Suppose that $a, b, c$, and $d$ are real numbers simultaneously satisfying the following equations:
\[
\begin{align*}
&a + b - c - d &= 3, \\
&ab - 3bc + cd - 3da &= 4, \\
&3ab - bc + 3cd - da &= 5.
\end{align*}
\]
Find the value of $11(a - c)^2 + 17(b - d)^2$.

Let's think step by step and output the final answer within \boxed{}.
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