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:

• An integer, N, indicating the number of vertices making up the polygon. End of input is signaled by any N less than 3.
• Next are N lines, each containing a pair of floating-point numbers, (x_i, y_i), each denoting one vertex of the polygon. Vertices will be presented in clockwise order (relative to the closest interior point) proceeding around the perimeter of the polygon. The x_i and y_i values are in units of meters.
• The data set is terminated by a floating point value indicating the amount of molten metal available (in cubic meters).

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.

expressed as a polygon (vertices visited in clockwise order, each vertex described via (x,y) coordinates expressed in units of meters) and the volume of the available molten metal (in cubic meters),

Sample Input

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

Sample Output

BAR LENGTH: 100.00
BAR LENGTH: 318.73