Let
$$
\begin{aligned}
& A=\{z \in \mathbb{C}:|z-2| \leqslant 4\} \text { and } \\
& B=\{z \in \mathbb{C}:|z-2|+|z+2|=5\}
\end{aligned}
$$
Then the max $\left\{\left|z_1-z_2\right|: z_1 \in \mathrm{~A}\right.$ and $\left.z_2 \in \mathrm{~B}\right\}$ is:
