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.*;

public class Solution {
    public void solve() {
        real();
    }

    private void real() {
        for (int t = reader.nextInt(); t > 0; t--) {
            int n = reader.nextInt();
            int k = reader.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = reader.nextInt();
            writer.println(find(n, k, a));
        }
    }

    private void test() {
        Random random = new Random();

        for (int run = 0; run <= 10000; run++) {
            int n = 8;
            int k = random.nextInt(20) + 1;
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = random.nextInt(k) + 1;
            int ans = findBrute(n, k, a);
            int out = find(n, k, a);
            if (ans != out) {
                writer.println("WA");
                writer.println(n + " " + k);
                for (int i = 0; i < n; i++) writer.print(a[i] + " ");
                writer.println();
            }
        }

        writer.println("AC");
    }

    private int[] cntEqual;
    private int[] cntMin;
    private int[] cntMax;

    private int find(int n, int k, int[] arr) {
        cntEqual = new int[2 * k + 1];
        cntMin = new int[k + 1];
        cntMax = new int[k + 1];

        for (int i = 0; i < n / 2; i++) {
            int a = arr[i];
            int b = arr[n - 1 - i];
            int s = a + b;
            cntEqual[s]++;
            cntMin[Math.min(a, b)]++;
            cntMax[Math.max(a, b)]++;
        }

        for (int x = k - 1; x >= 0; x--) cntMin[x] += cntMin[x + 1];
        for (int x = 1; x <= k; x++) cntMax[x] += cntMax[x - 1];

        int res = n;

        for (int x = 2; x <= 2 * k; x++) {
            int cnt = changes(n, k, arr, x);
            res = Math.min(res, cnt);
        }

        return res;
    }

    private int changes(int n, int k, int[] arr, int x) {
        int equal = cntEqual[x];

        int both = x <= k ? cntMin[x] : 0;
        both += (x - k - 1 >= 1) ? cntMax[x - k - 1] : 0;

        int one = n / 2 - equal - both;
        return one + both * 2;
    }

    private int findBrute(int n, int k, int[] arr) {
        int res = n;

        for (int x = 2; x <= 2 * k; x++) {
            int cnt = brute(n, k, arr, x);
            res = Math.min(res, cnt);
        }

        return res;
    }

    private int brute(int n, int k, int[] arr, int x) {
        int equal = 0;
        int both = 0;
        for (int i = 0; i < n / 2; i++) {
            int a = arr[i];
            int b = arr[n - 1 - i];
            if (a + b == x) equal++;
            if (Math.min(a, b) >= x || Math.max(a, b) <= x - k - 1) both++;
        }
        int one = n / 2 - equal - both;
        return one + both * 2;
    }

    private InputReader reader;
    private PrintWriter writer;

    public Solution(InputReader reader, PrintWriter writer) {
        this.reader = reader;
        this.writer = writer;
    }

    public static void main(String[] args) {
        InputReader reader = new InputReader(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        Solution solution = new Solution(reader, writer);
        solution.solve();

        writer.flush();
    }

    static class InputReader {
        private static final int BUFFER_SIZE = 1 << 20;

        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), BUFFER_SIZE);
            tokenizer = null;
        }

        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }
    }
}