Too Many Cars

Fajeem has recently bought N - 1 brand new cars that he has labelled as, say, $1, 2, 3, \dots, N - 1$. All of his cars are unique, naturally. In his garage, he has a circular parking space for N cars. Starting from an arbitrary parking slot, Fajeem moves in the clockwise direction, listing all the cars that he sees (he lists the slot where there is no car by 0). One day Fajeem decides to clean up