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:
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

import java.io.*;
import java.util.*;

import static java.lang.Math.*;


public class Main {
    static int infi = Integer.MAX_VALUE / 2, mod = 1000000007, maxn = 3 * (int) 1e5;
    static long infl = Long.MAX_VALUE / 2;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int t = nextInt();
        for (int t123 = 0; t123 < t; t123++) {
            int n = nextInt();
            int k = nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            int[] sum = new int[2 * k + 2];
            for (int i = 0; i < n / 2; i++) {
                int x = max(a[i], a[n - 1 - i]);
                int y = min(a[i], a[n - 1 - i]);
                sum[2] += 2;
                sum[y + 1]--;
                sum[x + k + 1]++;
                sum[x + y]--;
                sum[x + y + 1]++;
            }
            int ans = infi;
            int kol = 0;
            for (int i = 2; i < sum.length; i++) {
                kol += sum[i];
                ans = min(ans, kol);
            }
            out.println(ans);
        }
        out.close();
    }

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

    static String next() throws IOException {
        while (!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());
    }

}

class f {
    int v, c;

    public f(int x, int y) {
        this.v = x;
        this.c = y;
    }
}