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 stone {
    public static void main(String args[]) throws IOException {
        //System.out.println("enter the number of test cases");
        int t = 0;
        FastReader sc = new FastReader();
        BufferedWriter w = new BufferedWriter(new PrintWriter(System.out));
        t = sc.nextInt();
        for (int i = 0; i < t; i++) {
           // System.out.println("enter the value of n and k");
            int n = sc.nextInt();
            int k=sc.nextInt();
            int a[]=new int[n];
           // System.out.println("enter the values of array");
            for(int x=0;x<n;x++)
            {
                a[x]=sc.nextInt();
            }
          //  List min=new ArrayList();
           // List max=new ArrayList();
            int sum[]=new int[2*k+1];
            for(int c=0;c<n/2;c++)
            {
                int temp=a[c]+a[(n-c)-1];
                sum[temp]++;
            }
           // System.out.println("SUM: "+sum.toString());
            //int minch=Integer.MAX_VALUE;
            int[] pref =new int[2*k+2];
                for (int z = 0; z < n / 2; z++)
                {
                    int min1 = Math.min(a[z], a[(n - z) - 1]) + 1;
                    int max1 = Math.max(a[z], a[(n - z) - 1]) + k;
                    pref[min1]++;
                    pref[max1+1]--;
                }
            for (int v = 1; v <= 2 * k + 1; ++v)
            {
                pref[v] += pref[v - 1];
            }
            int ans = Integer.MAX_VALUE;
            for (int sum1 = 2; sum1 <= 2 * k; ++sum1) {
                ans = Math.min(ans, (pref[sum1] - sum[sum1]) + (n / 2 - pref[sum1]) * 2);
            }
            w.write(ans+"\n");
        }
        w.close();

    }
}

class FastReader
{
    BufferedReader br;
    StringTokenizer st;

    public FastReader() throws IOException {
        br = new BufferedReader(new
                InputStreamReader(System.in));

    }

    String next() throws NumberFormatException,IOException,NullPointerException
    {
        while (st == null || !st.hasMoreElements())
        {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

    int nextInt()throws NumberFormatException,IOException,NullPointerException
    {
        return Integer.parseInt(next());
    }

    long nextLong()throws NumberFormatException,IOException,NullPointerException
    {
        return Long.parseLong(next());
    }

    double nextDouble()throws NumberFormatException,IOException,NullPointerException
    {
        return Double.parseDouble(next());
    }

    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}