Suppose that a rat is in a maze with four possible directions. If it goes in the first direction, it gets out in three minutes. If it chooses the second direction, it returns ti the starting point in five minutes. If it chooses the third direction, with probability $0\mathrm{.}2$ it returns to the start in four minutes, and with probability $0\mathrm{.}8$ it returns to the start in seven minutes. If it chooses the fourth direction, it gets out of the maze in six minutes with probability $0\mathrm{.}3$ And returns to the maze in eight minutes with probability $0\mathrm{.}7.$ Each time the rat returns it chooses each direction with probability $1/4.$ What is the expected time until the rat escapes the maze?