Construct an npda for the following language:

$L=\{a^{3n}{b}^{2n}$:$n0\}$

$($a$)$ How do we balance push and pop operations to accept aaabb by an empty stack?

$($b$)$ Show the construction of the npda with $=\{1,z\}.$Design a PDA for the following language: L $=\{03$n$1$n $|$ n $>=0\}$