In the $$strip$$ part of the Divide$-$and$-$Conquer Closest Pair algorithm, suppose we check each point P$($x$0,$ y$0)$

on the left against all points Q$($x$,$ y$)$ on the right that are within the strip and have $|$y $$ y$0|<$ d$,$ where d

is the minimum distance found in the recursive steps. Argue that we will check at most $8$ points for given

P$.$ Hint: divide the rectangle in the following picture into $8$ subregions.