sum([],0).
sum([X|Xs],Total):-  sum(Xs,Rest) , Total is X+Rest.



add_N_spaces(Line, Line,0).
add_N_spaces([' '|Line],RestLine,N) :-N>0,  N1 is N-1,
add_N_spaces(Line, RestLine,N1).


add_N_stars(Line, Line,0).
add_N_stars([*|Line],RestLine,N) :- N>0,N1 is N-1,
add_N_stars(Line, RestLine,N1).



 vecLine2BitLine(X,[Y|Ys],N,BitLine):-
    LastSpace is Y-1,
    last(X,LastStarLoc),
    last([Y|Ys],LastStarLen),
    vecLine2BitLine_aux(X,[Y|Ys],N,Tmp,LastSpace),
    LastSpaces =  N - LastStarLoc - LastStarLen + 1,
    add_N_spaces(ListOfSpaces,[],LastSpaces),
    append(Tmp,ListOfSpaces,BitLine).

 vecLine2BitLine_aux([],[],_,[],_).
 vecLine2BitLine_aux([X|Xs],[Y|Ys],N,BitLine,LastSpace):-
    	NumOfSpaces is Y-LastSpace ,

    	add_N_spaces(ListOfSpaces,[],NumOfSpaces),
    	add_N_stars(ListOfStars,[],X),
    	append(ListOfSpaces,ListOfStars,Tmp),
    	length(Tmp,Size),
    	NewN is N-Size,
    	LastSpace2 is X+Y,
   	  	vecLine2BitLine_aux(Xs,Ys,NewN,Tmp2,LastSpace2),
    	append(Tmp,Tmp2,BitLine).


insertBegining([Element|List],List,Element).




makeListc([],_,[]).
makeListc([M|Rest],Index,List):-
    nth1(Index,M,Element),
    insertBegining(AlmostList,[],Element),
    makeListc(Rest,Index,Temp),
    append(AlmostList,Temp,List).

trans(Matrix,TransposedMatrix):-

    length(Matrix,Len),
    NLen is Len+1,
    trans_aux(Matrix,1,TransposedMatrix,NLen).


trans_aux(_,Len,[],Len).
trans_aux([M|Rest],Index,NewMatrix,Len):-
    makeListc([M|Rest],Index,Listi),
    IndexNew is Index + 1,
    trans_aux([M|Rest],IndexNew,Almost,Len),
    insertBegining(NewMatrix,Almost,Listi).

trim(L,N,S) :-    % to trim N elements from a list
  append(P,S,L) , % - split L into a prefix and suffix
  length(P,N) .

starsInArow([' '|_],0).
starsInArow([' '],0).
starsInArow([],0).
starsInArow([*|RestBit],N):-
     starsInArow(RestBit,C),
   	 N is C + 1.


isBitLineLegal([],[]).
isBitLineLegal([' '|[]],[]).
isBitLineLegal([' '|RestBit],[LenLine|RestLine]):-
    isBitLineLegal(RestBit,[LenLine|RestLine]).

isBitLineLegal([*|RestBit],[LenLine|RestLine]):-
    starsInArow([*|RestBit],N),
    N =:= LenLine ,
    trim([*|RestBit],LenLine,S),
    isBitLineLegal(S,RestLine).


vecLineAll2BitLineAll([],[],_,[]).
vecLineAll2BitLineAll([LenLineAll|RestL],[PosLineAll|RestP],N,BitLineAll):-
    vecLine2BitLine(LenLineAll,PosLineAll,N,Temp),
    vecLineAll2BitLineAll(RestL,RestP,N,Rest),
    insertBegining(BitLineAll,Rest,Temp).


isBitLineLegalAll([],[]).
isBitLineLegalAll([BitLineAll|RestBit],[LenLineAll|RestL]):-
    isBitLineLegal(BitLineAll,LenLineAll),
    isBitLineLegalAll(RestBit,RestL).