Let \(P(x)\) be a \(17\)th degree real polynomial given by the 17th degree determinant \(det(a_{ij})\) where \(a_{ij} = x\) iff. \(\delta_{ij} = 1\) and \(= 17\) iff. \(\delta_{ij} = 0\)
Determine the last three digits of \(P(12)\).

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