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.ArrayList;
import java.util.StringTokenizer;
 
public class Main {
    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;
        }
    }
 
    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        int t= sc.nextInt();
        for (int j=0;j<t;j++){
            int l=sc.nextInt();
            int even=2;
            int odd=1;
            int sum=0;
            int sumo=0;
            if(l%4==0){
                System.out.println("YES");
                ArrayList<Integer> v= new ArrayList<Integer>();
                for (int i=1;i<=l/2;i++){
                    sum+=even;
                     v.add(even);
                     even+=2;
 
                }
                for (int i=2;i<=l/2;i++){
                    sumo+=odd;
                    v.add(odd);
                    odd+=2;
 
                }
                v.add(sum-sumo);
                for (int i=0;i<l;i++){
                    System.out.print(v.get(i)+" ");
                }
            }
            else System.out.println("NO");
        }
    }
}