A bunch of telecommunications stations are located on the boundary of a circle. Starting from some arbitrary station s1, the stations are numbered consecutively s1 . . . sn in the clockwise direction. Various pairs of stations want to communicate with each other. A pair of stations can communicate via a laser beam shot in a straight line (i.e. a chord of the circle) between them. A station can communicate with only one other station at a time, and two pairs of stations cannot communicate simultaneously if their laser beams would cross doing so would corrupt both pairs messages. Say that communication between stations si and sj has priority ij . Give a polynomial-time algorithm to select a subset of pairs of stations that can communicate simultaneously, such that the total priority of their communication is maximized.