|Bs], X) :-
    A \= "",
    split1(As, Bs, X).

split2([], []).
split2([A|As], [B|Bs]) :-
    split1([A|As], B, C),
    split2(C, Bs).

remove_x(_, [], []).
remove_x(X, [X|As], Bs) :-
    remove_x(X, As, Bs).
remove_x(X, [A|As], [A|Bs]) :-
    A \= X,
    remove_x(X, As, Bs).

numbers_strings([], []).
numbers_strings([A|As], [B|Bs]) :-
    number_string(A, B),
    numbers_strings(As, Bs).

strings_board([], []).
strings_board([A|As], [B|Bs]) :-
    split_string(A, " ", "", C),
    remove_x("", C, D),
    numbers_strings(B, D),
    strings_board(As, Bs).

stringss_boards([], []).
stringss_boards([A|As], [B|Bs]) :-
    strings_board(A, B),
    stringss_boards(As, Bs).

parse_boards(L, A) :-
    split2(L, B),
    remove_x([], B, C),
    stringss_boards(C, A).

parse_file([X|L], N, B) :-
    split_string(X, ",", "", A),
    numbers_strings(N, A),
    parse_boards(L, B).

main :-
    open('../input/04', read, Stream),
    read_file(Stream, Lines), !,
    close(Stream),

    parse_file(Lines, A, B),
    solve(A, B, C),
    print(C).

mark_nums_row(_, [], []).
mark_nums_row(N, [R|Rs], [1|Xs]) :-
    append([_, [R], _], N),
    mark_nums_row(N, Rs, Xs).
mark_nums_row(N, [R|Rs], [0|Xs]) :-
    \+ append([_, [R], _], N),
    mark_nums_row(N, Rs, Xs).

mark_nums_board(_, [], []).
mark_nums_board(N, [B|Bs], [C|Cs]) :-
    mark_nums_row(N, B, C),
    mark_nums_board(N, Bs, Cs).

rows_win([R|Rs]) :-
    (R = [1,1,1,1,1]; rows_win(Rs)).

transpose([[]|_], []).
transpose(A, [B|Bs]) :-
    first_column(A, B, C),
    transpose(C, Bs).

first_column([], [], []).
first_column([[B|C]|As], [B|Bs], [C|Cs]) :-
    first_column(As, Bs, Cs).

marked_board_win(B) :-
    rows_win(B).
marked_board_win(B) :-
    transpose(B, T),
    rows_win(T).

unmarked_row_sum([], [], 0).
unmarked_row_sum([_|As], [1|Ms], C) :-
    unmarked_row_sum(As, Ms, C).
unmarked_row_sum([A|As], [0|Ms], C) :-
    unmarked_row_sum(As, Ms, C1),
    C is A + C1.

unmarked_board_sum([], [], 0).
unmarked_board_sum([A|As], [B|Bs], C) :-
    unmarked_row_sum(A, B, C1),
    unmarked_board_sum(As, Bs, C2),
    C is C1 + C2.

last_num([R], R).
last_num([_|Rs], X) :-
    last_num(Rs, X).

board_win(N, B, X) :-
    mark_nums_board(N, B, C),
    marked_board_win(C),
    unmarked_board_sum(B, C, Z),
    last_num(N, Y),
    X is Y * Z.

win_order(_, [], [], []).
win_order(N, [B|Bs], C, [B|Rs]) :-
    \+ board_win(N, B, _),
    win_order(N, Bs, C, Rs).
win_order(N, [B|Bs], [C|Cs], R) :-
    board_win(N, B, C),
    win_order(N, Bs, Cs, R).

step_win_order(N, B, C) :-
    step_win_order(N, [], B, C).
step_win_order(_, _, [], []).
step_win_order([A|As], [], B, C) :-
    step_win_order(As, [A], B, C).
step_win_order([A|As], [N|Ns], B, C) :-
    win_order([N|Ns], B, C0, R),
    append([N|Ns], [A], D),
    step_win_order(As, D, R, C1),
    append(C0, C1, C).
step_win_order([], N, B, C) :-
    win_order(N, B, C, _).

solve(N, B, C) :-
    step_win_order(N, B, D),
    last_num(D, C).