2 shows the structure of a Doubly linked list. (no duplicates) size : number of nodes trailer element node Figure 2 Structure of a Doably Linked List This doubly linked list has header and trailer nodes. The variable size stores the number of this list. Each node has an integer element, next and prev reference. (You do not know the codes of this list) Assume that we defined a Node class already e current You can use statement below to allocate a new node named newest whose element is 100, n and prev is null. Node newest new Node "100) Please write methods to accomplish following operations (6 points) Write a method, addBetween, to handle the general case of an insertion betwen the two nodes a) private void addBetween(int newElement, Node predecessor, Node successor) b) (6 points) Write a method, remove, to handle the general case of a deletion of a given node private Node remove(Node node) c) (5 points) ) Insert a new node at the head by calling the a head by calling the addBetween method. (5 points) Delete the last node by calling the remove method. d) e) (6 points) Search a node according to a given key. ) (Extra 7 points) Insert a new node with new Element after a given node with the key by calling the search and addBetween method. public Node addAfter int key, int newElement)