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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class CF1343B {
    public static void main(String[] args) {
        FastReader input = new FastReader();
        int t = input.nextInt();
        while (t > 0){
            int n = input.nextInt();
            if(n == 2){
                System.out.println("NO");
            }
            else{
                Map<Long,Long> map = new HashMap<Long,Long>();
                long[] arr = new long[n];
                long even = 2;
                long odd = 1;
                long sum1 = 0;
                for(int i = 0;i < (n/2);i++){
                    arr[i] = even;
                    sum1 += arr[i];
                    even += 2;
                }
                long sum2 = 0;
                for(int j = (n/2); j < n-1;j++){
                    arr[j] = odd;
                    map.put(odd,1L);
                    sum2 += arr[j];
                    odd += 2;
                }
                long diff = sum1 - sum2;
                if(diff % 2 == 0 || map.get(diff) != null){
                    System.out.println("NO");
                }
                else{
                    arr[n-1] = diff;
                    System.out.println("YES");
                    for(int i = 0;i < n;i++){
                        System.out.print(arr[i] + " ");
                    }
                    System.out.println();
                }
            }

            t--;
        }


    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

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

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

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