Problem $2.($NFAs$)(30$ points$)$ Show that the following languages are regular by giving non$-$deterministic$$finite automata $($NFA$)$ that accept them:$($i$)$ Consider the English alphabet $\backslash$Sigma $=\{$a$,$ b$,...,$ z$,$ A$,$B$,...,$Z$\}.$ Give a language L$1$ with the names of $10$cities that hosted summer Olympic games. As for example L$1=\{$Athens$,$ Atlanta, $...\}.$ Design a NFA$$that accepts L$1($ii$)$ L$2=\{$w in $\{$a$,$ b$\}$ : w does not contain substrings aaa and aba$\}.($iii$)$ L$3=\{$aibjak : i$,$ j$,$ k $>=0\}\backslash$cup $\{$blambn : l$,$ m$,$ n $>=0\}$