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

//run without debug: ctrl+a
//clear terminal: ctrl+space

public class CodeForces
{   

     public static void main(String[] args) throws java.lang.Exception 
    {

          Scanner s = new Scanner(System.in);
          long t = s.nextLong();
   
          while (t-- > 0) {
                int n=s.nextInt();
                int k=s.nextInt();
                int []a=new int[n];
                for(int i=0;i<n;i++)
a[i]=s.nextInt();
int ans=n;
            Map<Integer,Integer>map=new HashMap();
            for(int i=0;i<n/2;i++)
            {
                  map.put(a[i]+a[n-i-1],map.getOrDefault(a[i]+a[n-i-1], 0)+1);
            }        

            int []pref=new int[2*k+10];
            Arrays.fill(pref,0);
            for(int i=0;i<n/2;i++)
            {
                  int small=(a[i]<a[n-i-1]?a[i]:a[n-i-1]);
                  int large=(a[i]>a[n-i-1]?a[i]:a[n-i-1]);

                  small++;
                  large+=k;

                  pref[small]++;
                  pref[large+1]--;
            }
            int sum=0;
            for(int i=1;i<2*k+10;i++)
            pref[i]+=pref[i-1];

            for(int i=2;i<=2*k;i++)
            {
                  int cnt0=0;
                  if(map.get(i)!=null)cnt0=map.get(i);
                  int cnt1=pref[i]-cnt0;
                  int su=(n/2)-cnt1-cnt0;
                  int su2=cnt1+su*2;
                  ans=Math.min(ans,su2);
                  

            }
            System.out.println(ans);


       }     
	}
}