KZ-MO 2000 Problem 3

In a country with $n$ ( $n \geq 3$ ) airports, the government only licenses air travel to those airlines whose airline system meets the following conditions: a) Each airline must connect any two airports with one and only one one-way airline; b) For each airline there is an airport from which the passenger could fly off and fly back, using the services of only this airline. What is the maximum number of airlines with different airline systems?