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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;


/* Name of the class has to be "Main" only if the class is public. */
public class p4
{
         static class Input {
        private StringTokenizer tokenizer = null;
        private BufferedReader reader;
 
        public Input(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }
 
        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(nextLine());
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public int[] nextIntArray(int n, int add) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt() + add;
            }
            return result;
        }
 
        public long[] nextLongArray(int n, long add) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong() + add;
            }
            return result;
        }
 
        public int[] nextIntArray(int n) {
            return nextIntArray(n, 0);
        }
 
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		Input s=new Input(System.in);
		int t=s.nextInt();
		PrintWriter out=new PrintWriter(System.out);
        
        ArrayList<Integer> arr=new ArrayList<>();
        

		while(t-->0)
		{
            int n=s.nextInt();
            int k=s.nextInt();
            int a[]=s.nextIntArray(n);
            HashMap<Integer,Integer> hs=new HashMap<>();
            int rl=2,rr=2*k;
            int pref[]=new int[2*k+2];
            for(int i=0;i<n/2;i++)
            {
               int sum=a[i]+a[n-1-i];
               hs.put(sum,hs.getOrDefault(sum,0)+1);
               int trl=Math.min(a[i],a[n-1-i])+1;
               int trr=Math.max(a[i],a[n-1-i])+k;
               pref[trl]++;
               pref[trr+1]--;
            }
            //System.out.println("rl "+rl+"rr "+rr);
            int cnt=0,ans=n/2;
            for(int i=2;i<=2*k;i++)
            {
                cnt+=pref[i];
                ans=Math.min(cnt-hs.getOrDefault(i,0)+(n/2-cnt)*2,ans);
                //System.out.println(" "+i+" "+cnt+" "+ans);
            }

            System.out.println(ans);

		}
	}
}