# The Minimum Number of Tiles

A tromino is an L-shaped tile consisting of three unit squares arranged as shown in the figure below.

Consider a $$2013 \times 2013$$ chessboard whose cells are colored black and white alternatively, with the four corners colored black. Find the last three digits of the minimum number of non-overlapping trominoes needed to cover all the black cells.

Details and assumptions

• Two trominoes are called non-overlapping if they share no common cell.

• Here's an example of a $$3 \times 3$$ chessboard with its cells colored black and white alternatively.

• There's no restriction on whether a tromino can be placed on a white cell.

• If the last three digits are $$_{\cdots }012,$$ enter 12 as your answer.

• This problem is not original.

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