Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in JAVA):

Solution:
import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            int k=sc.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=sc.nextInt();
            }
            int zero[]=new int[2*k+2];
            int one[]=new int[2*k+2];
            
            for(int i=0;i<n/2;i++)
            {
                int minc=Math.min(a[i],a[n-i-1]);
                int maxc=Math.max(a[i],a[n-i-1]);
                zero[minc+maxc]++;
                one[minc+1]++;
                one[maxc+k+1]--;
            }
            
            for(int i=2;i<2*k+1;i++)
            {
                one[i]+=one[i-1];
            }
            
            int min=Integer.MAX_VALUE;
            
            for(int i=2;i<=2*k;i++)
            {
                int z=zero[i];
                int o=one[i];
                int to=n/2 - o;
                min=Math.min(min,(o-z)+2*to);
            }
            System.out.println(min);
            
        }
       // System.out.println("XXXXXXXX");
    }
}