Not a fan of 3

How many positive integers \( n \leq 1000 \) are there which satisfy the following condition:

We can rearrange the positive integers from 1 to \(n \) in a row, where the sum of the first \(k \) terms is not a multiple of 3, for every \( 1 \leq k < n \).

Note: To avoid ambiguity, the integer 1 satisfies the above condition.

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