Write a CFG $($Context$-$Free Grammar$)$ that generates the language of strings over $\{$a$,$b$,$ c$\}$ where there are more a$$s before the first c than b$$s after it$.$ Keep in mind that there can be any number of c$\text{'}$s$,$ not just $1.$ Additionally, the pattern may not be a sequence of as$,$ followed by a c$,$ followed by a sequence of bs$.$ There can be bs before the first c and as after the first c$,$ as long as there are more as before the first c than bs after the first c$,$ the string is valid. Here are some examples of rejected and accepted strings.

Accepted: aacb, aacab, aacac, aaacb, abababcb, aacbaaaaa, acaaaacacacab

Rejected: acb, accccb, ababcbb, acbb