Problem: 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 n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all 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 ≤ t ≤ 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 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 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, ..., a_n (1 ≤ a_i ≤ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 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.

Example

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


Output


0
1
4
2

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class D {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++) {
            String[] str = br.readLine().split(" ");
            int key = Integer.parseInt(str[1]);
            String[] data = br.readLine().split(" ");
            int[] arr = new int[data.length];
            for (int j = 0; j < arr.length; j++)
                arr[j] = Integer.parseInt(data[j]);

            int[] change = new int[key * 2 + 1];
            change[2] = arr.length;
            for (int j = 0; j < arr.length / 2; j++) {
                int sum = arr[j] + arr[arr.length - j - 1];
                change[Math.min(arr[j], arr[arr.length - j - 1]) + 1]--;
                change[sum]--;
                if (sum != 2 * key)
                    change[sum + 1]++;

                int maxNum = Math.max(arr[j], arr[arr.length - j - 1]);
                if (maxNum < key)
                    change[maxNum + key + 1]++;
                //System.out.println(Arrays.toString(change));
            }

            int moves = change[2];
            int minMoves = moves;
            for (int j = 3; j < change.length; j++) {
                moves += change[j];
                if (moves < minMoves)
                    minMoves = moves;
            }

            System.out.println(minMoves);
        }
    }

}