# Let's count!

A domino is a $$2\times1$$ or $$1\times2$$ tile.

Let $$N$$ be the number of ways placing $$100$$ dominoes without overlapping on a $$20\times20$$ chessboard so that every $$2\times2$$ square contains at least two uncovered unit squares which lie in the same row or column.

Find the last 4 digits of $$N$$.

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