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.*;
import java.util.*;
public class Balanced{
    public static void main(String[] args)throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        for(int l=0;l<t;l++){
            int n=Integer.parseInt(br.readLine());
            int a[]=new int[n];
            int e=2,o=1;
            int sum1=0,sum2=0;
            if((n/2)%2==1)
              System.out.println("NO");
            else{
                for(int i=0;i<n/2;i++){
                    a[i]=e;
                    e=e+2;
                    sum1+=a[i];
                }
                for(int j=n/2;j<n;j++){
                    a[j]=o;
                    //System.out.println(a[j]);
                    o=o+2;
                    sum2+=a[j];
                }
               if(sum1==sum2){
                   System.out.println("YES");
                   for(int z=0;z<n;z++)
                      System.out.print(a[z]+" ");
                   System.out.println();
                }
               else{
                 int c=0;
                 int s=a[n-1]+2;
                 sum2=sum2+s;
                 int sa=sum2;
                 for(int x=n/2;x<n;x++){
                  //  System.out.println(a[x]+" "+sum2);
                    sum2=sum2-a[x];
                   // System.out.println(sum2);
                    if(sum1==sum2){
                         a[x]=a[n-1]+2;
                         break;
                    }
                    sum2=sa;
                 }
                  System.out.println("YES");
                  for(int z=0;z<n;z++)
                     System.out.print(a[z]+" ");
                  System.out.println();
              }
            }
        }
    }
}