Minimize Inversions Number solution codeforces

SOLUTION:- CLICK HERE

You are given a permutation $p$ of length $n$ .

You can choose any subsequence, remove it from the permutation, and insert it at the beginning of the permutation keeping the same order.

For every $k$ from $0$ to $n$ , find the minimal possible number of inversions in the permutation after you choose a subsequence of length exactly $k$ .

Input

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

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

The second line of each test case contains the permutation $p_{1}, p_{2}, \dots, p_{n}$ ( $1 \leq p_{i} \leq n$ ).

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 $i - 1$ .

Example

input

Copy

output

Copy

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

Note

In the second test case:

For the length $0$ : $[4, 2, 1, 3] \to [4, 2, 1, 3]$ : $4$ inversions.
For the length $1$ : $[4, 2, 1, 3] \to [1, 4, 2, 3]$ : $2$ inversions.
For the length $2$ : $[4, 2, 1, 3] \to [2, 1, 4, 3]$ , or $[4, 2, 1, 3] \to [1, 3, 4, 2]$ : $2$ inversions.
For the length $3$ : $[4, 2, 1, 3] \to [2, 1, 3, 4]$ : $1$ inversion.
For the length $4$ : $[4, 2, 1, 3] \to [4, 2, 1, 3]$ : $4$ inversions.

Minimize Inversions Number solution codeforces

Minimize Inversions Number solution codeforces

SOLUTION:- CLICK HERE

SOLUTION:- CLICK HERE

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