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.InputStreamReader;

public class Main {

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        for (String ln; (ln = in.readLine()) != null; ) {
            int N = Integer.parseInt(ln);
            while(N-->0){
                int num = Integer.parseInt(in.readLine());
                boolean ws = false;
                StringBuilder sol = new StringBuilder();
                int sum = 0;
                for(int i=0;i<num/2;++i){
                    sol.append(2*(i+1)).append(" ");
                    sum += 2*(i+1);
                }
                sol.append("1");
                sum -= 1;
                
                for(int i=1;i<=(num/2)-2;++i){
                    sol.append(" ").append(((2*i)+1));
                    sum -= ((2*i)+1);
                }

                if(sum%2 !=0 && sum != 1 ){
                    ws = true;
                    sol.append(" ").append(sum);
                }
                System.out.println(ws?"YES\n"+new String(sol):"NO");
            }
        }
    }
}