$3.[$FSM Partitioning, $20$pts$]$ Given the following up$-$down counter, you are tasked to split its FSM into two separate FSMs$.$ Draw the two resulting FSMs$.($Ensure that the logic for state transitions in each FSM is limited to a maximum of $\backslash (\backslash$mathbf$\{2\}\backslash )$ terms.$)$

Hint: Assign a virtual state $($SA or SB$)$ to each of the divided FSMs$.$ During state transitions, utilize the state information from the other FSM where necessary.