Suppose a factory floor has width $W$ and length $L.$ There are $P$ packages on the factory floor at the start. The robot is able to

move North, South, East, or West on the floor.

$($a$)3pts$ For this subquestion only, the position of the robot is known, and it wants to pick up all $P$ packages in the factory.

However, the robot can move North at most $2$ times overall.

What is the minimal size of the state space for this problem? Write your answer in the box as a product of terms that

reference problem quantities $($such as$,$ but not limited to$,W,L,$ and $P).$ You may also use constants as part of your

expression. For each term in your expression, also state the information it encodes. For example, you might write $"4WL$

and write "number of directions" under the first term and "robot's position" under the second term. You will receive partial

credit for a complete but non$-$minimal state space.