$(20$pts$)$ Build a DFA for each of the following languages:

a$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{**}\end{array}$ : every $a$ in $w$ is immediately preceded and followed by $\{$:$b\}.$

b$)\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{**}\text{:}w\end{array}$ does not end in ba