Enhance the provided Treap class to incorporate additional functionalities that will help in

understanding the use of augmented data structures in tree$-$based algorithms and OOP

principles.

Tasks:

You are provided with a basic implementation of a Treap class that includes methods for

insertion, deletion, search, etc. Your task is to modify the Treap class so that

$1.$ each node can keep track of the sum of keys of nodes under this node, including

itself. Then, print the sum for each node.

For example, nodes under node $20$ include node $10,22,5$ and $12.$

$2.$ each node can keep track of the count of all nodes under this node, including itself.

Then, print the count for each node.

$3.$ Add a new function to the Treap class to return the count of nodes without children

$($leaf nodes$).$ Then, print this count.

$4.$ Add a new function to the Treap class to return the count of nodes with only one

child. Then, print this count.

$5.$ Add a new function to the Treap class to return the count of nodes with two

children. Then, print this count.

Input & Output:

You need to provide test cases in the main func$$on to test each additional functionality.