Minimize Inversions Number

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 50\,000$$$) — the number of test cases.

The first line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 5 \cdot 10^5$$$) — the length of the permutation.

The second line of each test case contains the permutation $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$).

It is guaranteed that the total sum of $$$n$$$ doesn't exceed $$$5 \cdot 10^5$$$.

Output:

For each test case output $$$n + 1$$$ integers. The $$$i$$$-th of them must be the answer for the subsequence length of $$$i - 1$$$.

Sample Input:

3
1
1
4
4 2 1 3
5
5 1 3 2 4

Sample Output:

0 0
4 2 2 1 4
5 4 2 2 1 5

Note:

In the second test case:

• For the length $$$0$$$: $$$[4, 2, 1, 3] \rightarrow [4, 2, 1, 3]$$$: $$$4$$$ inversions.
• For the length $$$1$$$: $$$[4, 2, \mathbf{1}, 3] \rightarrow [1, 4, 2, 3]$$$: $$$2$$$ inversions.
• For the length $$$2$$$: $$$[4, \mathbf{2}, \mathbf{1}, 3] \rightarrow [2, 1, 4, 3]$$$, or $$$[4, 2, \mathbf{1}, \textbf{3}] \rightarrow [1, 3, 4, 2]$$$: $$$2$$$ inversions.
• For the length $$$3$$$: $$$[4, \mathbf{2}, \mathbf{1}, \mathbf{3}] \rightarrow [2, 1, 3, 4]$$$: $$$1$$$ inversion.
• For the length $$$4$$$: $$$[\mathbf{4}, \mathbf{2}, \mathbf{1}, \mathbf{3}] \rightarrow [4, 2, 1, 3]$$$: $$$4$$$ inversions.