RU-ALLRUSSIAN 1989 Problem 7

One bird lives in each of n bird- nests in a forest. The birds change nests, so that after the change there is again one bird in each nest. Also for any birds A, B, C, D (not necessarily distinct), if the distance $\mathrm{AB} < \mathrm{CD}$ before the change, then $\mathrm{AB} > \mathrm{CD}$ after the change. Find all possible values of n.