Not a fan of 3

Probability Level 5

How many positive integers n1000 n \leq 1000 are there which satisfy the following condition:

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

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

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