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.File;
import java.io.IOException;
import java.util.Scanner;
 
public final class Main
{
	public static void main(String[] args) throws IOException
	{
		Scanner in = getScan(args);
 
		int t = in.nextInt();
		while (t-- > 0)
		{
			int n = in.nextInt();
			int k = in.nextInt();
			in.nextLine();
			String[] str = in.nextLine().split(" ");
 
			int[] nbVal = new int[2 * k + 1];
			int[] nb1 = new int[2 * k + 2];
			for (int i = 0; i < n - (n / 2); i++)
			{
				int a = Integer.parseInt(str[i]);
				int b = Integer.parseInt(str[n - 1 - i]);
				nbVal[a + b]++;
				nb1[Math.min(a, b) + 1]++;
				nb1[Math.max(a, b) + k + 1]--;
			}
			for (int i = 1; i < 2 * k + 1; i++)
			{
				nb1[i] += nb1[i - 1];
			}
 
			int best = n - 2;
			for (int i = 2; i < 2 * k + 1; i++)
			{
				int nb1toVal = nb1[i];
				int nbExactSum = nbVal[i];
				best = Math.min(best, n - nb1toVal - nbExactSum);
			}
			System.out.println(best);
		}
	}
 
	static Scanner getScan(String[] args) throws IOException
	{
		if (args.length == 0)
		{
			return new Scanner(System.in);
		}
		else
		{
			return new Scanner(new File(args[0]));
		}
	}
}