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:
// package Div3_636;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class ProblemD {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        StringBuilder print=new StringBuilder();
        int test=Integer.parseInt(br.readLine());
        while(test--!=0){
            st=new StringTokenizer(br.readLine());
            int n=Integer.parseInt(st.nextToken());
            int k=Integer.parseInt(st.nextToken());
            int a[]=new int[n+1];
            st=new StringTokenizer(br.readLine());
            for(int i=1;i<=n;i++){
                a[i]=Integer.parseInt(st.nextToken());
            }
            int sumcount[]=new int[2*k+1];
            for(int i=1;i<=n/2;i++){
                int sum=a[i]+a[n-i+1];
                sumcount[sum]++;
            }
            int mark[]=new int[2*k+2];
            for(int i=1;i<=n/2;i++){
                int l=a[i];
                int r=a[n-i+1];
                int p=Math.min(l+1,r+1);
                int q=Math.max(l+k,r+k);
//                System.out.println(p+" "+q);
                mark[p]++;
                mark[q+1]--;
            }
            int prefix[]=new int[2*k+1];
            for(int i=2;i<=2*k;i++){
                prefix[i]=prefix[i-1]+mark[i];
            }
            long ans=Integer.MAX_VALUE;
            for(int i=2;i<=2*k;i++){
                int set=sumcount[i];
                int possible=prefix[i];
                int temp=0;
                temp+=possible-set;
                int rem=n/2-possible;
                temp+=2*rem;
                ans=Math.min(ans,temp);
            }
            print.append(ans+"\n");
        }
        System.out.print(print.toString());
    }
}