Score : $500$ points

Problem Statement

Given is a sequence $p$ which is a permutation of $(1,2, \ldots, N)$. Initially, the $n$-th term of $p$ is $p_{n}$.

Your objective is to sort $p$ in ascending order in at most $N^2$ operations. In one operation, you make the following change on $p$:

• In the $1$-st, $3$-rd, and subsequent odd-numbered operations, you choose an odd number $n$ between $1$ and $N-1$ (inclusive) to swap $p_n$ and $p_{n+1}$.
• In the $2$-nd, $4$-th, and subsequent even-numbered operations, you choose an even number $n$ between $2$ and $N-1$ (inclusive) to swap $p_n$ and $p_{n+1}$.

We can prove that the objective is always achievable under the Constraints of this problem. Find one sequence of operations that achieves the objective.

You will be given $T$ test cases and asked to solve each of them.

Constraints

• All values in input are integers.
• $1 \leq T \leq 250$
• $2 \leq N \leq 500$
• $1 \leq p_i \leq N$
• $p$ is a permutation of $(1,2,\ldots,N)$.
• In one input file, the sum of $N$ does not exceed $500$.

Input

Input is given from Standard Input in the following format:

$T$

$\mathrm{case}_{1}$

$\vdots$

$\mathrm{case}_{T}$

Each case is in the following format:

$N$

$p_1$ $\cdots$ $p_N$

Output

For each of the $T$ test cases, in the order they are given, print your answer in the following format:

$M$

$a_1$ $\cdots$ $a_M$

Here, $M$ represents the length of your sequence of operations, and $a_i$ represents the integer you choose in the $i$-th operation.

Your output will be considered correct if, for every test case, your sequence of operations achieves the objective.

2
5
2 1 3 5 4
2
1 2

2
1 4
0

• Here is the description for the $1$-st test case.- Choosing $1$ in the $1$-st operation makes $p = (1,2,3,5,4)$.
  • Choosing $4$ in the $2$-nd operation makes $p = (1,2,3,4,5)$.
  • Note that although $(1,4)$ is a valid sequence of operations, $(4, 1)$ is not.
• Choosing $1$ in the $1$-st operation makes $p = (1,2,3,5,4)$.
• Choosing $4$ in the $2$-nd operation makes $p = (1,2,3,4,5)$.
• Note that although $(1,4)$ is a valid sequence of operations, $(4, 1)$ is not.
• Also note that it is allowed to perform no operation, and it is not required to minimize the number of operations.