Let an AVL*-tree be a binary search tree where for every node, the difference of heights of its left and right subtree is at most 2. Let N(h) be the minimum number of nodes for AVL-tree of height h. a) What is N(h) for h e {0, 1, 2, 3}?. For justification, it is sufficient to draw the smallest AVL*-trees of heights he {0,1,2,3}. b) Derive a recursive formula for N(h) for h > 3. Give a brief explanation of your derivation. c) Show that in any AVL*-tree of height h> 0 with n nodes, we have h 3. Give a brief explanation of your derivation. c) Show that in any AVL*-tree of height h> 0 with n nodes, we have h