Problem $2(20$ points$)$: Convert the following context$-$free grammar $($CFG$)$ into its equivalent Chomsky Normal Form $($CNF$)$ using the method described in class $($the start symbol is $S,$ the terminals are a and $b)$:

$SBa|aB||$

$A$bAA$|aS|a$

$B$aBB$|bS|b$