adjacent(X,Y,Map) :-  member([X,Y],Map) ; member([Y,X],Map). 


find_regions(Map,Regions):-
	flatten(Map,X),
	list_to_set(X,Regions).

color(Map,Colors,Coloring) :-
        find_regions(Map,Regions), 
        color_all(Regions,Colors,Coloring), 
        not(conflict(Map,Coloring)).

color_all([R|Rs],Colors,[[R,C]|A]) :- 
        member(C,Colors), 
        color_all(Rs,Colors,A). 
color_all([],_,[]). 

conflict(Map,Coloring) :- 
        member([R1,C],Coloring), 
        member([R2,C],Coloring), 
        adjacent(R1,R2,Map). 

map1([[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[3,4],[4,5]] ).