Let \( S=\{\, z\in \mathbb{C}:\ |z-1|=1 \ \text{and}\ (\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\, \} \). Let \( z_{1},z_{2}\in S \) be such that \( |z_{1}|=\max\limits_{z\in S}|z| \) and \( |z_{2}|=\min\limits_{z\in S}|z| \). Then \( |\sqrt{2}\,z_{1}-z_{2}|^{2} \) equals:
