Draw the extensive form game of a modified "centipede game" with three players. In each round, Player 1 moves 1st, followed by Player 2, then Player 3.

The rule is as follows. There is initially one dollar on the table. When- ever a player continues, a dollar is added to the pile. If Player 1 stops, the money is divided between Players 1 and 3 (Player 3 receives noth- ing); if Player 2 stops, Players 2 and 1; if Player 3 stops, Players 3 and 2. The way money is divided is as before: the stopping player receives half of the pile (if the number of dollars in the pile is odd, take only the integer part) plus one dollar; the other player in the pool receives the rest. The excluded player receives nothing.

Suppose they play 3 rounds. How many subgames does the game have? Find the subgame perfect Nash equilibria of the game.