Consider the following grammar:

$S$ A B C

$Aa$ b c

A $$ a b d

$Aab$ e

B $$

C $$ C ; f

$Cf$

a$.$ Write the bottom$-$up table for this grammar

b$.$ Use your table to parse the following:

a b d f ; f $

For each step show both the stack and the remaining symbols in the input stream.