Problem E

Ears Cutting

A famous way to cut polygon into triangles is ear cutting: each time cut off a triangle along a diagonal, after n-3 cuts only a single triangle remains. In the following picture, the ear {2,3,4} was cut off.

Find a way to cut ears of a simple polygon such that the sum of cut lengths is minimal.


There will be at most 30 test cases. The first line of each case contains the number of vertices, n (4<=n<=100). Each of the following n lines contains the coordinates of a vertex, in clockwise OR counter-clockwise order. Coordinates are integers whose absolute value does not exceed 10000.


For each test case, print the minimal sum of cut lengths, rounded to 4 decimal digits.

Sample Input

0 0
3 0
1 1
0 3
0 0
10 0
10 1
0 1

Output for the Sample Input

Case 1: 1.4142
Case 2: 10.0499

The Ninth Hunan Collegiate Programming Contest (2013)
Problemsetter: Rujia Liu
Special Thanks: Md. Mahbubul Hasan