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.*;

public class HelloWorld{
     public static void main(String []args){
        Scanner s = new Scanner(System.in);
        int numOfTestCases = s.nextInt();
        for(int i = 0; i < numOfTestCases; i++){
            int arrayLength = s.nextInt();
            if(arrayLength%4 == 0){
                System.out.println("YES");
                int[] evens = new int[arrayLength/2];
                int[] odds = new int[arrayLength/2];
                evens[0] = 2;
                System.out.print(evens[0] + " ");
                odds[0] = 1;
                int evenSum = 2;
                int oddSum = 1;
                for(int k = 1; k < evens.length; k++){
                    evens[k] = evens[k-1] + 2;
                    evenSum += evens[k];
                    System.out.print(evens[k] + " ");
                }
                System.out.print(odds[0] + " ");
                for(int w = 1; w < odds.length; w++){
                    if(w < odds.length-1){
                        odds[w] = odds[w-1]+2;
                        oddSum += odds[w];
                        System.out.print(odds[w] + " ");
                    }
                    else{
                        odds[w] = evenSum - oddSum;
                        System.out.print(odds[w]);
                    }
                }
                System.out.println("");
            }
            else{
                System.out.println("NO");
                
            }
        }
     }
}