(a) Nim is a two-player game. The rules are as follows. The game starts with a single stack of 7 tokens. At each move a player selects one stack and divides it into two non-empty, non-equal stacks. A player who is unable to move loses the game. i. Draw the complete search tree for Nim. [8 Marks] ii. Assume two players, Min and Max, play Nim. Min plays first. If a terminal state in the search tree developed above is a win for Min, a utility function of zero is assigned to that state. A utility function of 1 is assigned to a state if Max wins the game. Apply the minimax algorithm to the search tree to assign utility functions to all states in the search tree. [1 Marks]