Design a finite automaton that models the behaviour of a lift moving between two floors. The lift can be either up or down. Both floors have a simple 'call here' button for the lift, and inside the lift there are buttons for going 'up' and 'down'. In addition, the lift has a door that can be opened and closed; the lift only moves when the door is closed. The time required for the lift to travel between the two floors does not need to be taken into account, and any possible service requests occurring during this interval can be ignored. The automaton does not need to have any distinct "final states