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.*;

public class contest {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		
		while(t--!=0) {
			int n = s.nextInt();
			int k = s.nextInt();
			int a[] = new int[n];
			
			for(int i=0;i<n;i++) {
				a[i] = s.nextInt();
			}
			
			int zero[] = new int[2*k+5];
			int one[] = new int[2*k+5];
			
			for(int i=0;i<n/2;i++) {
				int A = Math.min(a[i], a[n-i-1]);
				int B = Math.max(a[i], a[n-i-1]);
				
				zero[A+B]++;
				one[A+1]++;
				one[B+k+1]--;
			}
			
			for(int i=2;i<=2*k;i++) {
				one[i]+=one[i-1];
			}
			int min = Integer.MAX_VALUE;
			for(int i=2;i<=2*k;i++) {
				int Z = zero[i];
				int O = one[i];
				int T = n/2 - one[i];
				
				min = Math.min(min, O-Z+2*T);
			}
			System.out.println(min);
		}
			
		
	}
}