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.util.*;
import java.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        for(int x=0;x<t;x++)
        {
            String str[]=br.readLine().split(" ");
            int n=Integer.parseInt(str[0]);
            int k=Integer.parseInt(str[1]);
            int sumcnt[]=new int[2*k+1];
            int pref[]=new int[2*k+2];
            int arr[]=new int[n];
            str=br.readLine().split(" ");
            for(int i=0;i<n;i++)
            arr[i]=Integer.parseInt(str[i]);
            for(int i=0;i<n/2;i++)
            {
                sumcnt[arr[i]+arr[n-1-i]]++;
                pref[Math.min(arr[i],arr[n-1-i])+1]++;
                pref[Math.max(arr[i],arr[n-1-i])+k+1]--;
            }
            for(int i=1;i<=2*k+1;i++)
            pref[i]+=pref[i-1];
            int ans=Integer.MAX_VALUE;
            for(int i=2;i<=2*k;i++)
            ans=Math.min(ans,(pref[i]-sumcnt[i]+(n/2-pref[i])*2));
            pw.println(ans);
        }
        pw.flush();
        pw.close();
    }
}