$(25$ points$)$ Create a PDA that recognizes the following context free language with terminals $\{a,b\}$:$L=\{a^{3n}{b}^n|n1\}$

$($i$)$ Give your PDA as a transition diagram $(20$ points$)$;

$($iii$)$ Show configuration sequences on aaab leading to acceptance $(5$ points$).$