Problem: You are given an array a consisting of n integers.

In one move, you can choose some index i (1 ≤ i ≤ n - 2) and shift the segment [a_i, a_{i + 1}, a_{i + 2}] cyclically to the right (i.e. replace the segment [a_i, a_{i + 1}, a_{i + 2}] with [a_{i + 2}, a_i, a_{i + 1}]). 

Your task is to sort the initial array by no more than n^2 such operations or say that it is impossible to do that.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (3 ≤ n ≤ 500) — the length of a. The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 500), where a_i is the i-th element a.

It is guaranteed that the sum of n does not exceed 500.

Output

For each test case, print the answer: -1 on the only line if it is impossible to sort the given array using operations described in the problem statement, or the number of operations ans on the first line and ans integers idx_1, idx_2, ..., idx_{ans} (1 ≤ idx_i ≤ n - 2), where idx_i is the index of left border of the segment for the i-th operation. You should print indices in order of performing operations.

Example

Input


5
5
1 2 3 4 5
5
5 4 3 2 1
8
8 4 5 2 3 6 7 3
7
5 2 1 6 4 7 3
6
1 2 3 3 6 4


Output


0

6
3 1 3 2 2 3 
13
2 1 1 6 4 2 4 3 3 4 4 6 6 
-1
4
3 3 4 4 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.stream.Collectors;

public final class Constructive {

    private static final FastReader fr = new FastReader();

    public static void main(String[] args) {
        int t = fr.nextInt();
        while (t-- > 0) {
            int[] input = readArray();
            int[] steps = new CyclicShiftsSorting(input).solve();

            if (steps == null) System.out.println(-1);
            else {
                System.out.println(steps.length);
                for (int step : steps) {
                    System.out.print((step + 1) + " ");
                }
                System.out.println();
            }
        }
    }

    private static final class CyclicShiftsSorting {
        private final int[] input;
        private final List<Integer> current;

        public CyclicShiftsSorting(final int[] input) {
            this.input = input;
            current = Arrays.stream(input).boxed().collect(Collectors.toList());
        }

        public int[] solve() {
            Queue<Integer> steps = new ArrayDeque<>();

            while (current.size() > 2) {
                int i = current.indexOf(Collections.min(current));
                while (i > 0) {
                    if (i - 2 >= 0) {
                        cycle(i - 2);
                        steps.add(actualIndex(i - 2));
                        i -= 2;
                    } else {
                        cycle(0);
                        steps.add(actualIndex(0));
                        i += 1;
                    }
                }
                current.remove(0);
            }

            if (isSorted()) return steps.stream().mapToInt((i) -> i).toArray();
            else {
                current.addAll(0, Arrays.stream(input).sorted().limit(input.length - 2).boxed().collect(Collectors.toList()));
                for (int i = current.size() - 1; i >= 2; i--) {
                    cycle(i - 2);
                    steps.add(i - 2);
                    if (isSorted()) break;
                }
                if (isSorted()) return steps.stream().mapToInt((i) -> i).toArray();
                else return null;
            }
        }

        private int actualIndex(int i) {
            return input.length - current.size() + i;
        }

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

        private void cycle(int i) {
            Collections.swap(current, i + 1, i + 2);
            Collections.swap(current, i, i + 1);
        }

    }

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

    private static final 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());
        }
    }

}