Problem Statement

You are given a sequence $p$ obtained by rearranging $(1,2, \cdots , N)$. Initially, the $i$-th term of $p$ is $p_i$.

Your goal is to sort $p$ in ascending order by performing at most $N^2$ operations. You may perform no operations at all. With an operation, you can change $p$ as follows.

• Declare an integer $i$ ( $1 \leq i \leq N-1$ ) such that the $i$-th term of $p$ is not $i$ and the $i+1$-th term of $p$ is not $i+1$, and swap the $i$-th term of $p$ and the $i+1$-th term of $p$.

Determine whether you can achieve your goal, and if it is possible, show one sequence of operations that achieves it.
You are given $T$ test cases, so find the answer for each of them.

Input

$T$

$N$
$p_1\ \ p_2\ \ \cdots \ \ p_N$

• $1 \leq T \leq 250$
• $2 \leq N \leq 500$
• $1 \leq p_i \leq N$ ( $1 \leq i \leq N$ )
• All inputs are integers.
• $p$ is obtained by rearranging $(1,2, \cdots , N)$.
• In $1$ input file, the sum of $N$ does not exceed $500$.

Output

If you cannot achieve your goal, output -1 followed by a newline.

If you can achieve your goal, output as follows, followed by a newline.

$Q$
$a_1\ \ a_2\ \ \cdots \ \ a_Q$

Do this for all $T$ test cases.

Sample

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

2
3 1
-1
0

1
1