A simpli$$ed telephone switching system allows the following strings as legal telephone numbers:

a$.$ A string of seven digits in which neither of the $$rst two digits a $0$

or a $1($a local call string$).$

b$.$ A $1$ followed by a three$-$digit area code string $($any digit except $0$ or $1$ followed by a $0$ or $1$ followed by any digit$)$ followed by a seven$-$digit local call string.

c$.$ A $0$ alone or followed by a three$-$digit area code string plus a seven$-$digit local call string.

Design a $$nite$-$state automaton to recognize all the legal telephone

numbers in $($a$),($b$)$ and $($c$).$ Include an $$error state$$ for invalid telephone numbers.