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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BalancedArray solver = new BalancedArray();
        solver.solve(1, in, out);
        out.close();
    }

    static class BalancedArray {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int t = in.nextInt();
            while (t-- > 0) {
                int n = in.nextInt();
                int[] nums = new int[n];
                if (n % 4 != 0) {
                    out.println("NO");
                } else {
                    int sum_pos = 0;
                    int even = 2;
                    for (int i = 0; i < n / 2; i++) {
                        nums[i] = even;
                        sum_pos += even;
                        even = even + 2;
                    }
                    int sum_neg = 0;
                    int no_even = 1;
                    for (int i = n / 2; i < n - 1; i++) {
                        nums[i] = no_even;
                        sum_neg += no_even;
                        no_even = no_even + 2;
                    }

                    int resto = sum_pos - sum_neg;
                    if (resto % 2 != 0) {
                        sum_neg += resto;
                        if (sum_neg == sum_pos) {
                            nums[n - 1] = resto;
                            out.println("YES");
                            for (int i = 0; i < nums.length; i++) {
                                if (i == nums.length - 1) {
                                    out.println(nums[i]);
                                } else {
                                    out.print(nums[i] + " ");
                                }
                            }
                        }
                    } else {
                        out.println("NO");
                    }


                }
            }
        }

    }
}