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
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(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, inputClass sc, PrintWriter out) {
            int t = sc.nextInt();
            while (t > 0) {
                t--;
                int n = sc.nextInt();
                int k = sc.nextInt();
                int[] tab = new int[n];
                for (int i = 0; i < n; i++) {
                    tab[i] = sc.nextInt();
                }
                int[] ans = new int[2 * k + 2];
                int[] occ = new int[2 * k + 2];
                for (int i = 0; i < n / 2; i++) {
                    int s = tab[i] + tab[n - i - 1];
                    occ[s]++;
                    int mn = Math.min(tab[i], tab[n - i - 1]);
                    int mx = Math.max(tab[i], tab[n - i - 1]);
                    ans[mn + 1]++;
                    ans[mx + k + 1]--;
                }
                for (int i = 1; i < 2 * k + 2; i++) {
                    ans[i] += ans[i - 1];
                }
                for (int i = 0; i < n / 2; i++) {
                    int s = tab[i] + tab[n - i - 1];
                    ans[s]--;
                }
                int best = Integer.MAX_VALUE;
                for (int i = 0; i < 2 * k + 2; i++) {
                    best = Math.min(best, ans[i] + 2 * (n / 2 - occ[i] - ans[i]));
                }
                out.println(best);
            }
        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}