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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class CyclicShiftsSorting {
    static FastScanner fs = new FastScanner();

    public static void main(String[] args) {
        int t = fs.nextInt();
        while(t-- > 0) {
            int n = fs.nextInt();
            Elem[] elements = new Elem[n], sorted = new Elem[n];
            for (int i = 0; i < n; i++) elements[i] = sorted[i] = new Elem(fs.nextInt());

            Arrays.sort(sorted);
            for (int i = 0; i < n; i++) sorted[i].value = i;

            int invs = 0;
            for (int i = 0; i < n; i++) {
                for (int j = i+1; j < n; j++) {
                    if (elements[i].value > elements[j].value) invs++;
                }
            }

            if ((invs & 1) != 0) {
                // swapping a duplicate's mapping to make invs even
                for (int i = 0; i < n-1; i++) {
                    if (sorted[i].original == sorted[i + 1].original) {
                        // Swap mappings to duplicate originals
                        int temp = sorted[i].value;
                        sorted[i].value = sorted[i+1].value;
                        sorted[i+1].value = temp;
                        invs++;
                        break;
                    }
                }
            }

            if ((invs & 1) != 0) {
                System.out.println("-1");
                continue;
            }

            ArrayList<Integer> result = new ArrayList<>();
            for (int i = 0; i < n-2; i++) {
                for (int j = i+1; j < n; j++) {
                    if (elements[j].value == i) {

                        // i is not at its position yet
                        while (elements[i].value != i) {
                            if (j - i >= 2) {
                                cyclicRightShift(elements, j-2, j, 1);
                                result.add(j-2);
                                j -= 2;
                            } else if (j - i == 1) {
                                cyclicRightShift(elements, j-1, j+1, 2);
                                result.add(j-1);
                                result.add(j-1);
                                j -= 1;
                            }
                        }

                        break;
                    }
                }
            }

            System.out.println(result.size());
            result.forEach(integer -> System.out.print(integer + 1 + " "));
            System.out.print(t > 0 ? "\n" : "");
        }
    }

    static void cyclicRightShift(Elem[] arr, int low, int high, int times) {
        while (times-- > 0) {
            swap(arr, low, high);
            swap(arr, high, high-1);
        }
    }

    static void swap(Elem []arr, int i, int j) {
        Elem temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    static class Elem implements Comparable<Elem> {
        int original, value;

        Elem (int original) {
            this.original = original;
        }

        @Override
        public int compareTo(Elem o) {
            return Integer.compare(original, o.original);
        }
    }

    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");

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

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

        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}