Two knights placed on distinct squares of an $8 \times 8$ chessboard, where each square is a unit square, are said to attack each other if the distance between the centers of the squares on which the knights lie is $\sqrt{5}$. In how many ways can two identical knights be placed on distinct squares of an $8 \times 8$ chessboard such that they do NOT attack each other?

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