Školjka

The two figures depicted below, consisting of $6$ and $10$ unit sqares respectively are called \emph{staircases}. [img attachment=1 height=300px] Consider a $2018 \times 2018$ board consisting of $2018^2$ cells, each being an unit square. Two arbitrary cells were removed from the same row of the board. Prove that the rest of the board cannot be cut (along the cell borders) into staircases (possibly rotated).