Description

The Acme Extrusion Company specializes in the production of steel bars with custom-designed cross-sections. The manufacturing process involves cutting a hole in a thick metal plate, the shape of the hole being determined by the customer's specifications.

Molten metal is then forced through the hole to form a long bar. The shape of the hole determines the shape of the cross-section of the resulting bar.

Given a description of a polygonal hole and the volume of molten metal available, determine how long a bar can be formed by this process.

Input

Input consists of one or more data sets consisting of the following information:

Output

For each data set, the program should produce a single line of output of the form:

BAR LENGTH: x

where ``x " is the maximum bar length, a floating point number expressed with two digits precision.

4
0.0 0.0
0.0 0.1
0.1 0.1
0.1 0.0  
1.0
7
0.5 1.25
0.9 1.6
0.9  1.1
0.85 1.0
0.9 0.85
0.9 0.5
0.5 0.75
100.0
0

BAR LENGTH: 100.00 
BAR LENGTH: 318.73

Source

Mid-Atlantic 2005