A run in a setting is a substring of length at least two, as long as possible, and consisting entirely of the same symbol. For instance, the string abbbaab contains a run of b's of length three and a run of a's of length two. Find dfa's for the following languages on {a, b}:

(a) L = {w: w contains no runs of lengths less than three}.

(b) L = {w: every run of a's has length either two or three}.

*Provide input to thoroughly test the DFA's.