writing a program that allows the user to enter a binary tree in a parenthesized prefix format and then allows it to be categorized and allows various features of that tree to be displayed. An example of a tree written in the input format is the following: (A(G(j) (1)) (z (5))) In the above example, data in each node of the tree contains a single alphanumeric character. No spaces are permitted. Each tree is enclosed in parentheses. Inside those parentheses, after the single character are either zero, one or two subtrees also enclosed in parentheses. When only one subtree is present, it is the left subtree and when two are present, they represent the left and right subtrees. So the above string represents the following binary tree: The various categorizations include the following: 1. Whether the binary tree is balanced, which means for each node in the tree, the absolute difference between the height of its left and right subtrees is at most 1. The above binary tree is balanced. 2. Whether the binary tree is full. A full binary tree has the maximum number of nodes for a tree of its height. The above tree is not full because a tree of that height can contain 7 nodes, but the above tree only has 6. 3. Whether the binary tree is proper. In a proper binary tree, every node has either 0 or 2 children. The above tree is not proper because the node containing z has only one child. In addition, the program should allow the user to request that each of the following features of the tree be displayed: 1. The height of the tree. The height of a tree is the maximum level of all of its nodes. The root node containing A is at the level 0. Because all three leaf nodes in the above tree are at level 2, its height is 2. 2. The number of nodes in the tree. As previously mentioned, the above tree has 6 nodes. 3. An fully parenthesized inorder traversal of the tree. The following should be displayed as the inorder traversal of the above tree: ((() G (1)) A ((5) Z )) This project should consist of three classes. The main class should create a GUI that allows the user to input a tree in the above described format and then construct the tree once the Make Tree button is clicked. The GUI should look as follows: Binary Tree Categorizer Make Tree Enter Tree: (A(G(X1))(z(5))) Is Balanced? Is Full? Output: ((()) G (1)) A (( 5 )z)) Is Proper? Height Nodes X Inorder The GUI must be generated by code that you write. You may not use a drag-and-drop GUI generator. The second class should be the BinaryTree class, which should contain a static nested class to define the nodes of the binary tree, together with a constructor that is called when the Make Tree button is clicked and is supplied the string representation of the tree and constructs the actual tree from that string. In addition, it should have public methods that are called when each of the remaining six buttons are clicked. All of those public methods should have corresponding private methods that accomplish their tasks using recursion. The third class should be named InvalidTreeSyntax, which defines a checked exception. It should be thrown when a invalid string is supplied and the Make Tree button is clicked. It should be caught in the main class and a JOptionPane window should be displayed that describes the reason for the invalid syntax. a. A UML class diagram that includes all classes you wrote. Do not include predefined classes. You need only include the class name for each individual class, not the variables or methods b. A test plan that includes test cases that you have created indicating what aspects of the program each one is testing c. A short paragraph on lessons learned from the project