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.*;
import java.util.*;

public class Solution { 

    public static void main(String[] args) throws IOException {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
        int t=Integer.parseInt(br.readLine());
        //String s[]=br.readLine().split(" ");
        while(t-->0){
            String s[]=br.readLine().split(" ");
            int n=Integer.parseInt(s[0]);
            int k=Integer.parseInt(s[1]);
            int arr[]=new int[n];
            String s1[]=br.readLine().split(" ");
            for(int i=0;i<n;i++){
                arr[i]=Integer.parseInt(s1[i]);
            }
           HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>();
            for(int i=0;i<n/2;i++){
                int temp=arr[i]+arr[n-i-1];
                if(hm.containsKey(temp)){
                    hm.put(temp,hm.get(temp)+1);
                }
                else hm.put(temp,1);
            }
            int pre[]=new int[2*k+2];
            for(int i=0;i<n/2;i++){
                int min=Math.min(arr[i],arr[n-i-1])+1;
                int max=Math.max(arr[i],arr[n-i-1])+k;
                pre[min]++;
                pre[max+1]--;
            }
            for(int i=3;i<2*k+1;i++){
                pre[i]=pre[i-1]+pre[i];
            }
            int ans=Integer.MAX_VALUE;
            
          for(int i=2;i<2*k+1;i++){
              int temp=0;
              if(hm.containsKey(i)) temp=hm.get(i);
                int c1=pre[i]-temp;
              
                int c2=n/2-c1-temp;
              
                ans=Math.min(c1+(c2*2),ans);
            }
            bw.write(ans+"\n");
        }
        bw.flush();
    }
}