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.*;
import java.io.*;
 
public class constant_palindrome_sum {
	
	public static void main(String[] args) throws Exception {
		
		Scanner sc = new Scanner(System.in);
		
        int testCases = sc.nextInt();
        
        for (int t = 0; t < testCases; t++) {
            int n = sc.nextInt();
            int k = sc.nextInt();
 
            int arr[] = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
            }

            int mp[] = new int[2 * k + 100];
            for (int i = 0; i < n / 2; i++) {
                int first = i;
                int last = n - i - 1;
 
                mp[arr[first] + arr[last]]++;
            }

            int pre[] = new int[2 * k + 100];
            for (int i = 0; i < n / 2; i++) {
                int first = i;
                int last = n - i - 1;
 
                int val = Math.min(arr[first], arr[last]) + 1;
                pre[val] += 1;
                val = Math.max(arr[first], arr[last]) + k;
                pre[val + 1] -= 1;
            }
 
            for (int i = 1; i < pre.length; i++) {
                pre[i] = pre[i - 1] + pre[i];
            }
            int minChanges = n;
            for (int i = 2; i <= 2 * k; i++) {
                int cnt0 = mp[i];
                int cnt1 = pre[i] - cnt0;
                int cnt2 = (n / 2) - cnt1 - cnt0;
 
                minChanges = Math.min(minChanges, 0 * cnt0 + 1 * cnt1 + 2 * cnt2);
            }
            System.out.println(minChanges);
        }
    }
	
}