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.io.*;

public class CJ6 {
	
	public static int n;
	public static int s;
	public static int e;
	public static int w;
	
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while (t>0)
		{
			String inp[]=br.readLine().split(" ");
			int n=Integer.parseInt(inp[0]);
			int k=Integer.parseInt(inp[1]);
			int arr[]=new int[n];
			int min=Integer.MAX_VALUE;
			inp=br.readLine().split(" ");
			HashSet<Integer> set=new HashSet<>();
			int max=Integer.MIN_VALUE;
			int nochanges[]=new int[2*k+2];
			for (int i=0;i<n;i++)
			{
				arr[i]=Integer.parseInt(inp[i]);
				int sum=arr[i]+arr[n-i-1];
				if (i>=n/2)
				{
					set.add(sum);
					min=Math.min(min, sum);
					max=Math.max(max, sum);
					nochanges[sum]++;
				}
			}
			int onechange[]=new int[2*k+2];
			for (int i=0;i<n/2;i++)
			{
				int maxposs=Math.max(arr[i],  arr[n-i-1])+k;
				int minposs=Math.min(arr[i], arr[n-i-1])+1;
				int sum=arr[i]+arr[n-i-1];
//				for (int j=minposs;j<=maxposs;j++)
//				{
//					if (j==sum)
//						continue;
//					onechange[j]++;
//				}
				onechange[maxposs+1]--;
				onechange[minposs]++;
			}
			int minchanges=n;
			for (int i=2;i<=2*k;i++)
			{
				onechange[i]+=onechange[i-1];
				int numofchanges=(onechange[i]-nochanges[i])+2*(n/2-onechange[i]);
				minchanges=Math.min(minchanges, numofchanges);
			}
			System.out.println(minchanges);
			t--;
		}
	}
}