C++ Data Structures (Binary Trees)- Write the definition of the function nodeCount that returns the number of nodes in the binary tree. Add this function to the class binaryTreeType and create a program to test this function. Here are the headers: binaryTree.h //Header File Binary Search Tree #ifndef H_binaryTree #define H_binaryTree #include using namespace std; //Definition of the Node template struct nodeType { elemType info; nodeType *lLink; nodeType *rLink; };    //Definition of the class template class binaryTreeType { public: const binaryTreeType& operator= (const binaryTreeType&); //Overload the assignment operator. bool isEmpty() const; //Function to determine whether the binary tree is empty. //Postcondition: Returns true if the binary tree is empty; // otherwise, returns false. void inorderTraversal() const; //Function to do an inorder traversal of the binary tree. //Postcondition: Nodes are printed in inorder sequence. void preorderTraversal() const; //Function to do a preorder traversal of the binary tree. //Postcondition: Nodes are printed in preorder sequence. void postorderTraversal() const; //Function to do a postorder traversal of the binary tree. //Postcondition: Nodes are printed in postorder sequence. int treeHeight() const; //Function to determine the height of a binary tree. //Postcondition: Returns the height of the binary tree. int treeNodeCount() const; //Function to determine the number of nodes in a //binary tree. //Postcondition: Returns the number of nodes in the // binary tree. int treeLeavesCount() const; //Function to determine the number of leaves in a //binary tree. //Postcondition: Returns the number of leaves in the // binary tree. void destroyTree(); //Function to destroy the binary tree. //Postcondition: Memory space occupied by each node // is deallocated. // root = nullptr; virtual bool search(const elemType& searchItem) const = 0; //Function to determine if searchItem is in the binary //tree. //Postcondition: Returns true if searchItem is found in // the binary tree; otherwise, returns // false. virtual void insert(const elemType& insertItem) = 0; //Function to insert insertItem in the binary tree. //Postcondition: If there is no node in the binary tree // that has the same info as insertItem, a // node with the info insertItem is created // and inserted in the binary search tree. virtual void deleteNode(const elemType& deleteItem) = 0; //Function to delete deleteItem from the binary tree //Postcondition: If a node with the same info as // deleteItem is found, it is deleted from // the binary tree. // If the binary tree is empty or // deleteItem is not in the binary tree, // an appropriate message is printed. binaryTreeType(const binaryTreeType& otherTree); //Copy constructor binaryTreeType(); //Default constructor ~binaryTreeType(); //Destructor protected: nodeType *root; private: void copyTree(nodeType* &copiedTreeRoot, nodeType* otherTreeRoot); //Makes a copy of the binary tree to which //otherTreeRoot points. //Postcondition: The pointer copiedTreeRoot points to // the root of the copied binary tree. void destroy(nodeType* &p); //Function to destroy the binary tree to which p points. //Postcondition: Memory space occupied by each node, in // the binary tree to which p points, is // deallocated. // p = nullptr; void inorder(nodeType *p) const; //Function to do an inorder traversal of the binary //tree to which p points. //Postcondition: Nodes of the binary tree, to which p // points, are printed in inorder sequence. void preorder(nodeType *p) const; //Function to do a preorder traversal of the binary //tree to which p points. //Postcondition: Nodes of the binary tree, to which p // points, are printed in preorder // sequence. void postorder(nodeType *p) const; //Function to do a postorder traversal of the binary //tree to which p points. //Postcondition: Nodes of the binary tree, to which p // points, are printed in postorder // sequence. int height(nodeType *p) const; //Function to determine the height of the binary tree //to which p points. //Postcondition: Height of the binary tree to which // p points is returned. int max(int x, int y) const; //Function to determine the larger of x and y. //Postcondition: Returns the larger of x and y. int nodeCount(nodeType *p) const; //Function to determine the number of nodes in //the binary tree to which p points. //Postcondition: The number of nodes in the binary // tree to which p points is returned. int leavesCount(nodeType *p) const; //Function to determine the number of leaves in //the binary tree to which p points //Postcondition: The number of leaves in the binary // tree to which p points is returned. };