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;

public class D {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++) {
            String[] str = br.readLine().split(" ");
            int key = Integer.parseInt(str[1]);
            String[] data = br.readLine().split(" ");
            int[] arr = new int[data.length];
            for (int j = 0; j < arr.length; j++)
                arr[j] = Integer.parseInt(data[j]);

            int[] change = new int[key * 2 + 1];
            change[2] = arr.length;
            for (int j = 0; j < arr.length / 2; j++) {
                int sum = arr[j] + arr[arr.length - j - 1];
                change[Math.min(arr[j], arr[arr.length - j - 1]) + 1]--;
                change[sum]--;
                if (sum != 2 * key)
                    change[sum + 1]++;

                int maxNum = Math.max(arr[j], arr[arr.length - j - 1]);
                if (maxNum < key)
                    change[maxNum + key + 1]++;
                //System.out.println(Arrays.toString(change));
            }

            int moves = change[2];
            int minMoves = moves;
            for (int j = 3; j < change.length; j++) {
                moves += change[j];
                if (moves < minMoves)
                    minMoves = moves;
            }

            System.out.println(minMoves);
        }
    }

}