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 CyclicShiftsSorting {

    private static final FastReader fr = new FastReader();

    public static void main(String[] args) {
        new CyclicShiftsSorting().solve();
    }

    private void solve() {
        int t = fr.nextInt();
        while (t-- > 0) {
            solveCase();
        }
    }

    private void solveCase() {
        int[] input = readArray();
        solve(input);
    }

    private void solve(int[] input) {
        solve(Arrays.asList(Arrays.stream(input).boxed().toArray(Integer[]::new)));
    }

    private void solve(List<Integer> input) {
        List<Integer> l = new ArrayList<>(input);
        Queue<Integer> steps = new ArrayDeque<>();
        while (l.size() > 2) {
            int i = l.indexOf(Collections.min(l));
            while (i > 0) {
                if (i - 2 >= 0) {
                    cycle(l, i - 2);
                    steps.add((input.size() - l.size()) + i - 2);
                    i -= 2;
                } else {
                    cycle(l, i - 1);
                    steps.add((input.size() - l.size()) + i - 1);
                    i += 1;
                }
            }
            l.remove(0);
        }
        if (l.get(0) <= l.get(1)) done(steps);
        else {
            Collections.sort(input);
            l.addAll(0, input.subList(0, input.size() - 2));
            goBackward(l, steps);
        }
    }

    private void goBackward(List<Integer> l, Queue<Integer> steps) {
        for (int i = l.size() - 1; i >= 2; i--) {
            cycle(l, i - 2);
            steps.add(i - 2);
            if (isSorted(l)) break;
        }
        if (l.get(0) <= l.get(1))
            done(steps);
        else
            System.out.println(-1);
    }

    private boolean isSorted(List<Integer> l) {
        if (l.isEmpty()) return true;
        int prev = Integer.MIN_VALUE;
        for (int value : l) {
            if (value < prev) return false;
            prev = value;
        }
        return true;
    }

    private void done(Queue<Integer> steps) {
        System.out.println(steps.size());
        for (int step : steps) {
            System.out.print((step + 1) + " ");
        }
        System.out.println();
    }

    private void cycle(List<Integer> list, int i) {
        int t1 = list.get(i), t2 = list.get(i + 1);
        list.set(i, list.get(i + 2));
        list.set(i + 1, t1);
        list.set(i + 2, t2);
    }

    private int[] readArray() {
        int[] arr = new int[fr.nextInt()];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = fr.nextInt();
        }
        return arr;
    }

    private static class FastReader {
        private final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st;

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

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

}