Around the Table

There will be $n$ people numbered from $1$ to $n$, and a room with a round table that has exactly $n$ seats, with each person having a distinct reserved seat that hasn't been revealed yet.

To figure out the reserved seat of each person, up to $60$ meetings of the $n$ guests can be organized in the dining room. Before each meeting, you can decide the order in which the guests will arrive. After each meeting, you will receive a list of the guests who arrived earlier than both of their neighbors in the secret seating arrangement at the table.

For each seat, find the person it is reserved for using the information gathered by the result of the meetings.