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.*;
import java.util.*;

public class pp1 {
    FastScanner in;
    PrintWriter out;
    class Graph{
        int V;
        ArrayList<Integer> adjlist[];
        Graph(int n){
            this.V = n;
            this.adjlist = new ArrayList[n];
            for(int i=0;i<this.V;i++){
                adjlist[i] = new ArrayList<>();
            }
        }
        void addEdge(int u, int v){
            adjlist[u].add(v);
            adjlist[v].add(u);
        }
        int dfs(int start, int dest, boolean[] vis, List<Integer> happy){
            vis[start]=true;
            int sum=0;
            boolean flag=false;
            for(int i=0;i<adjlist[start].size();i++){
                int b = adjlist[start].get(i);
                if(!vis[b]){
                    flag=true;
                    sum+=dfs(b, dest+1,vis, happy );
                }
            }
            int remain = dest-sum;
            happy.add(remain);
            return sum+1;
        }



    }


    void solve() {
        //This is the main logic code
        int t = in.nextInt();

        while(t-->0){
            int n = in.nextInt();
            int [] a = new int[n];
            int e=0;int o=0;
            for(int i=0;i<n;i++){
                a[i]=i+1;
                if(a[i]%2==0){e+=a[i];}
                else{o+=a[i];}
            }
            int d =e-o;
            if(d%2==0){
                out.println("YES");
                for(int i=1;i<n;i+=2){
                    out.print(a[i]+" ");
                }
                int i=0;
                for(;i<n;i+=2){
                    if(i+2>=n){break;}
                    out.print(a[i]+" ");

                }
                out.println(a[i]+d);
            }
            else{out.println("NO");}
        }

    }

    public static void main(String[] args) {
        new pp1().runIO();
    }

    void run() {
        try {
            in = new FastScanner(new File("A.in"));
            out = new PrintWriter(new File("A.out"));
            solve();
            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

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

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

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

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

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