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:- initialization(main).
increment_count_recur( _, _, [], []).
increment_count_recur( Index, Current, [O|Os], [N|Ns] ) :-
Index > Current, N = O, succ(Current, C1),
increment_count_recur( Index, C1, Os, Ns ).
increment_count_recur( Index, Index, [O|Os], [N|Os] ) :-
succ(O,N).
increment_count( Index, Old, New ) :-
increment_count_recur( Index, 0, Old, New ).
sum_inverses( [], _, 0 ).
sum_inverses( [H|T], Counts, X ) :-
Idx is H mod 24, InvIdx is (24 - Idx) mod 24,
succ(Idx, Idx1), nth(Idx1, Counts, Xplus),
increment_count(InvIdx, Counts, Counts1),
sum_inverses( T, Counts1, X1 ),
X is X1 + Xplus.
check_completed_days_v2( [], 0 ).
check_completed_days_v2( Days, Count ) :-
sum_inverses(
Days,
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
Count).
check_reciprocal_count( _, [], 0 ).
check_reciprocal_count( V, [H|T], X ) :-
0 =:= (V + H) mod 24,
check_reciprocal_count( V, T, X1 ),
succ(X1, X).
check_reciprocal_count( V, [H|T], X ) :-
0 =\= (V + H) mod 24,
check_reciprocal_count( V, T, X ).
check_completed_days_v1( [], 0 ).
check_completed_days_v1( [H|T], X ) :-
check_reciprocal_count( H, T, X1 ),
check_completed_days_v1( T, X2 ),
X is X1 + X2.
output_helper( X, X ) :-
format( " ~p ~n", [X] ).
main :-
Inputs = [
[12, 12, 30, 24, 24],
[72, 48, 24, 5],
[12, 18, 24],
[36, 36, 36, 1, 1, 1, 1, 1, 1, 47, 47, 47, 47]
],
maplist( check_completed_days_v1, Inputs, Outputs ),
maplist( output_helper, Outputs, _ ),
halt.
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