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.StringTokenizer;

public class q4 {

	public static void main(String[] args) {
		FastReader s = new FastReader();
		
		int t = s.nextInt();
		
		while(t-- > 0)
		{
			int n = s.nextInt();
			int k = s.nextInt();
			
			int[] inp = new int[n];
			int[] help = new int[2*k + 2];
			for(int i=0;i<n;++i)
			{
				inp[i] = s.nextInt();
			}
			help[0] = n;
			for(int i=0;i<n/2;++i)
			{
				help[Math.min(inp[i],inp[n-i-1])+1]--;
				help[Math.max(inp[i],inp[n-i-1])+k+1]++;
			}
			
			for(int i=1;i<2*k+2;++i)
			{
				help[i] += help[i-1];
			}
			
			for(int i=0;i<n/2;++i)
			{
				int sum = inp[i] + inp[n-i-1];
				help[sum]--;
			}
			int ans = Integer.MAX_VALUE;
			for(int i=0;i<2*k+2;++i)
			{
				ans = Math.min(ans,help[i]);
			}
		
			
			System.out.println(ans);
		}

	}
	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;
        }
	}
}