Consider a binary tree of height h which is perfectly balanced (also called simply "perfect"), with all of the leafs at the same depth from the root and all internal nodes possessing two children. Let the tree be of height h. a. What's the number of nodes in this tree expressed as a function of h? Explain how you got this number. (2 pts) b. What's the number of leaf nodes in such a tree? Explain how you got this number. (2 pts) c. What's the number of internal (non-leaf) nodes? Can you comment on the relative number of leaf and non-leaf nodes? (2 pts) d. If the tree has 8193 nodes is it possible to arrange the nodes into a perfect binary tree? Why? (2 pts)