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 BalancedArray {
    public static void main(String argv[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while(t-- > 0) {
            int n = Integer.parseInt(br.readLine());
            int size1 = n/2, size2 = n/2;
            if(size1%2!=0) System.out.print("NO");
            else {
                int ar[] = new int[n];
                int sum1 = 0, sum2 = 0;
                for(int i = 0; i < size1; i++) {
                    ar[i] = 2*(i+1);
                    sum1+=ar[i];
                    //System.out.println(sum1);
                }
                for(int i = size1, j = 1; i<n; i++, j+=2) {
                    ar[i] = j;
                    sum2 += ar[i];
                   //System.out.println(sum2);
                  
                }
                int diff = sum1 - sum2;
                //System.out.println(diff);
                ar[n-1] += (sum1 - sum2);
                System.out.println("YES");
                for(int i = 0; i<n; i++) System.out.print(ar[i]+" ");
            }
            System.out.println();
        }

    }
    
    
}