$(2+2+2$ points$)$ L$1=\{$ambmcn $|$ m $^31,$ n $^32\}$ L$2=\{$w $|$ w is any string in $\{$a$,$ b$,$ c$\}*$ except abc$\}($a$)$ Design a context$-$free grammar G for language L$1.$ G: $($b$)$ Design a context$-$free grammar H for the star of language L$1.$ H: $($c$)$ Construct a deterministic Turing machine F that reduces the language L$1$ to L$2$ in polynomial time. Justify your answer with detailed explanation. Answer: $[$Hint: Reuse TM S that decides ACFG using CYK algorithm$]$