:- use_module(library(lists), [member/2]).

station(Station) :-
	setof(Distance-City,good_city(City,Distance),[_-Station|_]).

good_city(City,Distance) :-
	small_city(City),
	setof(big_city(Distance,BigCity,OutRail),
		reachable_big_city(City,BigCity,Distance,OutRail),BigCities),
	BigCities = [big_city(Distance,City1,OutRail1)|Rest],
	Rest = [big_city(Distance,City2,OutRail2)|_],
	City1 \== City2,
	OutRail1 \== OutRail2.

reachable_big_city(City,BigCity,Distance,OutRail) :-
	rail_c(City,OutRail),
	Visited = [City],
	reachable(OutRail,BigCity,Visited,Distance),
	big_city(BigCity).

reachable(City,City,Visited,Distance) :- length(Visited,Distance).
reachable(City,TargetCity,Visited,Distance) :-
	rail_c(City,City1),
	\+ member(City1,Visited),
	reachable(City1,TargetCity,[City|Visited],Distance).

big_city(City) :-
	rail_c(City,CityA),
	rail_c(City,CityB),
	rail_c(City,CityC),
	CityA \== CityB,
	CityA \== CityC,
	CityB \== CityC.

small_city(City) :-
	rail_c(City,_),
	\+ big_city(City).

rail_c(From,To) :- rail(From,To).
rail_c(From,To) :- rail(To,From).