Let $S=\left\{\,z\in\mathbb{C}:\ |z-1|=1 \ \text{and}\ \left|(\sqrt2-1)(z+\bar z)-i(z-\bar z)\right|=2\sqrt2\,\right\}$. Let $z_1,z_2\in S$ be such that $|z_1|=\max_{z\in S}|z|$ and $|z_2|=\min_{z\in S}|z|$. Then $\ \left|\sqrt2\,z_1-z_2\right|^{2}$ equals: