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 Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i = 0; i < t; i++){
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] al = new int[n];
            for(int j = 0; j < n; j++){
                al[j] = sc.nextInt();
            }
            int rlen = k*2;
            int[] ruiseki = new int[rlen+2];
            for(int j = 0; j < n/2; j++){
                ruiseki[0] += 2;
                int min = Math.min(al[j],al[n-j-1]);
                int max = Math.max(al[j],al[n-j-1]);
                int sum = al[j] + al[n-j-1];
                ruiseki[Math.max(0,sum-max+1)]--;
                ruiseki[sum]--;
                ruiseki[Math.min(rlen+1,sum+1)]++;
                ruiseki[Math.min(rlen+1,sum+k-min+1)]++;
            }
            int ans = Integer.MAX_VALUE;
            for(int j = 1; j <= rlen; j++){
                ruiseki[j] += ruiseki[j-1];
                if(j != 1) ans = Math.min(ans,ruiseki[j]);
            }
            System.out.println(ans);
        }
    }
}