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

		}
	}
}