Suppose that a coin is tossed repeatedly in such a way that heads and tails are equally likely to appear on any given toss and that all tosses are independent, with the following exception: Whenever either three heads or three tails have been obtained on three successive tosses, then the outcome of the next toss is always of the opposite type. At time n (n ≥ 3), let the state of this process be specified by the outcomes on tosses n − 2, n − 1, and n. Show that this process is a Markov chain with stationary transition probabilities and construct the transition matrix.