\problem{Toys and Triangles}


Alaa fondly remembers playing with a building toy when she was a
child. It consisted of segments that could be fastened at each end.  A
game she liked to play was to start with one segment as a base, placed
flat against a straight wall.  Then she repeatedly added on triangles,
with one edge of the next triangle being a single segment already in
place on her structure, and the other two sides of the triangle being
newly added segments. Of course no segment could go through the wall,
but she did allow newly added segments to cross over already placed
ones.  Her aim was to see how far out from the wall she could make her
structure go.

\includegraphics[width=0.45\linewidth]{Toy/figures/better_42_40_32_30_25_18_15.png}
\hfill
\includegraphics[width=0.35\linewidth]{Toy/figures/bad_42_40_32_30_25_18_15.png}

She would experiment, building different ways with different
combinations of some or all of her pieces.  It was an easy, boring
task if all the segments that she used were the same length!  It got
more interesting if she went to the opposite extreme and started from
a group of segments that were all of distinct lengths.

\begin{center}
\includegraphics[width=0.6\linewidth]{Toy/figures/best_42_40_32_30_25_18_15.png}
\end{center}

For instance, with segments of length 42, 40, 32, 30, 25, 18 and 15,
the figures above show some of the structures she could have built,
including the one with the maximum distance.

Now looking back as a Computer Science student, Alaa wondered how well she did, and decided to write a program to check what the maximum distance really is.  This is also the challenge for you.

\subsection*{Input}

The input is a single line of positive integers,

\[ n \; L_1 \; L_2 \ldots L_n \]

Here $n$ is the number of segments, $3 \leq n \leq 10$, and then the
lengths of the segments are listed in strictly decreasing order.  Each
segment length is less than 100.  At least one triangle may be
constructed.

\subsection*{Output}

Print the maximum distance that one of Alaa's structures can go
from the wall to two decimal digits of precision.


\section*{Time Limit}

Solutions to this problem must run in no more than 5 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
  3 50 40 30 & 40.00 \\
  \hline
  4 50 40 30 29 & 40.00 \\
  \hline
  7 42 40 32 30 25 18 15 & 66.95 \\
  \hline
\end{tabular}
\end{center}

