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.*;
import java.awt.*;
public class B
{
    BufferedReader in;
    PrintWriter ob;
    StringTokenizer st;
  
    public static void main(String[] args) throws IOException {
        new B().run();
    }
    void run() throws IOException {
        in=new BufferedReader(new InputStreamReader(System.in));
        ob=new PrintWriter(System.out);
        int t = ni();
        while(t-->0)
            solve();
        ob.flush();
    }
    void solve() throws IOException {
          int n = ni();
          if( (n/2)%2 == 0 ) {

            ob.println("YES");

            int start = 2;
            int sum = 0;
            for(int i=1 ; i<=n/2 ; i++) {
                ob.print( start+" ");
                sum+=start;
                start+=2;
            }

            start = 1;
            for(int i=1 ; i<n/2 ; i++) {
                ob.print( start+" ");
                sum-=start;
                start+=2;
            }

            ob.print(sum+"\n");

          } else {
            ob.println("NO");
          }
    } 
 
    String ns() throws IOException {
        return nextToken();
    }
    long nl() throws IOException {
        return Long.parseLong(nextToken());
    }
    int ni() throws IOException {
        return Integer.parseInt(nextToken());
    }
    double nd() throws IOException {
        return Double.parseDouble(nextToken());
    } 
    String nextToken() throws IOException {
        if(st==null || !st.hasMoreTokens())
            st=new StringTokenizer(in.readLine());
        return st.nextToken();
    }
    int[] nia(int start,int b) throws IOException {
        int a[]=new int[b];
        for(int i=start;i<b;i++)
            a[i]=ni();
        return a;
    }
    long[] nla(int start,int n) throws IOException {
        long a[]=new long[n];
        for (int i=start; i<n ;i++ ) {
            a[i]=nl();
        }
        return a;
    }
    
    public void tr(Object... o) {
     System.out.println(Arrays.deepToString(o));
    }
}