Adding Ones And Twos

In how many ordered ways can you write the number 666 as a sum of 1's and 2's?

Submit your answer as the last three digits of the result.

As an explicit example, there are 3 ways to write the number 3 as a sum of 1's and 2's, namely: \(1 + 1 + 1, 1 + 2, 2 + 1\).

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