Suppose a robot is trying to get out of a maze. At one intersection,

there are 3 choices of where to go. Along one path, the robot will take 1 minute and then return to the same intersection. Along another path, the robot will take 2 minutes and then return to the same intersection. On the third path, the robot will take 3 minutes and escape the maze. Every time the robot returns to the same location, the robot chooses which path to take at random without remembering what happened before. Find the expected time until the robot escapes.

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