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.Arrays;
import java.util.Scanner;

/**
 * Spend 5 to 10 minutes analyzing different approaches to solve
 * Don't rush and start coding first solution that comes to mind
 * Right now best strategy is analyze for 20 minutes and code 20 minutes
 * 3 question 2 hour. Remaining 30 minutes is miscellaneous
 * Simply coding and coding won't solve problem, analyzing then coding will solve it
 */
public class Codeforces {

	public static void main(String args[]) {
		Scanner in = new Scanner(System.in);
		int t = in.nextInt();
		while (t-- > 0) {
			int n = in.nextInt(), k = in.nextInt();
			int a[] = new int[n];
			for (int i=0;i<n;i++) a[i] = in.nextInt();
			
			int s = 2*k+2;
			
			int zero[] = new int[s];
			Arrays.fill(zero, 0);
			for (int i=0;i<n/2;i++) {
				zero[a[i] + a[n-i-1]]++;
			}
			
			int one[] = new int[s];
			Arrays.fill(one, 0);
			for (int i=0;i<n/2;i++) {
				int l1 = a[i]+1, r1 = a[i]+k+1;
				int l2 = a[n-i-1]+1, r2 = a[n-i-1]+k+1;
				one[Math.min(l1, l2)]++;
				one[Math.max(r1, r2)]--;
			}
			
			for (int i=1;i<s;i++) {
				one[i] = one[i] + one[i-1];
			}
			
			int ans = Integer.MAX_VALUE;
			for (int i=2;i<=2*k;i++) {
				int sum = (one[i]-zero[i]) + (n/2-one[i])*2;
				ans = Math.min(ans, sum);
			}
			System.out.println(ans);
		}
		in.close();
	}
	
}