Fewest tray rotations to eat a three-course meal

A customer sits at a round table with a rotating tray; each tray position holds a starter, a main, a dessert or nothing. Turning the tray one position either way costs one rotation. The customer must eat a starter, then a main, then a dessert, each when it is in front of them. Return the fewest rotations needed. Try every choice of dish per course efficiently with a small dynamic program over positions on the circle.