Parking Spaces

In a lot with four spaces labeled 1–4, exactly two cars start in spaces 1 and 2, and no new cars arrive. At the start of each minute, each car independently attempts to move forward one space with probability 1/2; a move succeeds only if the destination space is empty at that minute, including if it becomes empty because the car ahead moves simultaneously. Cars cannot pass and cannot move beyond space 4. What is the expected number of minutes until the cars first occupy spaces 3 and 4?

Answer format: round to 3 decimal places.