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.*;
import java.math.*;

 
public class Main
{
   // static LinkedList<Integer> adj[];
    /*static void BFS(int s,boolean visited[]){
        visited[s]=true;
        Queue<Integer> queue=new LinkedList<>();
        while(queue.size()!=0){
            int n=queue.poll();
            visited[n]=true;
            Iterator<Integer> itr=adj[n].listIterator();
            while(itr.hasNext()){
                int q=itr.next();
                if(!visited[q]){
                    queue.add(q);
                }
            }
        }
    }*/
    /*static void DFS(int s,boolean visited[]){
        visited[s]=true;
        Iterator<Integer> itr=adj[s].listIterator();
        while(itr.hasNext()){
            int n=itr.next();
            if(visited[n]!=true){
                DFS(n,visited);
            }
        }
    }*/
    static class comparator implements Comparator<Map.Entry<Integer,Integer>> {
    public int compare(Map.Entry<Integer,Integer> e1, Map.Entry<Integer,Integer> e2) {
        if (e1.getValue() < e2.getValue()){
            return 1;
        } else if (e1.getValue() == e2.getValue()) {
            return 0;
        } else {
            return -1;
        }
    }
}
public static <K, V extends Comparable<V>> Map<K, V> 
    sortByValues(final Map<K, V> map) {
    Comparator<K> valueComparator = 
             new Comparator<K>() {
      public int compare(K k1, K k2) {
        int compare = 
              map.get(k1).compareTo(map.get(k2));
        if (compare == 0) 
          return 1;
        else 
          return compare;
      }
    };
 
    Map<K, V> sortedByValues = 
      new TreeMap<K, V>(valueComparator);
    sortedByValues.putAll(map);
    return sortedByValues;
  }
    public static void main(String[] args)
    {
        FastReader s=new FastReader();
		 int t=s.nextInt();
	   for(int f=0;f<t;f++)
        {
            int n=s.nextInt();
            int k=s.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++){
                a[i]=s.nextInt();
            }
           int count[]=new int[2*k+10];
           int b[]=new int[2*k+10];
           for(int i=0;i<n/2;i++){
               int l=a[i];int r=a[n-1-i];
               count[l+r]++;
               int min=Math.min(l,r)+1;
               int max=Math.max(l,r)+k;
               b[min]++;b[max+1]--;
           }
           for(int i=1;i<=2*k;i++){
               b[i]=b[i-1]+b[i];
           }
           int ans=n;
           for(int i=2;i<=2*k;i++){
               int c=count[i];
               int one=b[i];
               int changeOne=one-c;
               int two=n/2-one;two=2*two;
               int temp=changeOne+two;
               ans=Math.min(ans,temp);
           }
           System.out.println(ans);
        }
		
		
    }
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
 
   
}