Find the smallest possible Red-Black trees of heights up to 10. For the last few, rather than drawing every node, you may use the notation to indicate a perfect subtree of depth d. Try to deduce a general formula for the number of nodes in the smallest Red-Black tree of height h. Then, use big-O notation to write it as for some constant . As in problem 3, invert this formula to conclude that the maximum depth of a Red-Black tree on n nodes is C log(n), where C is a constant. Give C as an explicit formula, and also compute it to three decimal places using a calculator or math software. Hint: consider the cases where d is even or odd separately.