Problem $8[15$ points$]$: You want to write a parser for a program that can do some calculator functions $($add$,$ subtract, multiply, divide$),$ but you are missing the grammar to map it out. Given the following tokens, write a grammar for this parser and briefly justify your construction:

NUM $=0|1|2|3|4|5|6|7|8|9|)$

RPAREN $=($

Your grammar is expected to har$$dle inputs including, but not limited to$,$ the following:

$4+40$

$((8-4)+(32))$

$50+5-323\frac{97}{2}$