PROBLEM 1: Suppose a (vanilla) Binary Search Tree contains the keys {1, 2, 3, 4, 5 and the tree has the structure below. Part-A: Your job: correctly assign the keys to the nodes Part-B: What Insertion sequence results in the structure above? Part-c: In your sequence above which is the first insertion (if any) that results in a violation of the AVL properties? Part-D: The tree above has height 4. How many valid Binary Search Trees containing the values 1, 2, 3, 4, 5 have height 4 (including the one given)? Show your reasoning