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 com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class CN4 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            int k=scan.nextInt();
            int[] arr=new int[n];
            int[] f=new int[2*k+2];
            for(int i=0;i<n;i++){
                arr[i]=scan.nextInt();
            }
            for(int i=0;i<n/2;i++){
                int x=arr[i];
                int y=arr[n-1-i];
                int s=x+y;
                int l=Math.max(2,s-Math.max(x,y)+1);
                int r=Math.min(2*k,s+k-Math.min(x,y));
                f[l]-=1;
                f[r+1]+=1;
                if(l==2){
                    f[1]+=2;
                }else{
                    f[2]+=2;
                }
            }
            for(int i=1;i<=2*k;i++){
                f[i]+=f[i-1];
            }
            int ans=n/2;
            for(int i=0;i<n/2;i++){
                int s=arr[i]+arr[n-1-i];
                f[s]--;
                ans=Math.min(ans,f[s]);
            }
            out.println(ans);
        }
        out.flush();
        out.close();
    }
    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;
        }
    }

}