At most how many of the following statements are true?

1: Exactly one of statements 2 or 3 is true.

2: Exactly one of statements 3 or 4 is true.

.

.

.

998: Exactly one of statements 999 or 1000 is true.

999: Exactly one of statements 1000 or 1 is true.

1000: Exactly one of statements 1 or 2 is true.

I already know the solution to the problem; just giving this out as a fun little exercise.