We know that, among trees of depth d, the largest one is the perfect tree, which has 2^(d+1) - 1 nodes. This is an AVL tree, so we know the biggest an AVL tree of depth d can be. Prove that the smallest AVL tree of depth d has Fib(n+3) - 1 nodes. Include a diagram showing what they look like for d = 0 up to d = 4.