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:
//code written by a living bruh moment
import java.io.*;
import java.lang.*;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;
import java.util.Random;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Collections;

public class CodeforcesDiv3_636{
    static InputReader in = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int q = in.nextInt();
        while(q-->0){
            int n = in.nextInt();
            if(n%4==0){
                out.println("YES");
                ArrayList<Integer> ans = new ArrayList<Integer>(n);
                long sum = 0;
                long sum2 = 0;
                for(int i = 1; i<=n/2; i++){
                    ans.add(2*i);
                    sum+=2*i;
                }
                for(int i = 1; i<n/2; i++){
                    ans.add(2*i-1);
                    sum2+=2*i-1;
                }
                ans.add((int) ((int)sum-sum2));
                for(int i : ans){
                    out.print(i + " ");
                }
                out.println();
            }
            else{
                out.println("NO");
            }
        }
        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong()
        {
            return Long.parseLong(next());
        }
        public double nextDouble()
        {
            return Double.parseDouble(next());
        }
        public String nextLine()
        {
            try
            {
                return reader.readLine();
            }
            catch(Exception e)
            {
                e.printStackTrace();
            }
            return null;
        }
        public boolean hasNext()
        {
            String next=null;
            try
            {
                next=reader.readLine();
            }
            catch(Exception e)
            {
            }
            if(next==null)
            {
                return false;
            }
            tokenizer=new StringTokenizer(next);
            return true;
        }
    }
}