IN JAVA, PLEASE WRITE A CODE USING ECLIPSE AND THE FOLLOWING CODE BELOW, Also please show the output Write a program that maintains the top $15$ scores for the students of a class that has more than $15$ students $,$ implementing the add and remove methods using a doubly linked list. Moreover, your implementation of remove$($i$)$ should make the fewest number of pointer hops to get to the student at index i$.$ class DoublyNode $\{$

Student data;

DoublyNode next;

DoublyNode prev;

public DoublyNode$($Student data$)\{$

this.data $=$ data;

this.next $=$ null;

this.prev $=$ null;

$\}$

$\}$

class TopScoresDoublyList $\{$

private DoublyNode head;

private int size;

public TopScoresDoublyList$()\{$

this.head $=$ null;

this.size $=0$;

$\}$

public void add$($Student student$)\{$

DoublyNode newNode $=$ new DoublyNode$($student$)$;

if $($head $==$ null $||$ student.score $>$ head.data.score$)\{$

newNode.next $=$ head;

if $($head $!=$ null$)\{$

head.prev $=$ newNode;

$\}$

head $=$ newNode;

$\}$ else $\{$

DoublyNode current $=$ head;

while $($current$.$next $!=$ null && student.score $<=$ current.next.data.score$)\{$

current $=$ current.next;

$\}$

newNode.next $=$ current.next;

newNode.prev $=$ current;

if $($current$.$next $!=$ null$)\{$

current.next.prev $=$ newNode;

$\}$

current.next $=$ newNode;

$\}$

size$++$;

$//$ Keep only the top $15$ scores

if $($size $>15)\{$

remove$(15)$;

$\}$

$\}$

public void remove$($int index$)\{$

if $($index $<=0||$ index $>$ size$)\{$

System.out.println$("$Invalid index to remove."$)$;

return;

$\}$

DoublyNode current $=$ head;

for $($int i $=1$; i $<$ index; i$++)\{$

current $=$ current.next;

$\}$

if $($current$.$prev $!=$ null$)\{$

current.prev.next $=$ current.next;

$\}$ else $\{$

head $=$ current.next;

$\}$

if $($current$.$next $!=$ null$)\{$

current.next.prev $=$ current.prev;

$\}$

size$--$;

$\}$

public void display$()\{$

DoublyNode current $=$ head;

while $($current $!=$ null$)\{$

System.out.println$($current$.$data.name $+"$: $"+$ current.data.score$)$;

current $=$ current.next;

$\}$

$\}$

$\}$

public class Main $\{$

public static void main$($String$[]$ args$)\{$

TopScoresDoublyList scoresList $=$ new TopScoresDoublyList$()$;

$//$ Adding students

scoresList.add$($new Student$("$John$",95))$;

scoresList.add$($new Student$("$Alice$",89))$;

scoresList.add$($new Student$("$Bob$",92))$;

scoresList.add$($new Student$("$Charlie$",85))$;

scoresList.add$($new Student$("$David$",98))$;

scoresList.add$($new Student$("$Emma$",91))$;

scoresList.add$($new Student$("$Frank$",87))$;

scoresList.add$($new Student$("$Grace$",96))$;

scoresList.add$($new Student$("$Henry$",93))$;

scoresList.add$($new Student$("$Ivy$",90))$;

scoresList.add$($new Student$("$Jack$",94))$;

scoresList.add$($new Student$("$Kelly$",88))$;

scoresList.add$($new Student$("$Liam$",97))$;

scoresList.add$($new Student$("$Mia$",84))$;

scoresList.add$($new Student$("$Noah$",99))$;

scoresList.add$($new Student$("$Olivia$",82))$;

scoresList.add$($new Student$("$Sophia$",100))$;

System.out.println$("$Top $15$ Scores:"$)$;

scoresList.display$()$;

$\}$

$\}$