Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

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]));
		}
	}
}