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 {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(in.readLine());
		for (int i = 0; i < t; i++) {
			StringTokenizer token = new StringTokenizer(in.readLine());
			int n = Integer.parseInt(token.nextToken());
			int k = Integer.parseInt(token.nextToken());
			int[] pre = new int[2 * k + 1];
			token = new StringTokenizer(in.readLine());
			int[] A = new int[n];
			for (int a = 0; a < n; a++)
				A[a] = Integer.parseInt(token.nextToken());
			for (int a = 0; a < n / 2; a++) {
				int x = A[a];
				int y = A[n - 1 - a];
				int min = Math.min(x, y);
				int max = Math.max(y, x);
				int sum = x + y;
				pre[2] += 2;
				pre[Math.max(2, min + 1)] -= 1;
				pre[sum] -= 1;
				if (sum + 1 <= 2 * k)
					pre[sum + 1] += 1;
				if (max + k < 2 * k)
					pre[max + k + 1] += 1;
			}
			int best = Integer.MAX_VALUE;
			int curr = 0;
			for (int a = 2; a < pre.length; a++) {
				curr += pre[a];
				best = Math.min(best, curr);
			}
			System.out.println(best);
		}
	}
}