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.math.BigInteger;
import java.util.*;
public class Main {
	static Scanner sc=new Scanner(System.in);
	public static void main(String[] args) {
		for(int t=sc.nextInt();t>0;t--) {
			show();
		}
	}
	private static void show() {
		int n=sc.nextInt();
		int k=sc.nextInt();
		int a[]=new int [n+1];
		int arr[]=new int [2*(k+1)+1];
		int sum,minn,maxn;
		for(int i=1;i<=n;i++) {
			a[i]=sc.nextInt();
			if(i>n/2)
	        {
	            sum=a[i]+a[n-i+1];
	            minn=Math.min(a[i],a[n-i+1]);
	            maxn=sum-minn;

	            arr[2]+=2;
	            arr[minn+1]--;
	            arr[maxn+k+1]++;
	            arr[sum]--;
	            arr[sum+1]++;
	        }
		}
		int ans=arr[2];
		///System.out.println(Arrays.toString(arr));
	    for(int i=3;i<=2*k;i++){
	        arr[i]+=arr[i-1];
	        ans=Math.min(arr[i],ans);
	    }
	    
	    System.out.println(ans);
	}
}