Question: A lone knight performs a random walk on a chessboard. From any square, the knight looks at the squares that it can legally move to

A lone knight performs a random walk on a chessboard. From any square, the knight looks at the squares that it can legally move to in chess, and picks one uniformly at random to move to. If the knight starts this random walk at one of the corner squares of the chessboard, find the expected number of steps until the knight returns to its starting square.

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