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How many ways are there to paint a 3×33\times33×3 grid with three colors such that each row and column has all three distinct colors?
Note: If you rotate the above illustration by 90∘,180∘90^\circ, 180^\circ90∘,180∘ or 270∘270^\circ270∘, they each count as different ways to paint the 3×33\times33×3.
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