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.util.*;
import java.io.*;
import java.text.*;

public class F1374 {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int[] arr = sc.nextIntArr(n);
			Queue<Integer> q = new LinkedList<Integer>();

			for (int l = n - 1; l > 1; l--) {
				int max = arr[0];
				int idxmax = 0;
				for (int j = 0; j <= l; j++) {
					if (arr[j] >= max) {
						max = arr[j];
						idxmax = j;
					}
				}
				while (idxmax != l) {
					if (idxmax == l - 1) {
						int temp = arr[l];
						arr[l] = arr[l - 1];
						arr[l - 1] = arr[l - 2];
						arr[l - 2] = temp;
						q.add(l - 1);
					} else {
						int temp = arr[idxmax + 2];
						arr[idxmax + 2] = arr[idxmax + 1];
						arr[idxmax + 1] = arr[idxmax];
						arr[idxmax] = temp;
						q.add(idxmax + 1);
					}
					idxmax++;
				}
			}

			if (arr[2] >= arr[1] && arr[1] >= arr[0]) {
				pw.println(q.size());
				while (!q.isEmpty()) {
					pw.print(q.poll() + " ");
				}
				pw.println();
			} else if (arr[2] == arr[0]) {
				q.add(1);
				q.add(1);
				pw.println(q.size());
				while (!q.isEmpty()) {
					pw.print(q.poll() + " ");
				}
				pw.println();
			} else if (n > 3) {
				int v = -1;
				for (int i = 0; i < n - 1; i++) {
					if (arr[i] == arr[i + 1]) {
						v = i;
						break;
					}
				}
				if (v == -1) {
					pw.println(-1);
				} else {

					while (v != 0) {
						q.add(v);
						v--;
					}

					pw.println(q.size());
					while (!q.isEmpty()) {
						pw.print(q.poll() + " ");
					}
					pw.println();
				}
			} else {
				pw.println(-1);
			}
//			pw.println(Arrays.toString(arr));
		}
		pw.close();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

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

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}
}