A language consists of nouns, verbs, articles, and adverbs. A noun may be either "boy" or "givl". A verb can be either "runs" or "walks". An article can be either $"$a$"$ or "the". An adverb can be either "quickly" or "slowly". A noun phrase must consist of one article followed by one noun. A sentence can be either a noun phrase followed by a verb, or it can be a noun phrase followed by a verb and followed by an adverb. For example, the sentences "The girl runs" and "A boy walks slowly" are legal sentences. Construct a grammar for this language, using the BNF form.

For the grammar in $$2,$ draw the parse tree for "the girl runs quickly".