$(6$ points$)$ Using the concept of Pumping Lemma, show that $\{a^n{b}^n{c}^n|n0\}$ is not

context$-$free using two cases:

a$.$ The $v$ part of the string $S=$uvxyz contains only several $\text{'}a\text{'},$

and the $y$ part contains several $\text{'}c\text{'}.$

b$.$ The $v$ part of the string $S=$uvxyz contains several $\text{'}a\text{'}$ and $\text{'}b\text{'}$

and the $y$ part contains several $\text{'}b\text{'}$ and $\text{'}c\text{'}$