For $0 \leq d \leq 9$, we define the numbers 
\[S_{d}=1+d+d^{2}+\cdots+d^{2006}\]
Find the last digit of the number 
\[S_{0}+S_{1}+\cdots+S_{9}.\]

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