:- op(700, xfx, before).
:- table galaxy/2.
:- table no_galaxy_row/2.
:- table no_galaxy_col/2.
:- use_module(library(pio)).
:- initialization(start, main).

start :-
    input('input.txt', Map),
    findall(Dist, (galaxy(Map, A), galaxy(Map, B), A before B,
                   distance(Map, A, B, Dist)),
            Dists),
    sum_list(Dists, Answer),
    writef('Answer=%w\n', [Answer]).

distance(Map, X1-Y1, X2-Y2, Dist) :-
    findall(X, no_galaxy_row(Map, X), EmptyXs),
    findall(Y, no_galaxy_col(Map, Y), EmptyYs),
    include(between(X1, X2), EmptyXs, ExpandedX), length(ExpandedX, RowsToAdd),
    include(between(Y1, Y2), EmptyYs, ExpandedY), length(ExpandedY, ColsToAdd),
    Dist is abs(X1 - X2) + abs(Y1 - Y2) + RowsToAdd + ColsToAdd.

between(End1, End2, N) :- End1 < N, N < End2; End1 > N, N > End2.
no_galaxy_row(Map, X) :- nth0(X, Map, Row), maplist([46]>>(true), Row).
no_galaxy_col(Map, Y) :- maplist({Y}/[Row]>>(nth0(Y, Row, 46)), Map).

galaxy(Map, X-Y) :- nth0(X, Map, Row), nth0(Y, Row, 35).
before(X1-Y1, X2-Y2) :- X1 < X2; X1 =:= X2, Y1 < Y2.

input(FileName, Map) :- phrase_from_file(lines(Map), FileName).
lines([]) --> eos, !.
lines([Line|Lines]) --> line(Line), lines(Lines).
eos([], []).
line([]) --> ( "\n" ; eos ), !.
line([L|Ls]) --> [L], line(Ls).