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:


/* package codechef; // don't place package name! */
//devanshjsr

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Solution
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    StringTokenizer st=new StringTokenizer(br.readLine());
	    
		    int t=Integer.parseInt(st.nextToken());
		    
		    
		    while(t>0)
		    {
		        st=new StringTokenizer(br.readLine());
		        int n=Integer.parseInt(st.nextToken());
		        int k=Integer.parseInt(st.nextToken());
		        
		        int[] arr=new int[n];
		        int[] sf=new int[2*k+1];
		        int[] pf=new int[2*k+2];
		        st=new StringTokenizer(br.readLine());
		        
		        for(int i=0;i<n;i++)
		        {
		            arr[i]=Integer.parseInt(st.nextToken());
		        }
		        
                
                for(int i=0;i<n/2;i++)
                {
                    int s=arr[i]+arr[n-i-1];
                    sf[s]++;
                    
                }
                
                for(int i=0;i<n/2;i++)
                {
                    int sr=(int)Math.min(arr[i],arr[n-i-1])+1;
                    int lt=(int)Math.max(arr[i],arr[n-i-1])+k;
                    
                    pf[sr]++;
                    pf[lt+1]--;
                }
                
                for (int i = 1; i <= 2 * k + 1; ++i) 
                {
			        pf[i] += pf[i - 1];
		        }
                
                int ans=Integer.MAX_VALUE;
                
                for(int i=2;i<=2*k;i++)
                {
                    ans=(int)Math.min(ans,(pf[i]-sf[i])+(n/2-pf[i])*2);
                    
                }
                
                
                
		        System.out.println(ans);
		        
		        
		        t--;
		    }
	}
}