Problem Description
Little Ruins is a studious boy, recently he learned inequation!
As homework, his teacher gives him a problem of inequation: give you an array a with length N−1, please find an array x with length N and xi×xi+1≥ai for each i from 1 to N−1 and try to minimize the sum of x.
Input
First line contains an integer T, which indicates the number of test cases.
Every test case begins with an integers N, which is the length of array x.
The second line contains N−1 integers a1, a2, ⋯, aN−1, indicating the array a.
Limits
1≤T≤50.
1≤N≤2000.
0<ai≤104.
For 80\% of the use cases, 1≤N≤100 holds.
Output
For every test case, you should output 'Case #x: y', where x indicates the case number and counts from 1 and y is the result.
Round the y to the fifth digit after the decimal point.
Sample Input
2
4
2 3 2
4
1 2 3
Sample Output
Case #1: 5.77350
Case #2: 5.47723
