Josh's Exam Cramming

Josh has only 10 days to cram for an olympiad. On each of these 10 days he practices exactly 1 topic of either algebra, combinatorics or number theory. However, he never practices algebra the day after he practices combinatorics, and he never practices combinatorics the day after he practices algebra. What are the last 3 digits of the number of ways that he can cram for these 10 days?

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