那是废话！(纸牌游戏)

Question

BS是一个纸牌游戏，游戏的目标是输掉你所有的牌。

一场比赛由四个玩家和一个52张牌组成.每位玩家随机发放13张牌。通常情况下，牌标为2-10，Ace，Jack，Queen，King，但为了简单起见，卡片将被标记为0-12包含的数字。虽然牌手手中的牌数是公开信息，但只有玩家知道手中有哪些特定的牌。

游戏内容如下:第一位玩家在弃牌堆中放置标记为0的任意多张牌(请注意，他没有被要求使用标记为0的所有牌，尽管这样做通常符合他的最佳利益)。他必须至少打一张牌。第二个玩家想打多少牌就打多少牌，第三个玩家打2，以此类推。12之后，它将重置为0。

如果你没有任何你应该玩的牌，会发生什么？记住，你必须至少打一张牌--事实上，你可以打任何你想打的牌！(事实上，即使你有正确的牌，你也可以撒谎，玩另一张牌)。然而，有人可以叫你出来说：“废话！”如果那个人是对的，而且你撒谎了，那么你必须把所有的牌都拿走，作为奖励，叫你出来的玩家会随机地把他们的一张牌放进弃堆里。但是，如果原告错了，他必须把所有的卡片都拿走。请注意，你不能对你打的牌的数量撒谎。

更详细的信息：

• 在游戏开始的时候，四个随机的玩家被选中去玩。因为至少有1000场比赛，每个玩家都有机会上场。回合顺序是在游戏开始时随机决定的。
• 如果你退回一张正确的卡片和一张不正确的卡片，那么它就被认为是说谎的(也就是说，如果你应该给2_s，而你给了一个_2和一个1，那就是说谎)
• 如果两个或两个以上的玩家同时说BS，那么随机选择一个。
• 你的分数是你赢得比赛的百分比。
• 有一个最多1000轮，其中一轮是每名球员一次。通常在这之前有人会赢。如果没有人赢，那么它被算作玩的游戏总数，但没有人赢。

规格：

您应该编写一个扩展Player的类。它将看起来像：

package players;

import java.util.ArrayList;
import java.util.List;

import controller.*;

public class Player1 extends Player {

    @Override
    protected List<Card> requestCards(int card, Controller controller) {
        Card[] hand = getHand();
        List<Card> ret =  new ArrayList<Card>();
        for (Card c : hand) {
            if (c.getNumber() == card) {
                ret.add(c);
            }
        }
        if (ret.size() == 0) ret.add(hand[0]);
        return ret;
    }

    @Override
    protected boolean bs(Player player, int card, int numberOfCards, Controller controller) {
        return numberOfCards >= 3;
    }

    protected void update(Controller controller) {
      // This method gets called once at the end of every round
    }

    protected void initialize(Controller controller) {
      // This method gets called once at the beginning once all the cards are dealt
    }

    public String toString() {
        return "Player 1";
    }
}

轮到您时调用requestCards方法。参数card是您应该提供的卡号。您返回要放入丢弃堆中的卡片列表。上面的玩家检查他是否有所要求的牌类型的牌；如果没有，他只打他的第一张牌，希望没有人检查。

每当有人打牌时，都会调用bs方法。第一种观点是球员，第二种是他应该打的牌，第三种是他声称自己打过的那种牌的数量。如果要调用“BS”，请返回true。在上面的代码中，播放机只在其他玩家声称拥有3张或3张以上请求类型的卡片时才调用"BS“。

这两种方法的最后一个参数是controller，它只是控制游戏的控制器。从控制器中，您可以获得更多的公共信息，例如弃牌堆中的牌数或玩家的列表和转盘顺序。

toString方法是可选的。

GitHub上的Conroller：https://github.com/prakol16/bs

如果您想发布一个非java解决方案，您可以使用https://github.com/LegionMammal978/bs提供的接口(对LegionMammal978的学分)，我将尝试集成它。

到目前为止记分板：

class players.PlayerConMan: 2660/4446 = 59.82905982905983%
class players.CalculatingLiar: 2525/4426 = 57.049254405784005%
class players.PlayerTruthy: 1653/4497 = 36.75783855903936%
class players.Player4: 1446/4425 = 32.67796610169491%
class players.Player1: 536/4382 = 12.23185759926974%
class players.Player3: 493/4425 = 11.141242937853107%
class players.Player2: 370/4451 = 8.312738710402156%
class players.LiePlayer: 317/4432 = 7.152527075812275%
class players.Hoarder: 0/4516 = 0.0%

PlayerConMan赢了，但CalculatingLiar紧随其后。这些分数似乎是一致的--每次都是一样的。

Answer 1

ConMan

ConMan看着每一张通过他的手的卡片，当一场比赛由于牌在哪里而不可能时，打电话给BS。

当有能力的时候玩真理，但是如果胜利发生的话，聪明地使用最后一张牌。

我花了很长时间调整一种技术，当对手说谎的概率很高时，或者当呼叫BS是有益的(例如从丢弃的堆中获得有用的卡片)时，我会调用BS，但在实践中，根本不打BS就能让我得到最多的分数。

package players;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import controller.*;
import java.text.DecimalFormat;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Iterator;

public class PlayerConMan extends Player {

    private enum Location {

        PLAYER_0,
        PLAYER_1,
        PLAYER_2,
        PLAYER_3,
        DISCARD,
        UNKNOWN
    };

    private class MyCard {

        private final int number;
        private Location location;
        private double confidence;
        protected Card card;

        public MyCard(int x) {
            this.number = x;
            location = Location.UNKNOWN;
            confidence = 1.0;
        }

        @Override
        public String toString() {
            if (confidence > 0.75) {
                return ""+number;
            } else if (confidence > 0.25) {
                return number+"*";
            } else {
                return number+"_";
            }
        }
    }

    private final ArrayList<ArrayList<MyCard>> theDeck = new ArrayList();
    private Location myLocation;
    private ArrayList<Player> players;
    private final ArrayList<MyCard> myHand = new ArrayList();
    private final HashMap<Location, Integer> sizes = new HashMap();
    private ArrayList<Integer> lies = new ArrayList();
    private ArrayList<Integer> truths = new ArrayList();


    // Constructor
    public PlayerConMan() {
        for (int i = 0; i < 13; ++i) {
            ArrayList<MyCard> set = new ArrayList();
            for (int j = 0; j < 4; ++j) {
                set.add(new MyCard(i));
            }
            theDeck.add(set);
        }
        sizes.put(Location.PLAYER_0, 13);
        sizes.put(Location.PLAYER_1, 13);
        sizes.put(Location.PLAYER_2, 13);
        sizes.put(Location.PLAYER_3, 13);
        sizes.put(Location.DISCARD, 13);
        sizes.put(Location.UNKNOWN, 39);
    }

    //Gets the MyCard for this card, updating a MyCard with the lowest confidence if not already created
    private MyCard getCard(Card c) {
        ArrayList<MyCard> set = theDeck.get(c.getNumber());
        MyCard unknown = null;
        double confidence = 1.0;
        for (MyCard m : set) {
            if (m.card == c) {
                return m;
            }
            if (m.card == null) {
                if (m.location == Location.UNKNOWN) {
                    unknown = m;
                    confidence = 0.0;
                } else if (m.confidence < confidence || unknown == null) {
                    unknown = m;
                    confidence = m.confidence;
                }
            }
        }
        unknown.card = c;
        return unknown;
    }

    //Returns the Location of a player
    private Location getLocation(Player p) {
        return Location.values()[players.indexOf(p)];
    }

    @Override
    protected void initialize(Controller controller) {
        super.initialize(controller);
        players = new ArrayList(controller.getPlayers());
        for (Player p : players) {
            if (p == this) {
                myLocation = getLocation(p);
            }
        }
        for (Location loc : Location.values()) {
            sizes.put(loc, 0);
        }
    }

    private ArrayList<Integer>[] getTruthesAndLies(Player player, int card, ArrayList<MyCard> myHand) {
            //Determine our next plays
            int offset = players.indexOf(player);
            int myOffset = players.indexOf(this);
            int nextCard = (card + (myOffset - offset + 4) % 4)%13;
            ArrayList<Integer> truths = new ArrayList();
            ArrayList<Integer> lies = new ArrayList();
            ArrayList<MyCard> cardsLeft = new ArrayList(myHand);
            while (!cardsLeft.isEmpty()) {
                boolean isLie = true;
                Iterator<MyCard> it = cardsLeft.iterator();
                while (it.hasNext()) {
                    MyCard m = it.next();
                    if (m.number == nextCard) {
                        it.remove();
                        isLie = false;
                    }
                }
                if (isLie) {
                    lies.add(nextCard);
                } else {
                    truths.add(nextCard);
                }
                nextCard = (nextCard + 4)%13;
            }

            return new ArrayList[]{truths, lies};
    }

    private void updateDeck(Player player, int card, int numberOfCards, Controller controller) {
        Location loc = getLocation(player);

        //Update from BS
        if (sizes.get(Location.DISCARD) + numberOfCards != controller.getDiscardPileSize()) {

            //Move all cards from DISCARD to the losing player
            //  Losing player defaults to player playing, in the rare case of a tie
            Location losingPlayer = loc;
            Location winningPlayer = null;
            for (Player p : players) {
                Location pLoc = getLocation(p);
                int size = p.handSize();
                if (pLoc == loc) size += numberOfCards;
                if (p.handSize() > sizes.get(pLoc)) {
                    losingPlayer = pLoc;
                } else if (size < sizes.get(pLoc)) {
                    winningPlayer = pLoc;
                }
            }

            if (winningPlayer == null) {
                debug(losingPlayer+" lost a BS");
            } else {
                debug(losingPlayer+" lied and "+winningPlayer+" lost a card");
            }

            //Move the cards from the discard to the player
            ArrayList<MyCard> winnersHand = new ArrayList();
            for (ArrayList<MyCard> set : theDeck) {
                for (MyCard m : set) {
                    if (m.location == Location.DISCARD) {
                        if (losingPlayer == myLocation) {
                            //If we lost, update the discard cards to unknown;
                            //  They'll be updated when we look at our hand
                            m.location = Location.UNKNOWN;
                            m.confidence = 1.0;
                        } else {
                            //Move to the losing player
                            m.location = losingPlayer;
                        }
                    } else if (m.location == myLocation && winningPlayer == myLocation) {
                        //Update our old cards to the discard pile, in case we won
                        m.location = Location.DISCARD;
                        m.confidence = 1.0;
                    } else if (m.location == winningPlayer) {
                        //Add the card to the winner's hand for later processing
                        winnersHand.add(m);
                    }
                }
            }

            //If someone else won, adjust the probabilities on their cards
            if (winningPlayer != myLocation && winningPlayer != null) {
                int winningSize = players.get(winningPlayer.ordinal()).handSize();
                if (winningPlayer == loc) winningSize += numberOfCards;
                for (MyCard m : winnersHand) {
                    m.confidence *= 1-(1/winningSize);
                }
            }

        }
        sizes.put(Location.DISCARD, controller.getDiscardPileSize());
        //Update player handSize
        for (Player p : players) {
            sizes.put(getLocation(p), p.handSize());
        }


        //Detect if my hand size has changed to speed processing
        if (myHand.size() != handSize()) {
            //Update values from my hand
            myHand.clear();
            for (Card c : getHand()) {
                MyCard m = getCard(c);
                m.location = myLocation;
                m.confidence = 1.0;
                myHand.add(m);
            }

            //Determine our next plays
            ArrayList<Integer> tl[] = getTruthesAndLies(player, card, myHand);
            truths = tl[0];
            lies = tl[1];
            debug("Truthes: "+truths);
            debug("Lies: "+lies);
        }
    }


    @Override
    protected List<Card> requestCards(int card, Controller controller) {
        updateDeck(this, card, 0, controller);

        ArrayList<Card> ret = new ArrayList();
        int pick = card;
        boolean all = true;
        if (truths.get(0) != card) {
            pick = truths.get(truths.size()-1);
            all = false;
        }

        for (MyCard m : myHand) {
            if (m.number == pick) {
                m.location = Location.DISCARD;
                ret.add(m.card);
                if (!all) break;
            }
        }

        sizes.put(Location.DISCARD, controller.getDiscardPileSize() + ret.size());
        sizes.put(myLocation, myHand.size() - ret.size());
        printTheDeck();

        return ret;
    }

    @Override
    protected boolean bs(Player player, int card, int numberOfCards, Controller controller) {
        updateDeck(player, card, numberOfCards, controller);
        Location loc = getLocation(player);

        //Get total number of unknown cards and total number of cards the player must have
        int handSize = player.handSize() + numberOfCards;
        ArrayList<MyCard> playerHand = new ArrayList();
        ArrayList<MyCard> discardPile = new ArrayList();
        double totalUnknown = 0;
        double playerUnknown = handSize;
        double cardsHeld = 0;
        double cardsNotHeld = 0;
        for (ArrayList<MyCard> set : theDeck) {
            for (MyCard m : set) {
                if (m.location == Location.UNKNOWN) {
                    totalUnknown++;
                } else if (m.location == loc) {
                    playerHand.add(m);
                    playerUnknown -= m.confidence;
                    totalUnknown += 1.0 - m.confidence;
                    if (m.number == card) {
                        cardsHeld += m.confidence;
                    }
                } else {
                    if (m.location == Location.DISCARD) {
                        discardPile.add(m);
                    }
                    totalUnknown += 1.0 - m.confidence;
                    if (m.number == card) {
                        cardsNotHeld += m.confidence;
                    }
                }
            }
        }

        boolean callBS = false;
        double prob;
        int possible = (int)Math.round(4-cardsNotHeld);
        int needed = (int)Math.round(numberOfCards - cardsHeld);
        if (needed > possible) {
            //Player can't possibly have the cards
            prob = 0.0;
            debug("impossible");
            callBS = true;
        } else if (needed <= 0) {
            //Player guaranteed to have the cards
            prob = 1.0;
            debug("guaranteed");
        } else {
            //The probability that player has needed or more of the possible cards
            double successes = 0;
            for (int i = (int)needed; i <= (int)possible; i++) {
                successes += choose(possible, i) * choose(totalUnknown-possible, playerUnknown-i);
            }
            double outcomes = choose(totalUnknown, playerUnknown);
            prob = successes / outcomes;
            if (Double.isNaN(prob)) {
                prob = 0;
                callBS = true;
            }
            debug("prob = "+new DecimalFormat("0.000").format(prob));
        }

        //Update which cards they may have put down
        //  Assume they put down as many as they could truthfully
        int cardsMoved = 0;
        Iterator<MyCard> it = playerHand.iterator();
        while (it.hasNext()) {
            MyCard m = it.next();
            if (m.number == card) {
                it.remove();
                m.location = Location.DISCARD;
                discardPile.add(m);
                cardsMoved++;
                if (cardsMoved >= numberOfCards) {
                    break;
                }
            }
        }

        //We can't account for all the cards they put down
        //  Adjust existing probabilities and move our lowest confidence cards to the discard
        if (cardsMoved < numberOfCards) {
            //  Reduce the confidence of all remaining cards, in case they lied
            //  Assumes they lie at random
            double cardsLeft = handSize-cardsMoved;
            double cardsNeeded = numberOfCards-cardsMoved;
            double probChosen = 1 * choose(cardsLeft-1, cardsNeeded-1) / choose(cardsLeft, cardsNeeded);
            if (Double.compare(cardsLeft, cardsNeeded) == 0) {
                //They're gonna win, call their bluff
                callBS = true;
                for (MyCard m : playerHand) {
                    m.location = Location.DISCARD;
                }
            } else {
                for (MyCard m : playerHand) {
                    m.confidence *= (1-probChosen) * (1-prob) + prob;
                }
            }

            //  Move any UNKNOWN cards they could have played, assuming they told the truth
            Collections.sort(theDeck.get(card), new Comparator<MyCard>() {
                @Override
                public int compare(MyCard o1, MyCard o2) {
                    double p1 = o1.confidence - (o1.location == Location.UNKNOWN ? 10 : 0);
                    double p2 = o2.confidence - (o2.location == Location.UNKNOWN ? 10 : 0);
                    return (int)Math.signum(p1-p2);
                }
            });
            for (MyCard m : theDeck.get(card)) {
                if (m.location == Location.UNKNOWN || m.confidence < prob) {
                    m.location = Location.DISCARD;
                    m.confidence = prob;
                    cardsMoved++;
                    discardPile.add(m);
                    if (cardsMoved >= numberOfCards) break;
                }
            }
        }

        //Get the confidence of the discardPile
        double discardPileConfidence = 1.0;
        for (MyCard m : discardPile) {
            discardPileConfidence *= m.confidence;
        }
        discardPileConfidence *= Math.pow(0.5, controller.getDiscardPileSize() - discardPile.size());

        //Call BS if the cards in the discard pile consists only of cards we need / will play
        if (discardPileConfidence > 0.5 && discardPile.size() == controller.getDiscardPileSize()) {
            double truthCount = 0;
            double lieCount = 0;
            double unknownCount = 0;
            for (MyCard m : discardPile) {
                if (truths.contains(m.number)) {
                    truthCount += m.confidence;
                    unknownCount += 1-m.confidence;
                } else if (lies.contains(m.number)) {
                    lieCount += m.confidence;
                    unknownCount += 1-m.confidence;
                } else {
                    unknownCount += 1;
                    break;
                }
            }
            if (lieCount > 0 && unknownCount < 1) {
                debug("Strategic BS");
                //callBS = true;
            }
        }

        //What's the worst that could happen?
        //Test the decks' 
        ArrayList<MyCard> worstHand = new ArrayList<MyCard>(myHand);
        worstHand.addAll(discardPile);
        ArrayList<Integer> loseCase[] = getTruthesAndLies(player, card, worstHand);
        int winPlaysLeft = truths.size() + lies.size();
        int losePlaysLeft = loseCase[0].size() + loseCase[1].size();
        double randomPlaysLeft = Math.max(losePlaysLeft,7);
        double expectedPlaysLeft = losePlaysLeft * discardPileConfidence + randomPlaysLeft * (1-discardPileConfidence);
        double threshold = 0.0 - (expectedPlaysLeft - winPlaysLeft)/13.0;
        debug("winPlaysLeft = "+winPlaysLeft);
        debug("expectedPlaysLeft   = "+expectedPlaysLeft);
        debug("Threshold    = "+threshold);

        if(lies.isEmpty()) {
            threshold /= 2;
        }
        //callBS = callBS || prob < threshold;

        printTheDeck();
        return callBS;
    }

    static double logGamma(double x) {
        double tmp = (x - 0.5) * Math.log(x + 4.5) - (x + 4.5);
        double ser = 1.0 + 76.18009173 / (x + 0) - 86.50532033 / (x + 1)
                + 24.01409822 / (x + 2) - 1.231739516 / (x + 3)
                + 0.00120858003 / (x + 4) - 0.00000536382 / (x + 5);
        return tmp + Math.log(ser * Math.sqrt(2 * Math.PI));
    }

    static double gamma(double x) {
        return Math.exp(logGamma(x));
    }

    static double factorial(double x) {
        return x * gamma(x);
    }

    static double choose(double n, double k) {
        if (Double.compare(n, k) == 0 || Double.compare(k, 0) == 0) return 1.0;
        if (k < 0 || k > n) {
            return 0.0;
        }
        return factorial(n) / (factorial(n-k) * factorial(k));
    }

    public String toString() {
        return "ConMan";
    }

    public void printTheDeck() {
        HashMap<Location, ArrayList<MyCard>> map = new HashMap();
        for (Location loc : Location.values()) {
            map.put(loc, new ArrayList());
        }
        for (ArrayList<MyCard> set : theDeck) {
            for (MyCard m : set) {
                map.get(m.location).add(m);
            }
        }
        String ret = "";
        for (Player p : players) {
            ret += p.toString()+": "+map.get(getLocation(p))+"\n";
        }
        ret += "Discard pile: "+map.get(Location.DISCARD)+"\n";
        ret += "Unknown: ("+map.get(Location.UNKNOWN).size()+" cards)\n";
        debug(ret);
    }

    public void debug(Object s) {

    }
}

Answer 2

播放器3131961357_10

每场比赛都会随机挑选一名玩家，并总是对该玩家打电话给BS。

package players;

import java.util.ArrayList;
import java.util.List;

import controller.*;

public class Player3131961357_10 extends Player{
    private int[] ducks = new int[13];
    private Player target = null;
    private int cake = 0;

    @Override
    protected List<Card> requestCards(int bacon, Controller controller){
        Card[] hand = getHand();
        List<Card> ret = new ArrayList<Card>();
        List<Card> others = new ArrayList<Card>();
        for(Card c:hand){
            if(c.getNumber() == bacon){
                ret.add(c);
            }else{
                others.add(c);
            }
        }
        if(ret.size() == 0){
            ImperfectPlayer.moveRandom(others, ret);
        }
        if(others.size() > 0 && ret.size() < 3 && handSize() > ret.size() + 1){
            ImperfectPlayer.moveRandom(others, ret);
        }
        return ret;
    }

    private final int someoneLied = 0;
    @Override
    protected boolean bs(Player player, int bacon, int howMuchBacon, Controller controller){
        if(target == null){
            // Could not find my cake.
            // Someone must have taken it.
            // They are my target.
            List<Player> players = controller.getPlayers();
            do target = players.get((int)Math.floor(Math.random() * players.size()));
            while(target != this);
        }

        int count = 0;
        Card[] hand = getHand();
        for(Card c:hand){
            if(c.getNumber() == bacon) 
                ++count;
        }
        if(cake >= controller.getDiscardPileSize()){
            ducks = new int[13];
            cake = someoneLied;
        }
        ducks[bacon] += howMuchBacon;
        cake += howMuchBacon;

        if(player.handSize() == 0) return true;
        return player.handSize() == 0 
            || howMuchBacon + count > 4 
            || ducks[bacon] > 5 
            || player == target 
            || Math.random() < 0.025; // why not?
    }

    public String toString(){
        return "Player 3131961357_10";
    }

    public static <T> void moveRandom(List<T> from, List<T> to){
        T a = from.remove((int)Math.floor(Math.random() * from.size()));
        to.add(a);
    }
}

Answer 3

Truthy

还没有完全完成，因为我不知道怎么告诉BS的结果(如果他们拿走了一堆，或者其他人在领带的情况下，或者我打了)。

目前，只有在我能证明的情况下才打电话给BS。除非我不得不撒谎，否则不要撒谎。我需要改进说谎算法。我正试图使它尽可能接近我如何与其他球员打BS (减去随机放置额外的牌，以发挥5或6，而他们不知道)。

package players;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import controller.*;

public class PlayerTruthy extends Player {
    
    private List<Card> played;
    private int discardPileSize;
    private HashMap<String,Integer> handSizes;
    private boolean initialized;
    //controller.getDiscardPileSize()
    
    // Constructor
    public PlayerTruthy() {
        played = new ArrayList<Card>();
        handSizes = new HashMap<String,Integer>();
        discardPileSize = 0;
        initialized = false;
    }
    
    // Initialize (do once)
    private void init(Controller controller) {
        for (Player p : controller.getPlayers()) {
            handSizes.put(p, 0);
        }
        initialized = true;
    }
    
    @Override
    protected List<Card> requestCards(int card, Controller controller) {
        if (!initialized) {
            init(controller);
        }
        List<Card> cards = getCards(card);
        if (cards.size() == 0) {
            cards = lieCards(card);
        }
        played.addAll(cards);
        return cards;
    }

    @Override
    protected boolean bs(Player player, int card, int numberOfCards, Controller controller) {
        if (!initialized) {
            init(controller);
        }
        List<Card> hand = Arrays.asList(getHand());
        int count = countCards(hand, card);
        return numberOfCards > 4-count;
    }

    public String toString() {
        return "Truthy";
    }

    private int countCards(List<Card> list, int card) {
        int count = 0;
        for (Card c : list) {
            if (c.getNumber() == card) {
                count++;
            }
        }
        return count;
    }

    private List<Card> getCards(int card) {
        List<Card> cards = new ArrayList<Card>();
        Card[] hand = getHand();
        for (Card c : hand) {
            if (c.getNumber() == card) {
                cards.add(c);
            }
        }
        return cards;
    }
    
    private List<Card> lieCards(int card) {
        List<Card> hand = Arrays.asList(getHand());
        List<Card> cards = new ArrayList<Card>();
        int limit = 1;
        int count = 0;
        int index = (card+9) % 13;
        while (cards.size() == 0) {
            count = countCards(hand, index);
            if (count <= limit) {
                cards = getCards(index);
            }
            if (limit >= 3) {
                cards.removeRange(1, cards.size());
            }
            if (index == card) {
                limit++;
            }
            index = (index+9) % 13;
        }
        return cards;
    }
}