For the following grammar G $=($V$,\backslash$Sigma $,$ R$,$ S$),$ where V $=\{$S$,$ T$,$ X$\},\backslash$Sigma $=\{$a$,$ b$\},$ S is the the start variable, and the rules are:

S $->$ aT Xb

T $->$ XT S$|$

X $->$ b$|$a

convert G into a pushdown automata.