$2\mathrm{.}14.$ Let $z$ be a fixed string of length $n$ over the alphabet $\{a,b\}.$ Using the argument in Example $2\mathrm{.}5,$ we can find an FA with $n+1$ states accepting the language of all strings in $\{a,b{\}}^{**}$ that end in $z.$ The states correspond to the $n+1$ distinct prefixes of $z.$ Show that there can be no FA with fewer than $n+1$ states accepting this language.