Please fix the problem for below JAVA code, when i enter $($a$+$a$)$ $ as input I get invalid output which is not correct:

import java.util.$*$;

public class Project$2\{$

private static final Map$>$ parsingTable $=$ new HashMap;

private static final Set terminals $=$ new HashSetArrays$.$asList$(\text{'}+\text{'},\text{'}-\text{'},\text{'}*\text{'},\text{'}/\text{'},\text{'}(\text{'},\text{'})\text{'},\text{'}$a$\text{'},\text{'}$$$\text{'}))$;

private static final Set nonTerminals $=$ new HashSetArrays$.$asList$(\text{'}$E$\text{'},\text{'}$Q$\text{'},\text{'}$T$\text{'},\text{'}$R$\text{'},\text{'}$F$\text{'}))$;

static $\{$

Map eRow $=$ new HashMap;

eRow.put$(\text{'}(\text{'},"$TQ$")$;

eRow.put$(\text{'}$a$\text{'},"$TQ$")$;

parsingTable.put$(\text{'}$E$\text{'},$ eRow$)$;

Map qRow $=$ new HashMap;

qRow.put$(\text{'}+\text{'},"+$TQ$")$;

qRow.put$(\text{'}-\text{'},"-$TQ$")$;

qRow.put$(\text{'})\text{'},"")$;

qRow.put$(\text{'}$$$\text{'},"")$;

parsingTable.put$(\text{'}$Q$\text{'},$ qRow$)$;

Map tRow $=$ new HashMap;

tRow.put$(\text{'}(\text{'},"$FR$")$;

tRow.put$(\text{'}$a$\text{'},"$FR$")$;

parsingTable.put$(\text{'}$T$\text{'},$ tRow$)$;

Map rRow $=$ new HashMap;

rRow.put$(\text{'}+\text{'},"")$;

rRow.put$(\text{'}-\text{'},"")$;

rRow.put$(\text{'}*\text{'},"*$FR$")$;

rRow.put$(\text{'}/\text{'},"/$FR$")$;

rRow.put$(\text{'})\text{'},"")$;

rRow.put$(\text{'}$$$\text{'},"")$;

parsingTable.put$(\text{'}$R$\text{'},$ rRow$)$;

Map fRow $=$ new HashMap;

fRow.put$(\text{'}(\text{'},"($E$)")$;

fRow.put$(\text{'}$a$\text{'},"$a$")$;

parsingTable.put$(\text{'}$F$\text{'},$ fRow$)$;

$\}$

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

Scanner scanner $=$ new Scanner$($System$.$in$)$;

System.out.println$("$Enter the input string $($ending with $$)$:$")$;

String input $=$ scanner.nextLine$()$;

scanner.close$()$;

if $($parse$($input$))\{$

System.out.println$("$Output: String is accepted$/$valid$.")$;

$\}$ else $\{$

System.out.println$("$Output: String is not accepted$/$invalid$.")$;

$\}$

$\}$

private static boolean parse$($String input$)\{$

Stack stack $=$ new Stack;

stack.push$(\text{'}$$$\text{'})$;

stack.push$(\text{'}$E$\text{'})$;

int index $=0$;

while $($index $$ input.length$())\{$

char currentChar $=$ input.charAt$($index$)$;

if $(!$terminals.contains$($currentChar$)$ && currentChar $!=\text{'}\text{'})\{$

System.out.println$("$Invalid character in the input string."$)$;

return false;

$\}$

char top $=$ stack.peek$()$;

if $($top $==$ currentChar$)\{$

stack.pop$()$;

index$++$;

$\}$ else if $($nonTerminals$.$contains$($top$))\{$

stack.pop$()$;

if $($parsingTable$.$containsKey$($top$)$ && parsingTable.get$($top$).$containsKey$($currentChar$))\{$

String production $=$ parsingTable.get$($top$).$get$($currentChar$)$;

for $($int i $=$ production.length$()-1$; i $>=0$; i$--)\{$

char prodChar $=$ production.charAt$($i$)$;

if $($prodChar $!=\text{'}\text{'})\{$

stack.push$($prodChar$)$;

$\}$

$\}$

$\}$ else $\{$

return false;

$\}$

$\}$ else $\{$

return false;

$\}$

System.out.println$("$Stack: $"+$ stack$)$;

$\}$

return stack.size$()==1$ && stack.peek$()==\text{'}$$$\text{'}$;

$\}$

$\}$Given the following CFG and the parsing table, write a program to trace input strings

over the alphabet and ending with $$.$

Given the CFG and the Predictive Parsing table below:

poinls$]$ Write a program to trace an input string given by the user, Save it as

Prog$1$ and upload it in canvas $($either the zip file or $($GitHub link$).$ Test your

programwith the following $3$ input strings:

$(1)(a+a)**a$$

$(2)a^{**}(\frac{a}{a})S$

$(3)a(a+a)$$

$[20$ points$]$ Show the content of the stack implementation$/$stack flow after cach match.

$[20$ points$]$ Report file $-$ Your report file should contain explanation of your code, in$-$built

functions used, important checkpoints $[$if it is present$],$ explanation should be short and

crisp, output screenshot of your code and should not exceed more than $2$ pages.

Following is the grammar, and parsing table.

Predietive parsing table