Last month, Sichuan province secured funding to establish
the Great Panda National Park, a natural preserve for a
population of more than $1\,
800$ giant pandas. The park will be surrounded by a
polygonal fence. In order for researchers to track the pandas,
wireless receivers will be placed at each vertex of the
enclosing polygon and each animal will be outfitted with a
wireless transmitter. Each wireless receiver will cover a
circular area centered at the location of the receiver, and all
receivers will have the same range. Naturally, receivers with
smaller range are cheaper, so your goal is to determine the
smallest possible range that suffices to cover the entire
park.
As an example, Figure 1 shows the park described by the
first sample input. Notice that a wireless range of
$35$ does not suffice (a),
while the optimal range of $50$ covers the entire park (b).
Input
The first line of the input contains an integer $n$ ($3
\leq n \leq 2\, 000$) specifying the number of vertices
of the polygon bounding the park. This is followed by
$n$ lines, each containing
two integers $x$ and
$y$ ($x, y \leq 10^4$) that give the
coordinates $(x, y)$ of
the vertices of the polygon in counterclockwise order. The
polygon is simple; that is, its vertices are distinct and no
two edges of the polygon intersect or touch, except that
consecutive edges touch at their common vertex.
Output
Display the minimum wireless range that suffices to cover
the park, with an absolute or relative error of at most
$10^{6}$.
Sample Input 1 
Sample Output 1 
5
0 0
170 0
140 30
60 30
0 70

50

Sample Input 2 
Sample Output 2 
5
0 0
170 0
140 30
60 30
0 100

51.538820320

Sample Input 3 
Sample Output 3 
5
0 0
1 2
1 5
0 2
0 1

1.581138830
