$($a$)$ When we add a node to an AVL tree, at most one rotation is needed to restore the heightbalance property. Since the imbalance at any node X is caused by an increase in height of one of X$\text{'}$s children, and since a rotation decreases the height at X$,$ X$\text{'}$s ancestors will stay balanced. However, this is not true for removing nodes from an AVL tree... Find an example of an AVL tree with at least $17$ nodes where the delete operation will require O$($h$)$ rotations $($where h is the height of the tree$)$ from the leaf to the root in order to restore the height$-$balance property. $($b$)$ Give an algorithm for finding such a tree for any n$,$ show how you got it$.$