Please reason step by step, and put your final answer within \boxed{}.
Given a permutation of \(1, 2, 3, \ldots, n\), with consecutive elements \(a, b, c\) (in that order), we may perform either of the following moves:
- If \(a\) is the median of \(a, b\), and \(c\), we may replace \(a, b, c\) with \(b, c, a\) (in that order).
- If \(c\) is the median of \(a, b\), and \(c\), we may replace \(a, b, c\) with \(c, a, b\) (in that order).

What is the least number of sets in a partition of all \(n!\) permutations, such that any two permutations in the same set are obtainable from each other by a sequence of moves?
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