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

public class constantpalin {
    public static void main(String argv[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while(t-- > 0) {
            String s[] = br.readLine().split(" ");
            String inp[] = br.readLine().split(" ");
            int k = Integer.parseInt(s[1]);
            int n =Integer.parseInt(s[0]);
            int ar[] = new int[n];
            for(int i = 0; i < n; i++) {
                ar[i] = Integer.parseInt(inp[i]);
            }
            int a[] = new int[(2*k)+100], cnt[] = new int[(2*k)+100];
            Arrays.fill(a, 0);Arrays.fill(cnt, 0);
            for(int i = 0; i < n/2; i++) {
                a[ar[i]+ar[n-i-1]]++;
                int mn = Math.min(ar[i], ar[n-i-1]);
                int mx = Math.max(ar[i], ar[n-i-1]);
                mn++;mx+=k+1;
                cnt[mn]++;
                cnt[mx]--;
            }
            int ans = n;
            for(int i = 1; i <= 2*k; i++) {
                cnt[i] += cnt[i-1];
                int cur = n - a[i] - cnt[i];
                ans = Math.min(ans, cur);
            }

            
        
            System.out.println(ans);
        }

    }
    
    

}