Consider the two-player (Max player and Min Player) zero-sum game. The game begins with a set of eleven coins. On any player's move, the player must split the set of coins into two subsets. Max-player is not allowed to split a set/subset of coins into two equal sizes. If it is max player turn and all the sets/subsets of coins have either one or two coins, max player will lose the game. Propose an appropriate utility function for playing the game. (a) Apply the minimax algorithm for finding the best action for the max player at the root. (b)Apply the minimax algorithm with alpha-beta pruning for finding the best action for the max player at the root.