CF1558C 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.

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.