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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    static long pow(long a,long b){
        if(b==0) return 1;
        long temp=pow(a,b/2);
        if(b%2==0) return (temp%1000000007)*(temp%1000000007)%1000000007;
        else return (a*((temp%1000000007)*(temp%1000000007)%1000000007))%1000000007;
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
         BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
         int t=Integer.parseInt(br.readLine());
         while(t-->0){
             int n=Integer.parseInt(br.readLine());
             int check=n/2;
             if(check%2==1){
                 bw.write("NO\n");
                 continue;
             }
             int i;
             int even=2,odd=1;
             bw.write("YES\n");
             int a[]=new int[n];
             for(i=0;i<n;i++){
                 if(i<n/2){
                     a[i]=even;
                     even+=2;
                 }
                 else{
                     a[i]=odd;
                     odd+=2;
                 }
             }
             a[n-1]+=check;
             for(i=0;i<n;i++){
             
                 bw.write(a[i]+" ");
             }
             bw.newLine();
         }
         bw.flush();
	}
}