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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i = 0; i < t; i++){
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] al = new int[n];
            for(int j = 0; j < n; j++){
                al[j] = sc.nextInt();
            }
            int rlen = k*2;
            int[] ruiseki = new int[rlen+2];
            for(int j = 0; j < n/2; j++){
                ruiseki[0] += 2;
                int min = Math.min(al[j],al[n-j-1]);
                int max = Math.max(al[j],al[n-j-1]);
                int sum = al[j] + al[n-j-1];
                ruiseki[Math.max(0,sum-max+1)]--;
                ruiseki[sum]--;
                ruiseki[Math.min(rlen+1,sum+1)]++;
                ruiseki[Math.min(rlen+1,sum+k-min+1)]++;
            }
            int ans = Integer.MAX_VALUE;
            for(int j = 1; j <= rlen; j++){
                ruiseki[j] += ruiseki[j-1];
                if(j != 1) ans = Math.min(ans,ruiseki[j]);
            }
            System.out.println(ans);
        }
    }
}