Markov Chains & Long-Run Behavior · Superchallenge problem

Three web pages link to each other as follows: page $A$ links to $B$ and to $C$, page $B$ links to $C$, and page $C$ links to $A$. A random surfer, at each step, with probability $\tfrac45$ follows one of the links on the current page, chosen uniformly, and with probability $\tfrac15$ instead jumps to one of the three pages chosen uniformly (possibly the same page). In the long run, what fraction of the time is the surfer on page $C$? Express your answer as a common fraction.