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 Program {
    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        for(int i=0; i<t; i++) {
            int n = input.nextInt();
            if(n % 4 == 0) {
                System.out.println("YES");
                System.out.println(getNumbers(n));
            }
            else
                System.out.println("NO");
        }
    }

    public static String getNumbers(int n) {
        StringBuilder odds = new StringBuilder("");
        StringBuilder evens = new StringBuilder("");
        for(int i=1; i<n+2; i++) {
            if(i == n/2 + 1)
                continue;
            if(i % 2 == 0)
                evens.append(i + " ");
            else
                odds.append(i  + " ");
        }

        return evens.toString() + odds.toString();
    }
}