Bottom-Tier Reversals

2000ms

524288K

Description:

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.

Input:

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 $$$2021$$$.

Output:

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.

Sample Input:

Sample Output:

Note:

In the first test case, the permutation is already sorted. Any even number of reversals of the length $$$3$$$ prefix doesn't change that fact.

In the second test case, after reversing the prefix of length $$$3$$$ the permutation will change to $$$[5, 4, 3, 2, 1]$$$, and then after reversing the prefix of length $$$5$$$ the permutation will change to $$$[1, 2, 3, 4, 5]$$$.

In the third test case, it's impossible to sort the permutation.

Informação

Provedor Codeforces

Código CF1558C