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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mostafa
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DConstantPalindromeSum solver = new DConstantPalindromeSum();
        solver.solve(1, in, out);
        out.close();
    }

    static class DConstantPalindromeSum {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int tc = in.nextInt();
            while (tc-- > 0) {
                int n = in.nextInt();
                int k = in.nextInt();
                int[] a = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = in.nextInt();
                }
                int N = 2 * k + 2;
                int[] cnt = new int[N];
                int[] pref = new int[N];
                for (int i = 0; i < n / 2; i++) {
                    cnt[a[i] + a[n - i - 1]]++;
                }
                for (int i = 0; i < n / 2; i++) {
                    int from = Integer.min(a[i], a[n - i - 1]) + 1;
                    int to = Integer.max(a[i], a[n - i - 1]) + k;
                    pref[from]++;
                    pref[to + 1]--;
                }
                for (int i = 1; i < N; i++) {
                    pref[i] += pref[i - 1];
                }
                int ans = Integer.MAX_VALUE;
                for (int i = 2; i < N; i++) {
                    int sum = (pref[i] - cnt[i]) + (n / 2 - pref[i]) * 2;
                    ans = Integer.min(ans, sum);
                }
                out.println(ans);
            }
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }
}