\problem{Tsunami}

\parpic[r]{\includegraphics[width=0.2\linewidth]{Tsunami/wave.png}}

The country of Cartesia can be described simply by a Cartesian
plane. The $x$-axis is a shoreline. The positive $y$ half-plane is
land, and the negative $y$ half-plane is ocean. Several large cities
dot the mainland. Their positions can be described by coordinates
$(x,y)$, with $y>0$. Unfortunately, there are sometimes tsunamis in
the ocean near Cartesia. When this happens, the entire country can
flood. The waters will start at $y=0$ and advance uniformly in the
positive $y$ direction.

Cartesia is trying to develop a tsunami warning system. The warning
system consists of two components: a single meteorological center
which can detect a tsunami miles out, and wired connections which can
carry the warning from city to city in straight lines. (No wireless
communication!!)

A city is considered {\em safe} if it either has the meteorological
center, or if it has a direct wire connection to another {\em safe} city
(i.e. if it has a multi-hop cable path to the meteorological center).

The transmission time along the cables and through each city is
negligible. Nonetheless, a simple engineering problem is made more
complicated by politics! If a city A receives the warning via a wire
from city B, and city B is further away from the shore than city A,
then city A's leaders will complain! “We're closer to the ocean than
city B, so we should have gotten the word first!” With a sigh, you
agree to find a solution where no city will get the warning via a wire
from a city that's further from the shore. 

Given a description of Cartesia, find the least amount of cable
necessary to build a tsunami warning system where every city is safe,
and no city will receive the warning via a wire another city that is further
from the shore.

\subsection*{Input}

There may be several test cases in the input. 

Each test case will begin an integer $n$ ($1\leq n\leq 1,000$) on its own
line, indicating the number of cities. 

On each of the next $n$ lines
will be a pair of integers $x$ and $y$ ($-1,000\leq x\leq 1,000, 0<y\leq
1,000$), each of which is the $(x,y)$ location of a city. 

The input will end with a line containing a single 0.

\subsection*{Output}

For each test case, print a single line containing the minimum amount
of cable which must be used to build the tsunami warning system. This
should be printed as a floating point number to two decimal places
precision.


\subsection*{Example}

Given the input
\verbfile{Tsunami/sample.judge}

the output should be
\verbfile{Tsunami/sample.out}
