Consider the very simple CFG with the rules below. This grammar accepts sentences such as $$the man walked the dog in the park$$ and $$Walk the dog in the park$.$

$(1)$ S $$ VP $|$ NP VP$|$ NP VP PP

$(2)$ VP $$ Verb NP

$(3)$ PP $$ Prep NP

$(4)$ NP $$ the Nom

$(5)$ Nom $$ Noun PP $|$ Noun

$(6)$ Noun $$ man $|$ dog

$(7)$ Verb $$ walked $|$ walk

$(8)$ Prep $$ in $|$ to

Which grammar is a valid CNF form of the original CFG grammar?