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:
/**
 * @author Artur Chernov
 */

import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;

public class Template implements Runnable {

    private BufferedReader br = null;
    private PrintWriter pw = null;
    private StringTokenizer stk = new StringTokenizer("");

    public static void main(String[] args) {
        new Thread(new Template()).start();
    }

    public void run() {        /*
     * try { // br = new BufferedReader(new FileReader("input.txt")); pw =
     * new PrintWriter("output.txt"); } catch (FileNotFoundException e) {
     * e.printStackTrace(); }
     */
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new OutputStreamWriter(System.out));
        solver();
        pw.close();

    }

    private void nline() {
        try {
            if (!stk.hasMoreTokens())
                stk = new StringTokenizer(br.readLine());
        } catch (IOException e) {
            throw new RuntimeException("KaVaBUnGO!!!", e);
        }
    }

    private String nstr() {
        while (!stk.hasMoreTokens())
            nline();
        return stk.nextToken();
    }

    private int ni() {
        return Integer.parseInt(nstr());

    }

    private double nd() {
        return Double.parseDouble(nstr());

    }

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

    private void solver() {
        int t = ni();
        while (t-- > 0) {
            int n = ni();
            if (n % 4 == 0) {
                System.out.println("YES");
                int k = n / 2;
                for (int i = 0; i < k; i++) {
                    System.out.print(2 * (i + 1) + " ");
                }
                for (int i = 0; i < k - 1; i++) {
                    System.out.print(2 * (i + 1) - 1 + " ");
                }
                System.out.println(n - 1 + k);
            } else {
                System.out.println("NO");
            }
        }
    }

    private BigInteger nbi() {
        return new BigInteger(nstr());
    }

    void exit() {
        System.exit(0);
    }
}