So many numbers

Consider the above 8\(\times\)8 grid. How many ways are there to write a single digit (0, 1, ..., 8, 9) in each square such that the sum of all the numbers in any 3\(\times\)3 section is even. If you think the number of ways to fill in this grid with these restrictions is \(x\), type in the number of factors of \(x\) (including 1 and \(x\)).

Note: Rotations and reflections are considered to be distinct possibilities.

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