Constant Palindrome Sum

1000ms

262144K

Description:

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.

Input:

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 $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$, $$$\sum k \le 2 \cdot 10^5$$$).

Output:

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.

Sample Input:

4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4

Sample Output:

Informação

Provedor Codeforces

Código CF1343D