(20 pts) Consider the following simple game: we start with ten coins on the table, five heads-up and five tails-up. On your turn you may flip over two coins that are the same side up, or remove a coin from the table. The first player (MAX) wins if all the coins show heads, and loses if they all show tails. (Yes, this is probably not a very fun game, at least you don't have to play it.) a. Draw the game tree representing all possibilities for the first two moves of the game. (Simply to make grading easier) assume that a players' "flip options are evaluated and put in the tree before the "remove" options. b. What is the maximum branching factor of this search? c. What is the maximum depth of this game tree when using the basic minimax algorithm? d. Now consider an evaluation function for this game which is simply (# of heads)-(# of tails). Write the value for each leaf node alongside the game tree in part (a). When using minimax, what is the resulting value of each non-leaf node? e. If alpha-beta pruning is applied left-to-right in the game tree, indicate all nodes that would not need to be evaluated