Given a permutation(^{\text{∗}}) (p) of length (n), you may perform the following operation on it any number of times (possibly zero): Choose an index (i) where (1 \leq i \leq n-1), and move (p_i) to (p_1) (shifting everything in between to the right) and (p_{i+1}) to (p_n) (shifting everything in between to the left). Formally, you may transform (p = p_1, \ldots, p_n) into (p' = p_i, p_1, p_2, \ldots, p_{i-1}, p_{i+2}, p_{i+3}, \ldots, p_n, p_{i+1}.) Provide a valid sequence of operations of length at most (4n) to make (p_i = i) for all (i\,(1 \le i \le n)), or print (-1) if no sequence exists. It can be shown that if a valid sequence of operations exists, there is a valid sequence of length at most (4n) operations. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^3)). The description of the test cases follows. The first line contains an integer (n\,(2 \leq n \leq 5000)) — the length of the permutation. The second line contains (n) integers (p_1, p_2, \ldots, p_n \, (1 \le p_i \le n)). It is guaranteed that (p) is a permutation. It is guaranteed that the sum of (n) over all test cases does not exceed (5000). If there does not exist a valid sequence of operations, output (-1). Otherwise, on the first line, output (x\,(0 \leq x \leq 4n)), the number of operations needed to sort the permutation. On the second line, output (x) integers (i_1, \ldots, i_x) where (i_j) ((1 \leq i_j \leq n-1)) denotes the index corresponding t