Keep Magnets Separated

There are $N$ magnets on a tree of $N$ nodes numbered $1$ to $N$, one in each node. Upon introducing an external magnet at some node of the tree, all the magnets come closer by $1$ step, while the magnets at that node remains stationary. More formally, suppose we introduced an external magnet at node $x$, then : - Magnets placed at node $x$ will not move. - Magnets placed at any other node $u (