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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.*;

public class D {

    void solve() throws Exception {
        int n = ni();
        int k = ni();
        int[] a = nia(n);
        Map<Integer, Integer> counts = new HashMap<>();
        int[] mins = new int[n / 2];
        int[] maxs = new int[n / 2];
        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < n / 2; i++) {
            mins[i] = Math.min(a[i], a[n - 1 - i]);
            maxs[i] = Math.max(a[i], a[n - 1 - i]);
            if (!counts.containsKey(a[i] + a[n - 1 - i])) {
                counts.put(a[i] + a[n - 1 - i], 0);
            }
            counts.put(a[i] + a[n - 1 - i], counts.get(a[i] + a[n - 1 - i]) + 1);
        }

        Arrays.sort(mins);
        int j = 0;
        for (int i = 2; i <= k + 1; i++) {
            while (j < n / 2 && mins[j] < i) {
                j++;
            }
            ans = Math.min(ans, j - counts.getOrDefault(i, 0) + 2 * (n / 2 - j));
        }

        Arrays.sort(maxs);
        j = 0;
        for (int i = 2; i <= k; i++) {
            while (j < n / 2 && maxs[j] < i) {
                j++;
            }
            ans = Math.min(ans, n / 2 - j - counts.getOrDefault(k + i, 0) + 2 * j);
        }

        out.println(ans);
    }

    void run() throws Exception {
        initIO();
        int t = ni();
        while (t-- > 0) {
            solve();
            out.flush();
        }
    }

    public static void main(String[] args) throws Exception {
        new D().run();
    }

    /**
     * IO.
     */

    PrintWriter out;
    BufferedReader br;
    StringTokenizer tokenizer;

    void initIO() {
        out = new PrintWriter(System.out);
        br = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = null;
    }

    int ni() throws Exception {
        return Integer.parseInt(ns());
    }

    long nl() throws Exception {
        return Long.parseLong(ns());
    }

    double nd() throws Exception {
        return Double.parseDouble(ns());
    }

    int[] nia(int n) throws Exception {
        int[] x = new int[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = ni();
        }
        return x;
    }

    long[] nla(int n) throws Exception {
        long[] x = new long[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nl();
        }
        return x;
    }

    double[] nda(int n) throws Exception {
        double[] x = new double[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nd();
        }
        return x;
    }

    String ns() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(br.readLine());
        return tokenizer.nextToken();
    }

    String nline() throws Exception {
        tokenizer = null;
        return br.readLine();
    }
}