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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class BalancedArray {

    public static void main(String [] args){
        Scanner input = new Scanner(System.in);
        Integer totalTests = Integer.parseInt(input.nextLine());
        List<Long> tests = new ArrayList<>();

        for(int i = 0 ; i < totalTests ; i++){
            tests.add(Long.parseLong(input.nextLine()));
        }

        for (Long test:tests) {
            Long overTwo = test / 2;
            if(overTwo % 2 == 0){
                System.out.print("YES\n"+ getNumbersList(test) + "\n");
            }else{
                System.out.print("NO\n");
            }
        }
    }


    /**
     * Get numbers list for the input number
     *
     * @param number
     *
     * @return String
     * */
    public static String getNumbersList(Long number){
        StringBuilder result = new StringBuilder();
        Long counter = 2L;
        Long sum = 0L;

        // build even part
        for(Long i = 1L ; i <= number / 2 ; i++){
            result.append(counter.toString() + " ");
            sum += counter;
            counter += 2;
        }

        // build odd part
        counter = 1L;
        for(long i = (number / 2)+ 1 ; i <= number ; i++){
            if(i != number){
                result.append(counter.toString() + " ");
                sum -= counter;
                counter += 2;
            }else{
                result.append(sum.toString());
            }
        }

        return result.toString();
    }
}