\problem{Ghostbusters 2}

In the 1984 Ghostbusters\footnote{``Ghostbusters'' is a registered
  trademark of Columbia Pictures Industries, Inc., and the dialog
  quoted on this page is $\copyright$ Columbia Pictures Industries,
  Inc.} movie, the protagonists use proton pack weapons that fire
laser streams. This leads to the following memorable dialog between
scientists Peter Venkman and Egon Spengler:

\begin{quote}
\noindent
{\bf Spengler:} ``There's something very important I forgot to tell you.\\
{\bf Venkman:} What?\\
{\bf Spengler:} Don't cross the streams.\\
{\bf Venkman:} Why?\\
{\bf Spengler:} It would be bad.\\
{\bf Venkman:} I'm fuzzy on the whole good/bad thing. What do you mean, ``bad''?\\
{\bf Spengler:} Try to imagine all life as you know it stopping instantaneously and every molecule in your body exploding at the speed of light.\\
{\bf Venkman:} Right. That's bad. Okay. All right. Important safety tip''
\end{quote}

In the 30+ years since that time, there have been several technical advances in their weapons systems. They are currently trying out a new prototype:

\begin{itemize}

\item The streams have been polarized, firing either
  horizontally or vertically. There is no longer any danger if streams
  having opposite polarity cross each other. However, there will still
  be catastrophic results if two streams having the same orientation
  in any way touch each other.

\item The streams do not affect living creatures. A stream may pass
  through one of the ghostbusters with no ill effects.

\item A weapon now simultaneously fires its streams in opposite
  directions.

  More specifically, a weapon has an integer power $P$ and when fired
  will reach locations $P$ units to the left and $P$ units to the
  right of the ghostbuster, if fired horizontally, or $P$ units above
  and below the ghostbuster if fired vertically.
\end{itemize}

When stationed at their positions, the ghostbusters can communicate to
decide who will fire horizontally and who will fire vertically. They
will all use the same power value $P$ and would like
to use as much power as possible without causing a catastrophe. 

\begin{minipage}[c]{0.45\linewidth}
\includegraphics[width=\linewidth,keepaspectratio=true]{Ghostbusters/figures/sample1.png}
\end{minipage}
\hfill
\begin{minipage}[c]{0.45\linewidth}
\includegraphics[width=\linewidth,keepaspectratio=true]{Ghostbusters/figures/sample2.png}
\end{minipage}

As an example, the plot on the left shows a configuration of
ghostbusters in which an arbitrarily large power value can be used, so long as
the ghostbusters coordinate their orientations. The plot on the right
shows a configuration in which there is
an orientation to allow power level~$3$, but for which no
orientation allows power level~$4$. (Notice that the streams of the
bottom-left and bottom-right ghostbusters would touch if using
power level~$4$ with that same orientation of streams.)



\section*{Input}

The first line contains an integer $N$, such that $1 \leq N \leq
\num{1000}$, indicating the number of ghostbusters. Following that are
$N$ lines, each containing integers $x$ and $y$ which describe the
location of one ghostbuster, such that $0 \leq x,y \leq \num{1000000}$. No
two ghostbusters are at the same location.

\section*{Output}

If the ghostbusters can use arbitrarily large power without
catastrophe, print {\tt UNLIMITED}. Otherwise print the largest
integer power value that may be safely used with appropriately chosen
orientations.

\section*{Time Limit}

Solutions to this problem must run in no more than 10 seconds.

\subsection*{Examples}


\begin{center}
  \begin{tabular}{|p{0.45\linewidth}|p{0.45\linewidth}|}
    \multicolumn{1}{l}{\textbf{Sample Input}} &
    \multicolumn{1}{l}{\textbf{Sample Output}} \\
    \hline \noalign{\vskip 0.25em}
\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/001.in}

\end{minipage}
&
\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/001.ans}

\end{minipage} \\
  \noalign{\vskip 0.25em}  \hline \noalign{\vskip 0.25em}

\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/002.in}

\end{minipage}
&
\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/002.ans}


\end{minipage}    \\

\noalign{\vskip 0.25em}  \hline \noalign{\vskip 0.25em}

\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/003.in}

\end{minipage}
&
\begin{minipage}{\textwidth}

\verbfile{Ghostbusters/judgeData/003.ans}


\end{minipage} \\

   \noalign{\vskip 0.25em} \hline


  \end{tabular}
\end{center}
