1. (15p) Insert the following integer keys into a red-black tree. Show the tree after inserting each element. After an insertion, if a property is violated, write down the property and show each performed step in order to fix this problem. 40, 20, 70, 60, 10 2. (15p) Apply the following insert operations on AVL tree. After each balancing (rotation) operation, write which rotation you have performed and show the AVL tree. 40, 90, 20, 70, 50, 60, 30, 10, 80