Merlin summons the $n$ knights of Camelot for a conference. Each day, he assigns them to the $n$ seats at the Round Table. From the second day on, any two neighbors may interchange their seats if they were not neighbors on the first day. The knights try to sit in some cyclic order which has already occurred before on an earlier day. If they succeed, then the conference comes to an end when the day is over. What is the maximum number of days for which Merlin can guarantee that the conference will last?

Let's think step by step and output the final answer within \boxed{}.
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