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$\begin{cases} a &=& 100 + 85i \\ b &=& 208 + 39i \\ c &=& 188 + 22i \\ \end{cases}$

Given that $a, b, c$ are Gaussian integers shown above, if $d$ is the greatest common divisor (GCD) of $a, b, c,$ what is the value of $|d|^{2}?$

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