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 File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		int T = sc.nextInt();
		
		for (int t = 1; t <= T; t++) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			
			int[] a = new int[n];
			
			for (int i = 0; i < n; i++) {
				a[i] = sc.nextInt();
			}
			
			
						
			
			// How many pairs already equal to each sum.
			int[] counts = new int[2*k + 1];
			
			for (int i = 0; i < n / 2; i++) {
				int total = a[i] + a[n-i-1];
				counts[total]++;
			}
			
			
			
			// At each index, how many can reach the sum within at most 1 move.
			int[] prefix = new int[2*k + 2];
			
			for (int i = 0; i < n / 2; i++) {
				int x = a[i];
				int y = a[n-i-1];
				
				int min = Math.min(x, y) + 1;
				int max = Math.max(x, y) + k;
				
				prefix[min]++;
				prefix[max+1]--;
			}
			
			
			for (int i = 1; i <= 2*k + 1; i++) {
				prefix[i] += prefix[i-1];
			}
			
			
			int min = n;
			
			
			for (int total = 2; total <= 2*k; total++) {
				int moves = 0;
				// Total pairs that can reach the target. 0 or 1 moves.
				moves += prefix[total];
				// Subtract pairs that need 0 moves.
				moves -= counts[total];
				
				// Pairs that require 2 moves to reach.
				int twoMoves = ((n/2) - prefix[total]);
				moves += 2 * twoMoves;
				
				min = Math.min(min, moves);
			}
			
			
			
			out.println(min);
		}
		
		out.close();
	}
}