C. Bottom-Tier Reversalstime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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.OutputFor 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.ExampleInput
3
3
1 2 3
5
3 4 5 2 1
3
2 1 3
Output
4
3 3 3 3
2
3 5
-1
NoteIn 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.
3
3
1 2 3
5
3 4 5 2 1
3
2 1 3

4 3 3 3 3 2 3 5 -1 
['constructive algorithms', 'greedy', '*2000']