Consider the following strategic setting. There are three people: Amy, Bart, and Chris. Amy and Bart have hats. These three people are arranged in a room so that Bart can see everything that Amy does, Chris can see everything that Bart does, but the players can see nothing else. In particular, Chris cannot see what Amy does. First, Amy chooses either to put her hat on her head (abbreviated by H) or on the floor (F). After observing Amy's move, Bart chooses between putting his hat on his head or on the floor. If Bart puts his hat on his head, the game ends and everyone gets a payoff of 0. If Bart puts his hat on the floor, then Chris must guess whether Amy's hat is on her head by saying either "yes" or "no." This ends the game. If Chris guesses correctly, then he gets a payoff of 1 and Amy gets a payoff of -1. If he guesses incorrectly, then these payoffs are reversed. Bart's payoff is 0, regardless of what happens. Represent this game in the extensive form (draw the game tree).