The ear clipping method can decompose a polygon into triangles: each time, a triangle (called an "ear") is cut off along a diagonal. After $n-3$ cuts, an $n$-sided polygon is decomposed into triangles. As shown in the figure below, the triangle $\{2, 3, 4\}$ has been cut off.

Given a polygon, how can we minimize the total length of the cut traces?

Input

The input contains at most 30 test cases. The first line of each test case contains the number of vertices $n$ ($4 \le n \le 100$). The following $n$ lines describe the coordinates of each vertex of the polygon (all are integers with absolute values not exceeding 10000), arranged in counter-clockwise or clockwise order.

Output

For each test case, output the minimum total length of the cut traces, rounded to 4 decimal places.

Examples

Input 1

4
0 0
3 0
1 1
0 3
4
0 0
10 0
10 1
0 1

Output 1

Case 1: 1.4142
Case 2: 10.0499