class Position $\{$ public: int& operator$*()$; Position parent$()$ const; PositionList children$()$ const; bool isRoot $()$ const; bool isExternal $()$ const; $\}$ class Tree $\{$ public: class Position $\{$ public: int& operator$*()$; Position parent$()$ const; PositionList children$()$ const; bool isRoot $()$ const; bool isExternal $()$ const; $\}$ std::list PositionList; public: Tree$()$; int size$()$ const; bool empty$()$ const; Position root $()$ const; PositionList positions$()$ const; void add $($const Tree& T$,$ const string& mn$,$ float p$,$ float m$,$ const string& t$)$; void preOrderPrint $($const Tree& T$,$ const Position& p$)$; void postOrderPrint $($const Tree& T$,$ const Position& p$)$; $\}$ Solve the following exercise: $1.$ Implement class Tree assuming the linked structure for a general tree shown in Figure $7\mathrm{.}5$ in the textbook. Each node stores the same information as class Vehicle of the previous exercise as well as one additional field called type $($string$)$ indicating if a vehicle is a Sedan, Truck, or Electric. $2.$ The main program should interactively ask for a character, and then execute the following actions depending on the received input character: a$.$ A $$ adds a new vehicle to the tree after reading the following information for the vehicle: manufacturer, price, milage, and type. b$.$ L $$ lists in preorder all vehicles with a price less than value V$.$ Value V is read from the input. c$.$ M $-$ lists in postorder all vehicles newer than the manufacturing year Y$.$ Value Y is read from the input. d$.$ I $$ lists the number of vehicles in the inventory. Page $5$ Implement all the methods that are needed to realize the four actions above.