\problemname{Circuit Board Design}

% Picture source: https://www.flickr.com/photos/mnsc/433436548/
\illustration{0.3}{circuitboard}{A circuit board. Public domain.}%
%
You have been hired at the \emph{Nano Wiring Efficient Route Company}
(NWERC) to help with the
design of their new circuit boards. The circuits themselves have
already been designed, and your task is to come up with a way to print
them onto the blank boards that the company has bought.

More specifically, each circuit design consists of a number of
connection points with some connections between them such that the
resulting graph is connected and does not have any cycles (i.e., the
graph is a tree).

You are free to place the connection points anywhere on the circuit board
and solder the connections between them so that no two connections
intersect (except at the connection points). The boards you ordered
are fairly large, so there is no danger of running out of space.
You can solder so precisely that connections and connection points can be
considered infinitesimal.

This would all be very easy, however your boss persists that each
connection needs to be a straight line of length exactly $1\text{ mm}$ (this
is, so he says, to make sure the electrons do not have to travel
around corners, which would be detrimental to the efficiency of the
design).

You soon realise that battling with him will be unsuccessful. Your quickest way
out of this is to etch a new design according to his specifications.

%You are given a tree. Find a planar embedding for this tree,
%i.e.~assign points in the plane to the tree vertices so that if the
%edges are drawn as straight lines betweeen these points,
%
%\begin{itemize}
%  \item each edge has length $1$ (up to an error of $10^{-6}$);
%  \item no two edges intersect.
%\end{itemize}

\section*{Input}

The input consists of:
\begin{itemize}
  \item One line with one integer $n$ ($2 \le n \le 1\,000$), the number
    of connection points.  The points are numbered from $1$ to $n$.
  \item $n-1$ lines, each with two integers $a$ and $b$ ($1 \le a,b \le n$),
    describing a connection between $a$ and $b$.
\end{itemize}

It is guaranteed that these edges describe a valid tree.

\section*{Output}

Output $n$ lines, the $i$th of which contains two real numbers $x_i,y_i$, the
coordinates of point $i$. To make the production feasible, the
following restrictions apply:
\begin{itemize}
\item The distance between each pair of points should be at least $10^{-4}$.
\item The length of each edge should be $1$, up to an \emph{absolute} error of at
  most $10^{-6}$.
\item Edges that are not incident to the same vertex should be at least a distance $10^{-6}$ apart.
\item The coordinates may not exceed an absolute value of $3\,000$.
\end{itemize}
If there are multiple valid solutions, you may output any one of them.
