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Determine the number of 8-tuples (in(1),...

Determine the number of 8-tuples `(in_(1), in_(2),…, in_(8))` such that `in_(1), in_(2),.., in_(8) in (1, -1) and in_(1) 2 in_(2) + 3 in_(3) + …+ 8 in_(8)` is a multiple of 3.

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