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 Main {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static void solve() throws Exception {
		int n = sc.nextInt() / 2, k = sc.nextInt(), arr[][] = new int[2][n];
		for(int i = 0; i < n; i++) {
			arr[0][i] = sc.nextInt();
		}
		
		for(int i = n - 1; i >= 0; i--) {
			arr[1][i] = sc.nextInt();
		}
		
		int presum[] = new int[2 * k + 5];
		for(int i = 0; i < n; i++) {
			int sum = arr[0][i] + arr[1][i];
			int mx = Math.max(arr[0][i], arr[1][i]) - 1;
			int mn = k - Math.min(arr[0][i], arr[1][i]) + 1;
			
			presum[sum]--;
			presum[0] += 2;
			presum[sum - mx]--;
			presum[sum + 1]++;
			presum[sum + mn]++;
		}

		int ans = Integer.MAX_VALUE;
		for(int i = 1; i <= 2 * k; i++) {
			presum[i] += presum[i - 1];
			ans = Math.min(ans,presum[i]);
		}
		
		out.println(ans);
	}

	public static void main(String[] args) throws Exception {
		int tc = sc.nextInt();
		while (tc-- > 0) {
			solve();
		}
		out.close();
	}
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public Scanner(String file) throws Exception {
		br = new BufferedReader(new FileReader(file));
	}

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

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

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

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