Swapping == Permuting?

Given a sequence of n first positive integers (n $\geq$ 3 and n must be odd ): 1, 2, 3, 4, 5, ..., n-2, n-1, n. We perform the following operations on the sequence repeatedly and infinitely:

• Swap the nth element and the (n-1)th element.

• Swap the (n-2)th element and the (n-3)th element.

• Swap the (n-4)th element and the (n-5)th element.

• ...

• Swap the 5th element and the 4th element.

• Swap the 3rd element and the 2nd element.

• Swap the 1st element and the 2nd element .

• Swap the 3rd element and the 4th element.

• Swap the 5th element and the 6th element.

• ...

• Swap the (n-4)th element and the (n-3)th element

• Swap the (n-2)th element and the (n-1)th element.

At each step, we create a different permutation from the previous one. Which of the following statements are true with all value of n?

A: The process will always go through the original sequence's reversal permutation. (n, n-1, n-2, n-3, ..., 4, 3, 2, 1)

B: The process will always go through all possible permutations of the original sequence.