F. Whoname and Unsorted Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given a permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$, you may perform the following operation on it any number of times (possibly zero):

  • Choose an index $$$i$$$ where $$$1 \leq i \leq n-1$$$, and move $$$p_i$$$ to $$$p_1$$$ (shifting everything in between to the right) and $$$p_{i+1}$$$ to $$$p_n$$$ (shifting everything in between to the left). Formally, you may transform $$$p = [p_1, \ldots, p_n]$$$ into $$$p' = [p_i, p_1, p_2, \ldots, p_{i-1}, p_{i+2}, p_{i+3}, \ldots, p_n, p_{i+1}].$$$

Provide a valid sequence of operations of length at most $$$4n$$$ to make $$$p_i = i$$$ for all $$$i\,(1 \le i \le n)$$$, or print $$$-1$$$ if no sequence exists.

It can be shown that if a valid sequence of operations exists, there is a valid sequence of length at most $$$4n$$$ operations.

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). The description of the test cases follows.

The first line contains an integer $$$n\,(2 \leq n \leq 5000)$$$ — the length of the permutation.

The second line contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n \, (1 \le p_i \le n)$$$.

It is guaranteed that $$$p$$$ is a permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5000$$$.

Output

If there does not exist a valid sequence of operations, output $$$-1$$$.

Otherwise, on the first line, output $$$x\,(0 \leq x \leq 4n)$$$, the number of operations needed to sort the permutation. On the second line, output $$$x$$$ integers $$$i_1, \ldots, i_x$$$ where $$$i_j$$$ ($$$1 \leq i_j \leq n-1$$$) denotes the index corresponding to the $$$j$$$-th operation.

Example
Input
4
2
2 1
3
3 2 1
5
1 5 4 3 2
4
4 3 2 1
Output
-1
3
1 2 1
4
2 2 3 2
3
1 3 1
Note

For the first example, it can be shown that no sequence of operations can sort the permutation.

For the second example, one valid sequence of operations is $$$ [3, 2, 1] \xrightarrow{i_1=1} [3, 1, 2] \xrightarrow{i_2=2} [1, 3, 2] \xrightarrow{i_3=1} [1, 2, 3]. $$$

For the third example, one valid sequence of operations is $$$ [1, 5, 4, 3, 2] \xrightarrow{i_1=2} [5, 1, 3, 2, 4] \xrightarrow{i_2=2} [1, 5, 2, 4, 3] \xrightarrow{i_3=3} [2, 1, 5, 3, 4] \xrightarrow{i_4=2} [1, 2, 3, 4, 5] $$$

For the fourth example, one valid sequence of operations is $$$ [4, 3, 2, 1] \xrightarrow{i_1=1} [4, 2, 1, 3] \xrightarrow{i_2=3} [1, 4, 2 ,3] \xrightarrow{i_3=1} [1, 2, 3, 4] $$$