Consider the following input for the parser of the expression grammar that I covered in class:

$123456789101112131415$

LPAREN LPA REN NUM

$1$ PL US NUM

$2$ RPA REN M ULT LPA REN NUM

$3$ PLUS NU

$4$ M

RPA REN RPA REN PL US NUM

$5$

As we have seen, the parsing functions call each other recursively starting with parse$\_$input$()($refer to the first set of notes for the actual code of the parsing functions$).$

$1.$ Which token is consumed first by the second call to parse$\_$F$()($specify the number of the token. The numbers are highlighted in yellow in the first row of the table above$)$ NUM $1$

$2.$ The token RPAREN at $13$ is consumed by which call to parse$\_$F$()$

$3.$ What is the total number of calls to parse$\_$F$()$ when this input is parsed?

$4.$ What is the total number of calls to parse$\_$E$()$ when this input is parsed?

$5.$ How many calls to lexer.peek$(1)$ in the various parsing functions return EOF while parsing this input?