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:
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import java.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		
		while(t-- > 0)
		{
		    BalancedArray(sc.nextInt());
		}
	}
	
	static void BalancedArray(int n)
	{
	    if(n < 4 || (((n / 2) % 2) != 0))
	    {
	        System.out.println("NO");
	    } else
	    {
	        System.out.println("YES");
	        int evenSum, oddSum;
	        evenSum = oddSum = 0;
	        int half = n / 2;
	        for(int i = 2 ; half-- > 0 ; i += 2)
	        {
	            System.out.print(i + " ");
	            evenSum += i;
	        }
	        half = n/2;
	        for(int i = 1 ; half-- > 1 ; i += 2)
	        {
	            System.out.print(i + " ");
	            oddSum += i;
	        }
	        System.out.print(evenSum - oddSum);
	        System.out.println();
	    }
	}
}