Threatened Rooks

Probability Level 5

Find the largest number of rooks that can be placed in a $3000 \times 3000$ chessboard in such a way that each rook is threatened by no more than one rook.

Details and Assumptions:

Rooks can attack in any range but can only attack in a horizontal or vertical direction.
A rook is considered to be "threatened" if another rook can attack it.