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.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder();
        int tst = Integer.parseInt(br.readLine());
        HashMap<Integer, Integer> hm = new HashMap<>();
        while(tst-->0){
            hm.clear();
            String[] str = br.readLine().split(" ");
            int n = Integer.parseInt(str[0]), k = Integer.parseInt(str[1]);
            StringTokenizer st = new StringTokenizer(br.readLine());
            int[] arr = new int[n];
            for(int i = 0; i<n; i++){
                arr[i] = Integer.parseInt(st.nextToken());
            }
            for(int i = 0; i<n/2; i++){
                int c = arr[i]+arr[n-i-1];
                if(hm.containsKey(c)){
                    int z = hm.get(c);
                    hm.put(c, z+1);
                }
                else{
                    hm.put(c, 1);
                }
            }
            int[] pref = new int[2*k+2];
            for(int i = 0; i<n/2; i++){
                int a = Math.max(arr[i], arr[n-i-1]);
                int b = Math.min(arr[i], arr[n-i-1]);
                pref[b+1]++;
                pref[a+k+1]--;
            }
            for(int i = 2; i<(2*k+2); i++){
                pref[i]+=pref[i-1];
            }
            int ans = Integer.MAX_VALUE;
            for(int i = 2; i<=2*k; i++){
                int zero_chg = 0, one_chg, two_chg;
                if(hm.containsKey(i)){
                    zero_chg = hm.get(i);
                }
                one_chg = pref[i]-zero_chg;
                two_chg = (n/2)-pref[i];
                int total = one_chg + 2*two_chg;
                if(ans>total) ans = total;
            }
            sb.append(ans).append('\n');
        }
        System.out.println(sb);
    }
}