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 Solution {
    static int[] a = new int[200000];
    static int[] cnt = new int[400001];
    static int[] pref = new int[400001];
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        for (int i = 0; i < t; i++){
            String[] nk = br.readLine().split(" ");
            String[] in = br.readLine().split(" ");
            int n = Integer.parseInt(nk[0]);
            int k = Integer.parseInt(nk[1]);
            for (int j = 0; j < n; j+=1){
                a[j] = Integer.parseInt(in[j]);
            }
            solve(n, k);
        }
    }
    private static void solve(int n, int k) {
        int i, l, r, target, au, min = n;
        for (i = 2; i <= 2 * k; i++){
            cnt[i] = 0;
            pref[i] = 0;
        }
        for (i = 0; i < n / 2; i++){
            cnt[a[i] + a[n - 1 - i]]++;
            l = Math.min(a[i], a[n - 1 - i]) + 1;
            r = Math.max(a[i], a[n - 1 - i]) + k + 1;
            pref[l]++;
            if (r <= 400000){
                pref[r]--;
            }
        }
        int prefsum = 0;
        for (target = 2; target <= 2 * k; target++){
            prefsum += pref[target];
            au =   n - cnt[target] - prefsum;
            min = Math.min(min, au);
        }
        System.out.println(min);
    }
}