#5 Red Nodes in Red-Black Tree (2 pts) Consider a red-black tree formed by inserting n nodes with RB-Insert. Prove that if n> 1, the tree has at least one red node. Hint: Nodes are red when inserted (line 16 of RB-Insert). Show that if n > 1 one node must be red after RB-Insert-Fixup is complete. (It is not sufficient to say that the second node inserted will be red. You must show that some node remains red under all possible insertion sequences and the transformations that result.)