Problem: You are given an array a consisting of n integers.

In one move, you can choose some index i (1 ≤ i ≤ n - 2) and shift the segment [a_i, a_{i + 1}, a_{i + 2}] cyclically to the right (i.e. replace the segment [a_i, a_{i + 1}, a_{i + 2}] with [a_{i + 2}, a_i, a_{i + 1}]). 

Your task is to sort the initial array by no more than n^2 such operations or say that it is impossible to do that.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 500) — the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 500), where a_i is the i-th element a.

It is guaranteed that the sum of n does not exceed 500.

Output

For each test case, print the answer: -1 on the only line if it is impossible to sort the given array using operations described in the problem statement, or the number of operations ans on the first line and ans integers idx_1, idx_2, ..., idx_{ans} (1 ≤ idx_i ≤ n - 2), where idx_i is the index of left border of the segment for the i-th operation. You should print indices in order of performing operations.

Example

Input


5
5
1 2 3 4 5
5
5 4 3 2 1
8
8 4 5 2 3 6 7 3
7
5 2 1 6 4 7 3
6
1 2 3 3 6 4


Output


0

6
3 1 3 2 2 3 
13
2 1 1 6 4 2 4 3 3 4 4 6 6 
-1
4
3 3 4 4 

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class F {
    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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }
    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
        int t = ri();
//        int t=1;
        while (t-- > 0)
        {
            int n=ri();
            int[] arr=rai(n);
            List<Integer> list=new ArrayList<>();
            for(int i:arr)
            {
                list.add(i);
            }
            List<Integer> res=new ArrayList<>();
            HashSet<Integer> set=new HashSet<>();
            for(int i=0;i<n-2;i++)
            {
                int min=Integer.MAX_VALUE;
                int ind=-1;
                for(int j=i;j<n;j++)
                {
                    if(list.get(j)<min && !set.contains(list.get(j)))
                    {
                        min=list.get(j);
                        ind=j;

                    }
                }
//                System.out.println(i+" "+ind);
                if(ind==-1)
                {
                    continue;
                }

                set.add(list.get(ind));

                if(ind!=i)
                {
                    while(ind-i>2)
                    {
                        int val=list.remove(ind);
                        ind-=2;
                        list.add(ind,val);
                        res.add(ind);

                    }
                    if(ind-i==1)
                    {
                        int j=i+2;
                        for(int x=0;x<2;x++)
                        {
                            res.add(i);
                            int val=list.remove(j);
                            list.add(i,val);

                        }
                    }
                    else if(ind-i==2)
                    {
                        int j=i+2;
                        for(int x=0;x<1;x++)
                        {
                            res.add(i);
                            int val=list.remove(j);
                            list.add(i,val);

                        }
                    }

                }
//                System.out.println(list);

            }
//            System.out.println(res.size());


                int last=-1;
                for(int i=0;i<n-1;i++)
                {
                    if(list.get(i)>list.get(i+1))
                    {

                        last=i;
                        break;
                    }
                }
                if(last==-1)
                {
                    ans.append(res.size()).append("\n");
                    for (int i : res) {
                        ans.append(i + 1).append(" ");
                    }
                    ans.append("\n");
                }
                else
                {
                    int flag=0;
                    int lastVal=list.get(last);
                    for(int i=last+1;i<list.size();i++)
                    {
                        if(list.get(i)>=lastVal)
                        {
                            lastVal=list.get(i);
                            continue;
                        }
                        if(!set.contains(list.get(i)))
                        {
                            flag=1;
                            break;
                        }
                        else
                        {
                            int j=i;
                            while(j>1)
                            {
                                int val=list.remove(j);
                                j-=2;
                                res.add(j);
                                list.add(j,val);
                                if(j>0)
                                {
                                    if(list.get(j+1)==val || list.get(j-1)==val)
                                    {
                                        break;
                                    }
                                }
                                else
                                {
                                    if(list.get(j+1)==val)
                                    {
                                        break;
                                    }
                                }
                            }


                        }
                    }
                    if(flag==1)
                    {
                        ans.append("-1\n");
                    }
                    else {
                        ans.append(res.size()).append("\n");
                        for (int i: res) {
                            ans.append(i + 1).append(" ");
                        }
                        ans.append("\n");
                    }
                }

        }
        out.print(ans.toString());
        out.flush();

    }
}