$($python code required$)2.$ Consider the grammar above which is an extension to what we had in class.

PROGRAM $->$ STMTS

STMTS $->$ STMT$|$ STMT ; STMTS

STMT $->$ id $=$ EXPR

EXPR $->$ EXPR $+$ TERM $|$ EXPR $-$ TERM $|$ TERM

TERM $->$ TERM $*$ FACTOR $|$ TERM $/$ FACTOR $|$ FACTOR

FACTOR $->($ EXPR $)|$ id $|$ integer

Where$\{$PROGRAM$,$ STMTS$,$ STMT$,$ EXPR, TERM, FACTOR$\}$ are non$-$terminals and $\{$ ; $,=,+,-,*,/,(,),$ id$,$ integer$\}$ are terminals. PROGRAM is the start non$-$terminal, and the terminal id is defined using the regular expression: letter$($letter $|$ digit$)*.$

a$)$ Modify the grammar to add the power operator $(^)$ and unary sign operators $+$and $-.$

b$)$ Re$-$write the grammar such that it can be parsed by an LL$(1)$parser$.$

c$)$ Use the written grammar as a base to implement LL$(1)$parser$.$

d$)$ Test your code with a correct and incorrect input code.

e$)$ Report $($Code of the parser, parsing table, testing the codes, a screenshot of the outputs or GUI if any$).$