$(1)$ Modify the BST so that it can keep track of its balance. For the purpose of this question, a

balanced tree is defined to be a tree such that the heights of the two subtrees of any node

never differs by more than one.

$$ You are expected to create a new field in each node which stores the balance of the node.

$$ Note, when a node is inserted and deleted, the balance must be updated.

$$ Write a function to test the balance of a tree, which returns True or False depending if the

tree is balanced or not.