\problemname{Hyacinth}

\illustration{.4}{hyacinth.jpg}{Photo by Wikimedia Commons user The\_wub}%
\noindent
As a new employee at the Northwestern Europe Routing Company (NWERC), you do a
lot of thinking about wireless network architectures. Lately you learned
about a multi-channel mesh network architecture (called
\emph{Hyacinth}) that equips each mesh network node with multiple network
interface cards (NICs) to increase the network throughput.
You can choose a channel frequency for each NIC. In order to communicate,
for every two network nodes that are in range of each other, their NICs
must share at least one common frequency.
The theoretical throughput is optimal when the total number of used frequencies
in the network is maximal.

Your bosses at NWERC want you to figure out a procedure for assigning
frequencies to the NICs such that the number of frequencies in use is
maximized, subject to the constraint that all pairs of adjacent nodes must be able to communicate.  A frequency is considered used if any pair of nodes within range
of each other share that frequency.  In the mesh network that you will be dealing with, each node is equipped with exactly two NICs (i.e., each node can use at most
two frequencies). Since you are new at NWERC, your bosses further restrict the
network layouts to make your job easier: the network graph will form a tree.

\section*{Input}

The input consists of:
\begin{itemize}
\item one line with one integer $n$ ($2 \leq n \leq 10\,000$), the number of nodes in the network;
\item $n-1$ lines, each with two space-separated integers $i$ and $j$, with $1 \leq i,j \leq n$ signifying that the (one-indexed) network nodes $i$ and $j$ are in range of each other.
\end{itemize}

\section*{Output}

Output a frequency assignment for each of the $2n$ NICs such that all
adjacent nodes can communicate and the number of used frequencies is
maximized.  You should output $n$ lines, where the $i$th line contains the
two frequencies of network node $i$. Valid frequencies are nonnegative
integers less than $10^9$.
