If $R_n=\frac{1}{2}(a^n+b^n)$ where $a=3+2\sqrt{2}$, $b=3-2\sqrt{2}$, and $n=0,1,2, \ldots$, then $R_{12345}$ is an integer. Find the units digit of $R_{12345}$.

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