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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;



public class Test38
{
	static int[] parseArray(String[] arr)
	{
		int[] result=new int[arr.length];
		for(int i=0; i<arr.length; i++)
		{
			result[i]=(Integer.parseInt(arr[i]));
		}
		return result;
	}
	
	public static void main(String[] args) throws IOException
	{
		BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
		
		int t=Integer.parseInt(f.readLine());
		while(t-->0)
		{
			
			String[] p=f.readLine().split(" ");
			int[] num=parseArray(f.readLine().split(" "));
			int n=Integer.parseInt(p[0]);
			int k=Integer.parseInt(p[1]);
			int[] delta=new int[2*(int)k+2];
			Arrays.fill(delta, 0);
			for(int i=0; i<n/2; i++)
			{
				int sum=num[i]+num[n-1-i];
				int minN=Math.min(num[i],num[n-1-i]), maxN=Math.max(num[i],num[n-1-i]);
				
				delta[2]+=2;
				delta[minN+1]--;
				delta[maxN+k+1]++;
				delta[sum]--;
				delta[sum+1]++;
			}
			int ans=delta[2];
			for(int i=3; i<=2*k; i++)
			{
				delta[i]+=delta[i-1];
				ans=Math.min(delta[i], ans);
			}
			System.out.println(ans);
			/*
			 sum left=sum right=len/2*x/2
			
			
			 */
		}
	}
}