Cell Shell

There is a checkered field with $10^5$ rows (numbered $1$ through $10^5$) and $10^5$ columns (numbered $1$ through $10^5$). $N$ different cells in this field (numbered $1$ through $N$) are marked; for each valid $i$, the coordinates of the $i$-th marked cell are $(x_i, y_i)$. A set of cells is *suitable* if it meets the following conditions: - All marked cells belong to this set. - For any two ce