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 javax.swing.text.html.HTMLDocument;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.IntStream;



public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        OutputStream fOut = System.out;
        Scanner fin = new Scanner(System.in);
        try {
            fin = new Scanner(new FileInputStream("anniversary.in"));
        } catch (Exception ignored) {
        }
        try {
            fOut = new FileOutputStream("anniversary.out");
        } catch (Exception ignored) {
        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        PrintWriter fout = new PrintWriter(fOut);


        int testcase =in.nextInt();
        for (int test = 0; test < testcase; test++) {
            int n = in.nextInt();
            if(n%4==0){
                out.println("YES");
                for(int i=1;i<=n/2;i++){
                    out.print(2*i+" ");
                }
                for(int i=1;i<=n/4;i++){
                    out.print(2*i-1+" ");
                }
                for(int i=1;i<=n/4;i++){
                    out.print(n/2+2*i+1+" ");
                }
                out.println();
            }else{
                out.println("NO");
            }
        }


        out.flush();
        out.close();
        fout.close();
    }


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

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

        public boolean hasNext() {
            try {
                String string = reader.readLine();
                if (string == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(string);
                return tokenizer.hasMoreTokens();
            } catch (IOException e) {
                return false;
            }
        }

        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 char[] nextCharArray() {
            return next().toCharArray();
        }
    }

    public static void heapSort(long[] a) {
        for (int i = a.length / 2 - 1; i >= 0; i--) {
            adjustHeap(a, i, a.length);
        }
        for (int j = a.length - 1; j > 0; j--) {
            swap(a, 0, j);
            adjustHeap(a, 0, j);
        }

    }

    public static void adjustHeap(long[] a, int i, int length) {
        long temp = a[i];
        for (int k = i * 2 + 1; k < length; k = k * 2 + 1) {
            if (k + 1 < length && a[k] < a[k + 1]) {
                k++;
            }
            if (a[k] > temp) {
                a[i] = a[k];
                i = k;
            } else {
                break;
            }
        }
        a[i] = temp;
    }

    public static void swap(long[] a, int a1, int a2) {
        long temp = a[a1];
        a[a1] = a[a2];
        a[a2] = temp;
    }
}