A board with dimensions $2018 \times 2018$ is divided into unit cells of size $1 \times 1$. In some cells of the board, black chips are placed, and in others, white chips are placed (each cell contains at most one chip). 

First, we remove all black chips from columns that contain white chips. Then, we remove all white chips from rows that contain black chips. 

Let $W$ be the number of remaining white chips, and $B$ be the number of remaining black chips on the board. Define $A = \min\{W, B\}$. Determine the maximum value of $A$.

Let's think step by step and output the final answer within \boxed{}.
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