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;
import java.util.*;

public class MainClass {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

        int numTestCases = Integer.parseInt(in.readLine());

        for (int i=0; i<numTestCases;i++) {
            int len = Integer.parseInt(in.readLine());
            int[] arr = findArray(len);
            if (arr.length == 0) {
                System.out.println("NO");
            } else {
                System.out.println("YES");
                StringBuffer stringBuffer = new StringBuffer();
                for (int j=0; j < arr.length; j++) {
                    stringBuffer.append(arr[j]);
                    if (j != arr.length - 1) {
                        stringBuffer.append(" ");
                    }
                }
                System.out.println(stringBuffer.toString());
            }
        }
    }

    public static int[] findArray(int len) {

        if (len%4 != 0) {
            return new int[0];
        }

        int[] retArr =  new int[len];
        retArr[0] = 2;

        for (int i=1; i<len/2;i++) {
            retArr[i] = retArr[i-1] + 2;
        }

        retArr[len/2] = 1;
        int totalOddSum = 1;
        for (int i=len/2+1; i<len-1; i++) {
            retArr[i] = retArr[i-1] + 2;
            totalOddSum += retArr[i];
        }

        int half = len/2;
        int totalEvenSum = half*(half+1);

        retArr[len-1] = totalEvenSum - totalOddSum;
        return retArr;
    }

}