Let $L=\{0^n{1}^n{2}^n|n0\}$ be a language over the alphabet $\{0,1,2\}.$

$($i$)$ Is $L$ a regular language? In the case your answer is either YES or NO$,$ prove your

claim.

$($ii$)$ Is $L$ a context$-$free language? In the case your answer is either YES or NO$,$ prove your

claim.

$($iii$)$ Is $L$ a decidable language? In the case your answer is either YES or NO$,$ prove your

claim.

$($iv$)$ Is $L$ a Turing$-$recognizable language? In the case your answer is either YES or NO$,$

prove your claim.