A13410 | Constant Palindrome Sum

You are given an array $a$ consisting of $n$ integers (it is guaranteed that $n$ is even, i.e. divisible by $2$ ). All $a_i$ does not exceed some integer $k$ .

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index $i$ from $1$ to $n$ and replace $a_i$ with some integer in range $[1; k]$ ) to satisfy the following conditions:

- after all replacements, all $a_i$ are positive integers not greater than $k$ ;
- for all $i$ from $1$ to $\frac{n}{2}$ the following equation is true: $a_i + a_{n - i + 1} = x$ , where $x$ should be the same for all $\frac{n}{2}$ pairs of elements.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains two integers $n$ and $k$ ( $2 \le n \le 2 \cdot 10^5, 1 \le k \le 2 \cdot 10^5$ ) — the length of $a$ and the maximum possible value of some $a_i$ correspondingly. It is guratanteed that $n$ is even (i.e. divisible by $2$ ). The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le k$ ), where $a_i$ is the $i$ -th element of $a$ .

It is guaranteed that the sum of $n$ (as well as the sum of $k$ ) over all test cases does not exceed $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ , $\sum k \le 2 \cdot 10^5$ ).

For each test case, print the answer — the minimum number of elements you have to replace in $a$ to satisfy the conditions from the problem statement.