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Math (please help steve)

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A crippled rook can move on a chessboard in the following way: from a square, it can move to an adjacent square sharing a common side, and every two consecutive moves must be at right angles (i.e., the rook makes a 90∘turn at every move).
A cycle is a sequence of squares which start and end at the same square, and traces out a valid path that the crippled rook can move according to the rules above. A non-intersecting cycle consists of pairwise distinct squares, with the sole exception of the starting and ending square.
What is the length of the longest possible cyclic, non-intersecting route of a crippled rook on a 15×15 chessboard?

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