Choose the next instantaneous description for the PDA given the previous description, and the following $$ function:

$(q_0,a,z)=\{(q_0,0z)\}$

$(q_0,a,0)=\{(q_0,00)\}$

$(q_0,,0)=\{(q_1,0)\}$

$(q_1,,z)=\{(q_3,z)\}$

$(q_1,,0)=\{(q_2,)\}$

$(q_2,,0)=\{(q_1,)\}$

$(q_0$ aaaaa $z)|--{?}^{**}(q_1,,00000z)|--?$

The string aaaa is not accepted by the PDA.

$(q_1,,0000z)$

$(q_2,,0000z)$

$(q_2,,00000z)$