:- op(700, xfx, l).
:- op(700, xfx, r).

From l To :- From to To-_.
From r To :- From to _-To.

answer(Answer) :- starts(Starts), path([], Starts, Answer).

path(_, EndNodes, []) :- all_ends(EndNodes), !.
path(Directions, FromList, Moves) :-
    next_step(Directions, Move, Remain),
    maplist(Move, FromList, ToList),
    path(Remain, ToList, RemainingMoves),
    Moves is RemainingMoves + 1.

next_step([Move | Remain], Move, Remain).
next_step([], Move, Remain) :- direction(Str), atom_chars(Str, [Move | Remain]).

starts(StartNodes) :-
    findall(Node, Node to _, Nodes),
    include(is_start, Nodes, StartNodes).
all_ends(Nodes) :- maplist(is_end, Nodes).

is_start(Node) :- atom_chars(Node, [_, _, a]).
is_end(Node) :- atom_chars(Node, [_, _, z]).