iii. Let $=\{a,b\}.$ Construct a DFA for the language $L=\{\begin{array}{cc}\text{w}\text{i}\text{n}& {}^{**}|w\end{array}$ contains the same

number of instances of the substring ab and the substring ba $\}.$ Note that substrings are

allowed to overlap, so we have aba inL $($one copy of each substring$)$ and babab inL $($two

copies of each substring$).$