Problem $2.$ Consider the following input for the parser of the expression grammar that I covered in class:

$\backslash$table$[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[$LPAREN$,$LPAREN,$\backslash$table$[[$NUM$],["1"]],$PLUS,$\backslash$table$[[$NUM$],["2"]],$RPAREN,MULT,LPAREN,$\backslash$table$[[$NUM$],["3"]],$PLUS,$\backslash$table$[[$NUM$],[4"]],$RPAREN,RPAREN,PLUS,$\backslash$table$[[$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$).$

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

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

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