Question 53
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 $\{AB\} \lt \{CD\}$ before the change, then $\{AB\} \gt \{CD\}$ after the change. Find all possible values of $n$.