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:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class D
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        int T=Integer.parseInt(br.readLine().trim());
        StringBuilder sb=new StringBuilder();

        while(T-->0)
        {
            String s[]=br.readLine().trim().split(" ");
            N=Integer.parseInt(s[0]);
            int K=Integer.parseInt(s[1]);

            s=br.readLine().trim().split(" ");
            int a[]=new int[N];
            for(i=0;i<N;i++) a[i]=Integer.parseInt(s[i]);

            int zero[]=new int[2*K+5]; //can be obtained with 0 changes
            int one[]=new int[2*K+5]; //can be obtained in 0 or 1 changes

            int min=Integer.MAX_VALUE;
            for(i=0;i<N/2;i++)
            {
                int A=Math.min(a[i],a[N-i-1]);
                int B=Math.max(a[i],a[N-i-1]);

                zero[A+B]++;
                one[A+1]++; //range update
                one[B+K+1]--; //range update
            }

            for(i=2;i<=2*K;i++) one[i]+=one[i-1]; //actual array after all updates

            for(i=2;i<=2*K;i++)
            {
                int zer=zero[i]; //number of pairs of elements which form i with 0 changes
                int ONE=one[i]; //0 or 1 changes
                int two=N/2-ONE; //two changes

                min=Math.min(min,ONE-zer+two*2);
            }
            sb.append(min).append("\n");
        }
        System.out.println(sb);
    }
}