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Default Recursive Classes - Design Pattern needed

I've got a class defined that instantiates itself internally. (It's a
simple binary tree implementation). Are there any OO gurus here can
help me to design the proper class structure so that I can track the
item count (# of nodes in the b-tree) and other statistics that would
apply to all instantiations ?
Do I just need to create a separate "parent" class that is
instantiated on the first instance of the bintree class ? I would
guess the parent class would house a Collection to track each instance
of the bintree, as well as the total count of the nodes.....correct ?
Am I on the right track ?

 
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