$1.$Given are the following $3$ separate grammars: $(10$ marks$)$A bAc eps $(1)$A bAb b $(2)$A bAb c $(3)$For all three grammars:$($i$)$ Calculate the First$-$ and Follow$-$sets of A$.($ii$)$ After extending the grammar with a new start symbol and production A A$,$draw the LR$(0)-$ DFA.