\problemname{Playing the Slots}

\illustration{0.2}{playingtheslots/problem_statement/coinInSlot.png}{}

The small nation of Erratica prides itself on defying conventions established
by the more ``boring" countries around the world. One of their more obvious
distinctions lies in the design of their coinage. Believing that a person
should be easily able to identify the value a coin in a pocket or change
purse by touch alone, Erratica designs its coins as polygons. For stability,
the coins are convex -- there are no notches cut into the coins. But the
overall shapes themselves can be quite irregular.

Erratica Vending, the only manufacturer of vending machines in the nation, has
been sent the design for a new coin to be issued. Their machines are designed
so that coins enter through a slot into channel shaped as a rectangular
prism with the slot being an open face of the prism. The channel is narrow
because the coins are thin, but long enough to contain the entire coin.
From the outside of the machine, the slot appears as a rectangular hole.

The company wants to know what would be the smallest slot size they
will need so that the new coin can be slipped, after some
rotation, into the slot.

\section*{Input}

Input begins with a line containing $N$, the number of sides to the polygonal
coin. $3 \leq N \leq 20$.

This is followed by $N$ lines, each containing two real numbers
$x$ and $y$, the coordinates of a vertex of the polygon. 
$0.0 \leq x, y \leq 100.0$

All $N$ vertices will be distinct, and the vertices will be presented in an
order proceeding clockwise around the perimeter of the coin.

\section*{Output}

Print a single line with a real number, to two decimal places
precision, denoting the minimum slot size allowing the coin to pass
through.  Outputs will be accepted that are within $\pm 0.01$ of the
judges' answer.


\section*{Examples}
