Use left-factoring and/or eliminate left-recursion to transform each of the below six grammars into a form that is suitable for recursive-descent parsing. Capital letters denote variables and lower case letters are terminals.

a) S -> abSa | abcSc | abdc | bcc

b) S -> bSa | ccaSb | ccbSa | abc

c) S -> Sa | Sbc | cc |

d) S -> SB |

B -> Bb | a

e) S -> abcSd | abddS | cdabS | cdbb

f) S -> Sab | Sac | b | c (Hint: Here after elimination of left recursion you need to also use left-factoring or vice-versa)