Problem

You are given a sequence of distinct integers A = [A₁, A₂, ..., A_N], and would like to rearrange it into an up and down sequence (one where A₁ < A₂ < ... < A_m > A_m+1 > ... > A_N for some index m, with m between 1 and N inclusive).

The rearrangement is accomplished by swapping two adjacent elements of the sequence at a time. Predictably, you are particularly interested in the minimum number of such swaps needed to reach an up and down sequence.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing a single integer: N. The next line contains N distinct integers: A₁, ..., A_N.

Output

For each test case, output one line containing "Case #x: y", where x is the test case number (starting from 1) and y is the minimum number of swaps required to rearrange A into an up and down sequence.

Limits

Memory limit: 1 GB.

1 ≤ T ≤ 100.

1 ≤ A_i ≤ 10⁹

The A_i will be pairwise distinct.

Small dataset (7 Points)

Time limit: 60 10 seconds.

1 ≤ N ≤ 10.

Large dataset (11 Points)

Time limit: 120 20 seconds.

1 ≤ N ≤ 1000.

Sample

2
3
1 2 3
5
1 8 10 3 7

Case #1: 0
Case #2: 1

In the first case, the sequence is already in the desired form (with m=N=3) so no swaps are required.

In the second case, swapping 3 and 7 produces an up and down sequence (with m=3).