$4\mathrm{.}5$ The AND$-$OR$-$GRAPH$-$SEARCH algorithm in Figure $4\mathrm{.}11$ checks for repeated states only on the path from the root to the current state. Suppose that, in addition, the algorithm were to store every visited state and check against that list. $($See BREADTH$-$FIRST$-$SEARCH in Figure $3\mathrm{.}11$ for an example.$)$ Determine the information that should be stored and how the algorithm should use that information when a repeated state is found. $($Hint: You will need to distinguish at least between states for which a successful subplan was constructed previously and states for which no subplan could be found.$)$ Explain how to use labels, as defined in Section $4\mathrm{.}3\mathrm{.}3,$ to avoid having multiple copies of subplans.