Implement a sub$-$class of the TreeMap class to include the modifications listed below. Each modification should be done in the same class so that the final version supports all of the additional functionality. Your tree class should be tested thoroughly and you must provide code demonstrating the functionality of the class and the new and updated methods.

modify the $\_$search$($k$)$ function according to problem R$-11\mathrm{.}6$

implement remove$\_$range$($start$,$stop$)$ according to C$-11\mathrm{.}35$

implement count$\_$range$($start$,$stop$)$ according to C$-11\mathrm{.}37$

implement the find$\_$min$()$ function according to C$-11\mathrm{.}41$

implement the find$\_$max$()$ function with specifications from C$-11\mathrm{.}41$

implement find$\_$lt$($k$)$ according to Sorted Map ADT function $($see pg$.427)$

implement find$\_$gt$($k$)$ according to Sorted Map ADT function $($see pg$.427)$

implement after$($p$)$ and before$($p$)$ according to C$-11\mathrm{.}43($Implement these methods first and use on the other problems$)$

modify the $\_$delete$($p$)$ method according to C$-11\mathrm{.}45$

implement the reversed$($m$)$ Sorted Map ADT function $($see pg$.427)$