In a football tournament, $n$ teams play one round ($n \vdots 2$). In each round should play $n / 2$ pairs of teams that have not yet played. Schedule of each round takes place before its holding. For which smallest natural $k$ such that the following situation is possible: after $k$ tours, making a schedule of $k + 1$ rounds already is not possible, i.e. these $n$ teams cannot be divided into $n / 2$ pairs, in each of which there are teams that have not played in the previous $k$ rounds. PS. The 3 vertical dots notation in the first row, I do not know what it means.