Design a dfa corresponding to the classical paper-scissors-stone game. the alphabet consists of three symbols, say (a, b, c) for paper, scissors and stone, respectively, and each game is a sequence of pairs where (x_i, y_i) denote the choice of player 1 and 2 at round i. the game ends once x_i notequalto y_i (remaining moves can be ignored). a) how many states are needed? (answer, e. g., 17) b) if players choose their moves independently and uniformly in random (i. e., each symbol with probability of 1/3), what is the mean number of transitions before the game ends? (answer, e. g., 17)