Solve it handwritten only

$(6$ points$)$ Using the concept of Pumping Lemma, show that $\{\begin{array}{c}{a}^n\end{array}\{$:$b^n{c}^n|n0\}$ 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 $\text{'}c\text{'}$