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.util.*;
import java.io.*;
public class d {
	static int n, k;
	static int[] arr;
	static int[] num;
	public static void main(String[] args) {
		FS sc = new FS();
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = sc.nextInt();
		for(int tt = 1; tt <= t; ++tt) {
			n = sc.nextInt();
			k = sc.nextInt();
			
			arr = new int[n];
			for(int i = 0; i < n; ++i) arr[i] = sc.nextInt();
			
			num = new int[k + k + 1];
			BIT bit = new BIT(k + k);
			
			for(int i = 0; i < n / 2; ++i) {
				int a1 = arr[i], a2 = arr[n - 1 - i];
				int min = Math.min(a1, a2), max = Math.max(a1, a2);
				int curr = a1 + a2;
				int l = curr - (max - 1);
				int r = curr + (k - min);
				
				++num[curr];
				bit.update(l, 1);
				if(r + 1 <= bit.n) bit.update(r + 1, -1);
			}
			
			int out = Integer.MAX_VALUE / 4;
			for(int sum = 2; sum <= k + k; ++sum) {
				int x = bit.sum(sum);
				int y = n / 2 - x;
				int curr = x - num[sum] + 2 * y;
				
				out = Math.min(out, curr);
			}
			
			pw.println(out);
		}
		pw.flush();
	}
	static class BIT{
		int n;
		int[] arr;
		BIT(int nn){
			arr = new int[(n = nn) + 1];
		}
		void update(int i, int v) {
			if(i > n) return;
			arr[i] += v;
			update(i + (i & -i), v);
		}
		int sum(int i) {
			if(i < 1) return 0;
			return arr[i] + sum(i - (i & -i));
		}
	}
	static class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while(!st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch(Exception e) {}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}