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

public class D
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(bu.readLine());
        StringBuilder sb=new StringBuilder();
        while(t-->0)
        {
            String s[]=bu.readLine().split(" ");
            int n=Integer.parseInt(s[0]),k=Integer.parseInt(s[1]);
            int a[]=new int[n],i,min=0;
            s=bu.readLine().split(" ");
            int sweep[]=new int[2*k+2],count[]=new int[2*k+2];
            for(i=0;i<n/2;i++)
            {
                a[i]=Integer.parseInt(s[i]);
                a[n-1-i]=Integer.parseInt(s[n-1-i]);
                min=a[i]>a[n-i-1]?a[n-i-1]:a[i];
                sweep[min+1]++;
                sweep[a[i]+a[n-i-1]-min+k+1]--;
                count[a[i]+a[n-i-1]]++;
            }
            for(i=1;i<2*k+2;i++)
            sweep[i]+=sweep[i-1];
            min=Integer.MAX_VALUE;
            for(i=2;i<2*k+1;i++)
            {
                int val=(sweep[i]-count[i])+2*(n/2-sweep[i]);
                if(val<min) min=val;
            }
            sb.append(min+"\n");
        }
        System.out.print(sb);
    }
}