Let us define a context$-$free grammar G to be in $2-$Form$$

if$,$ for every nonterminal A$,$ there are at most two options for replacing A in a

derivation. That is$,$ there are at most two rules in G that have A on the left

hand side, where the $$rule$$ A $->$ B$|$C$|$D is considered to be three rules. Show

that, for any context$-$free grammar, there is a $2-$Form context$-$free grammar that

recognizes the same language.