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.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int t = nextInt();
        for (int q = 0; q < t; q++) {
            int n = nextInt();
            int k = nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            int[] cnt = new int[2 * k + 1];
            int[] pref = new int[2 * k + 2];
            for (int i = 0; i < n / 2; i++) {
                cnt[a[i] + a[n - i - 1]]++;
            }
            for (int i = 0; i < n / 2; i++) {
                int lower = min(a[i], a[n - i - 1]) + 1;
                int upper = max(a[i], a[n - i - 1]) + k;
                pref[lower]++;
                pref[upper + 1]--;
            }
            for (int i = 1; i < pref.length; i++) {
                pref[i] += pref[i - 1];
            }
            int ans = Integer.MAX_VALUE;
            for (int i = 2; i < cnt.length; i++) {
                ans = min(ans, pref[i] - cnt[i] + (n / 2 - pref[i]) * 2);
            }
            pw.println(ans);
        }
        pw.close();
    }

    static StringTokenizer st = new StringTokenizer("");
    static BufferedReader br;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}