A recursive sequence is defined by F(0) = 0, F(1)=1, and F(n) = the remainder when F(n-1)+F(n-2) is divided by 3, for all n >= 2. Therefore the sequence starts with 0,1,1,2,0,2...

What is F(2017)+F(2018)+F(2019)+F(2020)+F(2021)+F(2022)+F(2023)+F(2024)?

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