A park ranger provides you with a map of a forest trail network, represented as an undirected tree T $=($V$,$ E$)($in adjacency list format$),$ where each node corresponds to a specific location $($e$.$g$.,$ a cafe$)$ along the trail and edges denote connections between locations. Furthermore, the ranger designates a specific starting point r in V where all hikers commence their journey. It$$s crucial for the ranger to efficiently determine whether one location can be reached from an $$early checkpoint$,$ meaning that the path from the starting point r to the location v in T passes through the early checkpoint u$.$ Additionally, hikers should not visit a location more than once so they do not get bored. How can you preprocess the trail map to allow the ranger to answer checkpoint queries of the form $$can v be reached by going through checkpoint u starting from r without visiting locations more than once$$ in constant O$(1)$ time, with the preprocessing itself taking O$(|$V$|)?$