Count Idle Drives

Question

A company moves products around its warehouses with robots called "Drives". Think of a warehouse floor as a Cartesian plane: every robot stands on a point (x, y) whose coordinates are integers. A robot is called "idle" when there is at least one other robot straight above it, one straight below it, one straight to its left and one straight to its right. The other robot only has to share the row or column; it does not have to be the nearest neighbor. Every point holds at most one robot. ...