$4\mathrm{.}9$ Consider the following grammar: lexp $->$ atom $|$ list atom $->$ number $|$ identifier list$->($lexp$-$seq$)$ lexp$-$seq$->$ lexp$-$seq, lexp $|$ lexp a$.$ Eliminate the left recursive rule of this grammar. b$.$ Construct First and Follow sets for the nonterminals of the resulting grammar. c$.$ Show that the resulting grammar is LL$(1).$ d$.$ Construct the LL$(1)$ parsing table for the resulting grammar. e$.$Show the actions of the corresponding LL$(1)$ parser, given the input string $($a$,($b$,(2)),($c$)).$