Consider a 2-D map with a horizontal river passing through its center. There are n cities on the southern bank with x-coordinates a1 . . . an and n cities on the northern bank with x-coordinates b1 . . . bn. You want to connect as many north-south pairs of cities as possible, with bridges such that no two bridges cross. When connecting cities, you are only allowed to connect the the ith city on the northern bank to the ith city on the southern bank.