Given $n$ points in the plane, how can one efficiently (or even inefficiently!) compute the number of corner-points belonging to the boundary of the intersection of the unit disks centered on those points? (This number is 0 when the intersection of the disks is empty and 2 or more otherwise, leaving aside the measure-0 case in which the intersection is a single point.)

Given $n \geq 2$ points in the plane, how can one efficiently (or even inefficiently!) compute the number of corner-points belonging to the boundary of the intersection of the unit disks centered on those points? (This number is 0 when the intersection of the disks is empty and 2 or more otherwise, leaving aside measure-0 cases in which the intersection is a single point or a disk.)