Extrusion

The Acme Extrusion Company makes steel bars with custom-designed cross-sections. To make a bar, a hole is cut into a thick metal plate; the shape of the hole is chosen by the customer.

Molten metal is then forced through the hole to form a long bar, so the shape of the hole becomes the shape of the cross-section of the 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.

The input contains one or more data sets. Each data set consists of the following information:

• An integer $N$, the number of vertices of the polygon. Input ends at the first value of $N$ that is less than $3$.
• $N$ lines follow. The $i$-th line contains two floating-point numbers $x_i$ and $y_i$, the coordinates of one vertex of the polygon, in meters. The vertices are given in clockwise order around the perimeter of the polygon.
• A single floating-point number giving the volume of molten metal available, in cubic meters.

For each data set, print a single line of the form

BAR LENGTH: x

where $x$ is the maximum bar length, printed with exactly two digits after the decimal point.