stars(Commands) :-
	buildStars(0,0,Commands,Stars),
	mins(Stars,X,Y),
	shift(X,Y,Stars,Shifted),
	sortPairs(Shifted,Sorted),
	printStars(0,0,Sorted).

buildStars(_,_,[],[]).
buildStars(X,Y,[left |Cs],Stars) :- X1 is X-1, buildStars(X1,Y,Cs,Stars).
buildStars(X,Y,[up   |Cs],Stars) :- Y1 is Y-1, buildStars(X,Y1,Cs,Stars).
buildStars(X,Y,[right|Cs],Stars) :- X1 is X+1, buildStars(X1,Y,Cs,Stars).
buildStars(X,Y,[down |Cs],Stars) :- Y1 is Y+1, buildStars(X,Y1,Cs,Stars).
buildStars(X,Y,[star |Cs],[(X,Y)|Stars]) :- buildStars(X,Y,Cs,Stars).

mins([(X,Y)|Ps],Mx,My) :- mins(X,Y,Ps,Mx,My).

mins(X,Y,[],X,Y).
mins(X,Y,[(A,B)|Ps],Mx,My) :-
	X1 is min(X,A), Y1 is min(Y,B), mins(X1,Y1,Ps,Mx,My).

shift(_,_,[],[]).
shift(X,Y,[(A,B)|Ps],[(C,D)|SPs]) :- C is A-X, D is B-Y, shift(X,Y,Ps,SPs).

sortPairs([],[]).
sortPairs([(X,Y)|Ps],SPs) :- sortPairs(Ps,SPs1), insertPair((X,Y),SPs1,SPs).

insertPair(P,[],[P]).
insertPair(P,[P|Ps],[P|Ps]) :- !.
insertPair(P,[Q|Ps],[P,Q|Ps]) :- leqPair(P,Q), !.
insertPair(P,[Q|Ps],[Q|Qs]) :- insertPair(P,Ps,Qs).

leqPair((B,A),(C,A)) :- B =< C.
leqPair((_,A),(_,C)) :- A < C.

printStars(_,[]) :- nl.
printStars(X,Y,[(X,Y)|Ps]) :- write('*'), X1 is X+1, printStars(X1,Y,Ps).
printStars(X,Y,[(Z,Y)|Ps]) :- X < Z,
	Tab is Z-X, tab(Tab), printStars(Z,Y,[(Z,Y)|Ps]).
printStars(_,Y,[(A,B)|Ps]) :- Y < B,
	nl, Y1 is Y+1, printStars(0,Y1,[(A,B)|Ps]).