Write code for an theta(n) worst-case algorithm that verifies that a tree is actually an AVL tree. You may assume the nodes of the tree look like: class AVLNode { int key: V value: int height: AVLNode left: AVLNode right: } You must verify the BST Property, the AVL Balance Condition, and the correctness of the height information (that is, the value stored in the height field may not be correct). In each of the cases where it fails a property, return false. Otherwise, return true. A null node is considered a proper AVL tree of height -1. You are welcome to (encouraged!) write helper functions. As you are writing your code, we recommend that you keep in mind the following tree. Is THIS tree a proper AVL Tree? Look carefully