write a regular expressio for:

(xE [a, b,., @]Jx is a syntactically valid email address) Definition of "syntactically valid email address": We assume email addresses contain only the characters a and b (no digits and none of the other Roman alphabet symbols), in addition to the and. symbols. Emails are of the form username@host domain where username and host are nonempty and may contain a, b, or., but never two .'s in a row, nor can either of them begin or end with a.), and domain must be of length 2 or 3 and contain only a and b. For example, aaa.bba.bbb@ababab.bbab.aaa and ababa@baba.ab are valid email addresses, but ab.ab is not (no @ symbol), nor is .ab@ab.ab (username starts with a.), nor is ab@ab.abab (domain is too long)