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[])
    {
        Scanner sc=new Scanner(System.in);
        int test=sc.nextInt();
        while(test-->0)
        {
            int n=sc.nextInt();
            int arr[]=new int[n];
            int k=sc.nextInt();
            for(int i=0;i<n;i++)
            {
                arr[i]=sc.nextInt();
            }
            HashMap <Integer,Integer> zero_ch=new HashMap<>();
            ArrayList<ArrayList<Integer>>one_ch=new ArrayList<>();
            for(int i=0;i<n/2;i++)
            {
                int l=arr[i]+arr[n-i-1];
                if(zero_ch.containsKey(l))
                {
                    zero_ch.put(l,zero_ch.get(l)+1);
                }
                else
                {
                    zero_ch.put(l,1);
                }
                int l1=Math.min(arr[i],arr[n-i-1])+1;
                int r1=Math.max(arr[i],arr[n-i-1])+k;
                ArrayList<Integer> a=new ArrayList<>();
                a.add(l1);
                a.add(r1);
                one_ch.add(a);
            }
//            System.out.println(zero_ch);
//            System.out.println(one_ch);
            int a[]=new int[2*k+10];
            for(ArrayList<Integer> t:one_ch )
            {
                int l=t.get(0);
                int r=t.get(1)+1;
                a[l]++;
                a[r]--;
            }
            int min=n/2;
            for(int i=1;i<a.length;i++)
            {
            	a[i]+=a[i-1];
            	int zero=0;
            	int ones=0;
            	if(zero_ch.containsKey(i))
            	{
            		zero=zero_ch.get(i);
            		ones=a[i]-zero;
            	}
            	else
            	{
            		ones=a[i];
            	}
            	int two=n/2-ones-zero;
            	int changes=two*2+ones*1;
            	if(changes<min)
            		min=changes;
            	
            }
            System.out.println(min);
            
            
            
        }
    }
}