Let M $=($Q$,\backslash$Sigma $,\backslash$Gamma $,\backslash$delta $,$ q$)$ be a deterministic pushdown automaton where Q $=\{$q$,$ r$\},\backslash$Sigma $=\{$a$,$ b$\}$ and $\backslash$Gamma $=\{$$$,$ S$\}.$

Complete the transition instructions below such that M accepts the language L $=\{$an b an : n $>=1\}.$

$($L contains the strings aba, aabaa, aaabaaa, $...)$

If you need the empty string symbol in your solution, you can copy it from here: $\backslash$epsi

Please do not use spaces or commas in your answers. Write your instructions without spaces$/$commas like: qNS

qa$ $->$

qaS $->$

qb$ $->$

qbS $->$

q$$$ $->$

q$$S $->$

ra$ $->$

raS $->$

rb$ $->$

rbS $->$

r$$$ $->$

r$$S $->$