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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Main().new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Main solver = new Main();
		solver.solve(1, in, out);
		out.close();
	}
	
	public void solve(int testNumber, Scanner in, PrintWriter out) {
		int t = in.nextInt();
		for(int i = 0; i < t; i++) {
			int n = in.nextInt();
			int k = in.nextInt();
			int[] arr = in.nextIntArray(n);
			
			int[] sumMap = new int[2 * k + 10];
			int[] pSum = new int[2 * k + 10];
			int[] result = new int[2 * k + 10];
			
			for(int j = 0; j < n / 2; j++) {
				int sum = arr[j] + arr[n-j-1];
				int min = arr[j] > arr[n-j-1] ? arr[n-j-1] : arr[j];
				int max = sum - min;
				sumMap[sum]++;
				pSum[min + 1] += 1;
				pSum[max + k + 1] -= 1;
			}
			
			for(int j = 2; j <= 2 * k + 1; j++) {
				pSum[j] = pSum[j-1] + pSum[j];
			}
			
			int minRepl = n / 2;
			for(int j = 2; j <= 2 * k; j++) {
				int c0 = sumMap[j];
				int c1 = pSum[j];
				int c2 = n / 2 - c1;
				int repl = -c0 + c1 * 1 + c2 * 2;
				if(repl < minRepl) minRepl = repl;
			}
			
			out.println(minRepl);
		}
	}
	
	class Scanner {
		BufferedReader br;
		StringTokenizer in;

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

		public String next() {
			return hasMoreTokens() ? in.nextToken() : null;
		}

		public String readLine() {
			try {
				return br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
				return null;
			}
		}

		boolean hasMoreTokens() {
			while (in == null || !in.hasMoreTokens()) {
				String s = readLine();
				if (s == null)
					return false;
				in = new StringTokenizer(s);
			}
			return true;
		}

		public String nextString() {
			return next();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}
	}
}