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;

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 sz = 2*k+1;
			int cnt[] = new int[sz];
			Arrays.fill(cnt, 0);
			for (int i=0;i<n/2;i++) {
				int sum = a[i] + a[n-i-1];
				cnt[sum]++;
			}
			
			int pref[] = new int[sz+1];
			for (int i=0;i<n/2;i++) {
				int l1 = 1 + a[i], r1 = k + a[i];
				int l2 = 1+a[n-i-1], r2 = k + a[n-i-1];
				pref[Math.min(l1, l2)]++;
				pref[Math.max(r1, r2)+1]--;
			}
			for (int i=1;i<sz+1;i++) {
				pref[i] = pref[i] + pref[i-1];
			}
			
			int ans = (int) 1e9;
			for (int sum=2;sum<sz;sum++) {
				int minop = pref[sum]-cnt[sum] + (n/2-pref[sum])*2;
				ans = Math.min(ans, minop);
			}
			
			System.out.println(ans);
		}
		in.close();
	}
	
}