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.util.*;
import java.io.*;
public class D636
{
    public static void main(String [] args)
    {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = sc.nextInt();
        while (t > 0) {
            int n = sc.nextInt(); int k = sc.nextInt(); int []a = new int[n];
            for (int i = 0; i < n; i++) a[i] = sc.nextInt();
            int [] max = new int [n/2]; int [] min = new int [n/2]; int [] sum = new int [n/2];
            Map<Integer, Integer> sums = new HashMap<>();
            FenwickTree bitMax = new FenwickTree(2*k+5);
            FenwickTree bitMin = new FenwickTree(2*k+5);
            for (int i = 0; i < n/2; i++) {
                max[i] = Math.max(a[i], a[n-1-i]);
                min[i] = Math.min(a[i], a[n-1-i]);
                sum[i] = a[i] + a[n-1-i];
                bitMax.update(max[i], 1);
                bitMin.update(min[i], 1);
                sums.put(sum[i], sums.getOrDefault(sum[i], 0) + 1);
            }
            long ans = Integer.MAX_VALUE;
            for (int i = 2; i <= 2 * k; i++) {
                int qry1 = bitMax.rangeSum(0, Math.max(i - k - 1, 0));
                int qry2 = bitMin.rangeSum(i, 2 * k + 4);
                ans = Math.min(ans, (n + 2 * (qry1 + qry2) - 2 * sums.getOrDefault(i, 0)) / 2);
            }
            out.println(ans);
            t--;
        }
        out.close();
    }

    static class FenwickTree
    {
        int size;
        int [] table;

        FenwickTree(int size)
        {
            table = new int [size];
            this.size = size;
        }

        void init(int [] nums)
        {
            for (int i = 1; i < nums.length; i++)
            {
                update(i, nums[i]);
            }
        }

        void update(int i, int delta)
        {
            while (i < size)
            {
                table[i] += delta;
                i += Integer.lowestOneBit(i);
            }
        }

        int sum(int i)
        {
            int sum = 0;
            while (i > 0)
            {
                sum += table[i];
                i -= Integer.lowestOneBit(i);
            }
            return sum;
        }

        int rangeSum(int i, int j)
        {
            return sum(j) - sum(i - 1);
        }
    }




    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }



    }

}