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 Constant_Palindrom_Sum {
 
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int test = sc.nextInt();
        while(test-- >0){
            int n = sc.nextInt();
            int k = sc.nextInt();
            int input[] = new int[n];
            int min = Integer.MIN_VALUE;
            
            for(int i = 0; i < n; i++){
                input[i] = sc.nextInt();
            }
 
            HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
            int prefix[] = new int[2 * k + 2];
            for(int i=0;i<n/2;i++){
                int mini = Math.min(input[i],input[n-i-1]);
                int maxi = Math.max(input[i],input[n-i-1]);
                
                map.put(maxi+mini,map.getOrDefault(mini+maxi, 0)+1);
                prefix[mini + 1] += 1;
                prefix[maxi + 1 +k] -= 1;
            }
            
            int sum = 0;
            for(int i = 0; i < 2 * k + 2; i++){
                sum += prefix[i];
                prefix[i] = sum;
            }
 
            int minimum = n;
            for(int i = 2; i <= 2 * k; i++){
                int change0 = map.getOrDefault(i,0);
                int change1 = prefix[i]-change0;
                int change2 = n/2 - change1 - change0;
                
                minimum = Math.min(minimum, change1 + 2*change2);
 
            }
            System.out.println(minimum);
        }
    }
}