Two distinct squares of the 8 by 8 chessboard C are said to be adjacent if they have a vertex or side in common. Also, g is called a C-gap if for every numbering of the squares of C with all the integers $1,2,\ldots,64$ there exist two adjacent squares whose numbers differ by at least g. Determine the largest C-gap g.

Let's think step by step and output the final answer within \boxed{}.
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