Design: Vehicle Parking Area Problem

Problem: Design a logic(electrical or pneumatic), when any Vehicle near the entrance area the door automatically open when Vehicle enter the parking area door closed, and similarly when any Vehicle near the exit area which is already parked, the door automatically open, when Vehicle exit the exit door closed. Only 4 Vehicle allow in the parking, if 5th Vehicle near the entrance and 4 already in the parking area, the entrance door must not be open.