Solve the problems manually using paper and pen. $1.$ Perform the following operations on an AVL tree. Assume the tree is empty initially. After each operations recalculate the height of the nodes on the path from the added node to the root. If any of the node is unbalanced, perform appropriate rotations to balance the tree. Scan the work and submit as a single file on elearning. Your work should show the intermediate steps. Add $10,$ Add $20,$ Add $80,$ Add $60,$ Add $40,$ Add $50.$ Practice problem $($no need to submit$)2.$ Perform the following additional operations to the tree constructed in problem $1.$ Add $5,$ Add $15,$ Add $30,$ Add $0,$ Add $35,$ Add $16,$ Add $90,$ delete $5,$ delete $0$