answer(Answer) :-
    input(Input),
    convert_input(Input, Hands, Bets),
    convlist(score, Hands, Scores),
    zip(Scores, Bets, ScoresBets),
    sort(ScoresBets, SortedScoreBetsInv),
    reverse(SortedScoreBetsInv, SortedScoreBets),
    payout(SortedScoreBets, _, Answer).

% payout([Hand-Bet], _, Payout) computes total payout from [Hand-Bet] map.
payout([], 0, 0).
payout([_-Bet | Cdr], Rank, Payout) :-
    payout(Cdr, LastRank, LastPayout),
    Rank is LastRank + 1,
    Payout is LastPayout + Rank*Bet.

% score(Hand, Score) gets the score for one hand, that can be directly compared.
score([A, B, C, D, E], Score) :-
    max_type([A, B, C, D, E], Type),
    tiebreaker([A, B, C, D, E], Tiebreaker),
    Score is Tiebreaker + (100**5)*Type.

tiebreaker([A, B, C, D, E], Score) :-
    Score is E + 100*D + (100**2)*C + (100**3)*B + (100**4)*A.

% max_type gets the max possible type from a hand including wildcards
max_type([A, B, C, D, E], Type) :-
    (
        type([A, B, C, D, E], 7) -> Type is 7;
        type([A, B, C, D, E], 6) -> Type is 6;
        type([A, B, C, D, E], 5) -> Type is 5;
        type([A, B, C, D, E], 4) -> Type is 4;
        type([A, B, C, D, E], 3) -> Type is 3;
        type([A, B, C, D, E], 2) -> Type is 2;
        type([A, B, C, D, E], 1) -> Type is 1
    ).

% type(Hand, Type) get the type rank for one hand, ordered.
type([A, B, C, D, E], Type) :-
    wild(A, [A, B, C, D, E], Ax),
    wild(B, [A, B, C, D, E], Bx),
    wild(C, [A, B, C, D, E], Cx),
    wild(D, [A, B, C, D, E], Dx),
    wild(E, [A, B, C, D, E], Ex), 
    sort(0, @=<, [Ax, Bx, Cx, Dx, Ex], Sorted),
    sorted_type(Sorted, Type).
sorted_type([X, X, X, X, X], 7).
sorted_type([X, X, X, X, A], 6) :- X =\= A.
sorted_type([A, X, X, X, X], 6) :- X =\= A.
sorted_type([Y, Y, X, X, X], 5) :- X =\= Y.
sorted_type([X, X, X, Y, Y], 5) :- X =\= Y.
sorted_type([X, X, X, A, B], 4) :- X =\= A, A =\= B.
sorted_type([A, X, X, X, B], 4) :- A =\= X, X =\= B.
sorted_type([A, B, X, X, X], 4) :- A =\= B, B =\= X.
sorted_type([X, X, Y, Y, A], 3) :- X =\= Y, Y =\= A.
sorted_type([X, X, A, Y, Y], 3) :- X =\= A, A =\= Y.
sorted_type([A, X, X, Y, Y], 3) :- A =\= X, X =\= Y.
sorted_type([X, X, A, B, C], 2) :- X =\= A, A =\= B, B =\= C.
sorted_type([A, X, X, B, C], 2) :- A =\= X, X =\= B, B =\= C.
sorted_type([A, B, X, X, C], 2) :- A =\= B, B =\= X, X =\= C.
sorted_type([A, B, C, X, X], 2) :- A =\= B, B =\= C, C =\= X.
sorted_type([A, B, C, D, E], 1) :- A =\= B, B =\= C, C =\= D, D =\= E.

% convert_input(InputList, Cards, Bets)
convert_input([], [], []).
convert_input([[Cards, Bet] | Cdr],
              [[C1, C2, C3, C4, C5] | HandCdr],
              [Bet | BetCdr]) :-
    string_to_list(Cards, [A1, A2, A3, A4, A5]),
    card(A1, C1), card(A2, C2), card(A3, C3), card(A4, C4), card(A5, C5), 
    convert_input(Cdr, HandCdr, BetCdr).

wild(X, _, Y) :- X =\= 1, Y is X.
wild(X, [A, B, C, D, E], Y) :-
    X =:= 1,
    (Y is A; Y is B; Y is C; Y is D; Y is E).

% card(Ascii, Value) converts between card ascii value and internal values
card(84, 10). % T
card(74, 1). % J
card(81, 12). % Q
card(75, 13). % K
card(65, 14). % A
card(Char, Card) :- Char >= 48, Char =< 57, Card is Char - 48.

% zip 2 lists into a map
zip([], [], []).
zip([A | ACdr], [B | BCdr], [A-B | ABCdr]) :- zip(ACdr, BCdr, ABCdr).