Construct a context-free grammar that generates each of the following sets of strings.
"Document" all the non-start variables in your grammar with an English description of the set of strings it generates. (You do not need to document the start variable because it is documented by the problem statement.)

Binary strings matching the regular expression "1(0∪111)*∪000".
Hint: You can use the technique described in lecture to convert this RE to a CFG.