Minimize the following DFA:

\begin{tabular}{l|ll|l|} \cline { 2 - 3 } Present state & Next & state & Output \\ \cline { 2 - 3 } & Present & input & \\ & 0 & 1 & \\ \hline 0={q0} & 1 & 2 & 0 \\ 1={q0.q1} & 3 & 4 & 1 \\ 2={q1} & 5 & 5 & 1 \\ 3={q0,q1,q2} & 3 & 4 & 1 \\ 4={q1,q2} & 5 & 5 & 1 \\ 5={q2} & 6 & 5 & 0 \\ 6={} & 6 & 6 & 0 \end{tabular}