A gizmo is composed of a widget that fits in a corresponding doodad. Given a collection of n widgets of different sizes and n matching doodads, the problem is to assemble the gizmos. You are allowed to test a widget and a doodad together, which tells you whether the widget is smaller than the doodad, larger than the doodad, or matches the doodad exactly. However, there is no way to test two widgets together or two doodads together. Design an algorithm for this problem with average-case efficiency in (n log2 n)