Consider the following strategic setting. There are three players, numbered 1, 2, and 3. Player 1 has two cards, labeled King and Ace. At the beginning of the game, player 1 deals one of the cards to player 2 and the other card to player 3; that is, player 1 either gives the Ace to player 3 and the King to player 2 (call this the action A) or the King to player 3 and the Ace to player 2 (action K). Player 2 observes the card dealt with him; player 3 does not get to see the card dealt with her. Player 2 then must decide between switching cards with player 3 (S) or not (N). Player 3 observes whether player 2 made the switch, but does not see her card. Finally, player 3 responds to the question "Is your card the Ace"? by saying either "yes" (Y) or "no" (N). If player 3 correctly states whether her card is the Ace, then she obtains a payoff of 1 and the other players get 0; otherwise, players 1 and 2 both get a payoff of 1, and player 3 obtains 0. Represent this game in extensive form.