One variation in how we write down US phone numbers is that we sometimes leave off the parentheses around the area code and instead use a dash after it: $757-555-0000$ for example.

Many businesses have adopted the practice of using $"."($period$)$ instead of $"-"($dash$)$ between the number groups: $757\mathrm{.}555\mathrm{.}0000$ for example.

By convention, international telephone numbers begin with a plus sign $(+)$ followed by a $1,2,$ or $3-$digit country code. The US country code is $"1".$ So the example US phone number would be written as $+1757\mathrm{.}555\mathrm{.}0000$ in this international style.

THE CHALLENGE

$1.$ Write down a BNF grammar and State Diagram for US phone numbers that uses the star $(*)$ after the area code instead of parentheses around it$.$

$2.$ Write down a BNF grammar and State Diagram for US phone number written in the international style.