A14370 | Bottom-Tier Reversals

You have a permutation: an array $a = [a_1, a_2, \ldots, a_n]$ of distinct integers from $1$ to $n$ . The length of the permutation $n$ is odd.

You need to sort the permutation in increasing order.

In one step, you can choose any prefix of the permutation with an odd length and reverse it. Formally, if $a = [a_1, a_2, \ldots, a_n]$ , you can choose any odd integer $p$ between $1$ and $n$ , inclusive, and set $a$ to $[a_p, a_{p-1}, \ldots, a_1, a_{p+1}, a_{p+2}, \ldots, a_n]$ .

Find a way to sort $a$ using no more than $\frac{5n}{2}$ reversals of the above kind, or determine that such a way doesn't exist. The number of reversals doesn't have to be minimized.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 100$ ). Description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $3 \le n \le 2021$ ; $n$ is odd) — the length of the permutation.

The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — the permutation itself.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2021$ .

For each test case, if it's impossible to sort the given permutation in at most $\frac{5n}{2}$ reversals, print a single integer $-1$ .

Otherwise, print an integer $m$ ( $0 \le m \le \frac{5n}{2}$ ), denoting the number of reversals in your sequence of steps, followed by $m$ integers $p_i$ ( $1 \le p_i \le n$ ; $p_i$ is odd), denoting the lengths of the prefixes of $a$ to be reversed, in chronological order.

Note that $m$ doesn't have to be minimized. If there are multiple answers, print any.