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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class F {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Solution sol = new Solution();
		int t = in.ni();
		for (int i = 0; i < t; ++i)
			sol.solve(in, out);
		out.close();
	}

	private static final boolean debug = false;

	private static class Solution {
		private void solve(InputReader in, PrintWriter out) {
			int n = in.ni();
			Element[] elements = new Element[n], sorted = new Element[n];
			for (int i = 0; i < n; ++i)
				elements[i] = sorted[i] = new Element(in.ni());
			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 (debug)
				System.out.println("Initial inverstions: " + invs);
			if (invs % 2 == 1) {
				outer: for (int first = 0; first < n; ++first) {
					for (int second = first + 1; second < n; ++second) {
						if (elements[first].orig != elements[second].orig)
							continue;
						int changed = 0;
						for (int i = first; i < second; ++i)
							if (elements[i].value >= elements[first].value
									&& elements[i].value < elements[second].value)
								++changed;
						if (changed % 2 == 1) {
							++invs;
							int temp = elements[first].value;
							elements[first].value = elements[second].value;
							elements[second].value = temp;
							break outer;
						}
					}
				}
			}
			Arrays.sort(sorted);
			if (debug)
				System.out.println("Perm:");
			for (Element e : elements)
				if (debug)
					System.out.print(e.value + " ");
			if (debug)
				System.out.println();

			if (invs % 2 != 0) {
				out.println(-1);
				return;
			}
			List<Integer> indecies = new ArrayList<>();
			for (int toFixInd = n - 1; toFixInd >= 0; --toFixInd) {
				Element toFix = sorted[toFixInd];
				int index = 0;
				for (int i = 0; i < n; ++i)
					if (elements[i] == toFix)
						index = i;
				if (debug)
					System.out.println("Trying to fix thing at index " + index);
				while (index < toFixInd - 1) {
					swap(elements, index, indecies);
					++index;
				}
				if (index == toFixInd - 1) {
					swap(elements, toFixInd - 2, indecies);
					++index;
				}
			}
			out.println(indecies.size());
			for (int i : indecies) {
				out.print(i + 1 + " ");
			}
			out.println();
		}

		private void swap(Element[] elements, int index, List<Integer> indecies) {
			if (debug) System.out.println("Swapping from index "+index);
			indecies.add(index);
			Element e1 = elements[index], e2 = elements[index + 1], e3 = elements[index + 2];
			elements[index] = e3;
			elements[index + 1] = e1;
			elements[index + 2] = e2;
		}
	}

	private static class Element implements Comparable<Element> {
		int value, orig;

		public Element(int orig) {
			this.value = this.orig = orig;
		}

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

	private static class InputReader {
		private BufferedReader reader;
		private StringTokenizer tokenizer;

		private InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		private String n() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		private int ni() {
			return Integer.parseInt(n());
		}

		private long nl() {
			return Long.parseLong(n());
		}

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

}