PREPARATION Be sure you've developed a BNF grammar that describes the language of phone numbers according to the Practice BNF item. Let's call this the US phone number grammar.

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: 757.555.0000 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 +1757.555.0000 in this international style.

THE CHALLENGE

1. (5 pts) Write down a BNF grammar for US phone numbers that use the dash after the area code instead of parentheses around it.

2. (5 pts) Write down a BNF grammar for US phone number written in the international style.

3. (15 pts) Write a program that allows the user to input a character string from the keyboard, and tell the user if that string complies with the US phone number grammar (that is, the one from the Practice BNF item, like (757)530-4601 ). Your program should output the user's string, followed by "YES" if the string is acceptable, and "NO" if it is not. So, an example output from this program could be:

(757)555-1234 YES

The program should also run until the user enters the number '0' or word "zero".

4. (5 pts) Your program must give the correct (Yes/No) answer when presented with the following phone numbers:

757-555-0025

(757)555-1234

75-555-0000

757.555.1234

757-043-1234

057-555-1234

057-MH5-1234