need help with AI question

Consider a vacuuming robot located in a simple world which is a sequence of seven rooms as shown in the picture below. Each room can be either dirty or clean. The robot can perform one of three different actions (note that not all of these movement actions may be possible if the robot is located in certain types of rooms e.g. it can only perform one movement action if it is located in a room at one of the two ends): 1. move to the adjacent room to the east 2. move to the adjacent room to the west 3. suck up dirt from the room it is currently located The robot is tasked with cleaning all rooms. The picture below has an example current location of the robot shown with the letter R. The compass directions are also shown. The "..." show dirt so in this example three rooms are dirty. North West East South The maximum value of the forward branching factor considering all statesodes is The minimum value of the forward branching factor considering all statesodes is The number of states possible for this problem is If the cost of the robot in moving from one room to another is 1, then the optimal cost paid to get to a goal state where all rooms are clean, with the starting state in the picture above, is