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.io.*;
import java.util.*;

public class CF1374F extends PrintWriter {
	CF1374F() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1374F o = new CF1374F(); o.main(); o.flush();
	}

	void main() {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int[] aa = new int[n];
			for (int i = 0; i < n; i++)
				aa[i] = sc.nextInt();
			boolean inv = false;
			for (int i = 0; i < n; i++)
				for (int j = i + 1; j < n; j++)
					if (aa[i] > aa[j])
						inv = !inv;
			Integer[] ii = new Integer[n];
			for (int h = 0; h < n; h++)
				ii[h] = h;
			Arrays.sort(ii, (i, j) -> aa[i] != aa[j] ? aa[i] - aa[j] : i - j);
			if (inv)
				for (int h = 1; h < n; h++)
					if (aa[ii[h - 1]] == aa[ii[h]]) {
						int tmp = ii[h - 1]; ii[h - 1] = ii[h]; ii[h] = tmp;
						inv = false;
						break;
					}
			if (inv) {
				println(-1);
				continue;
			}
			for (int a = 0; a < n; a++)
				aa[ii[a]] = a;
			int[] qu = new int[n * n]; int cnt = 0;
			for (int a = n - 1; a >= 0; a--) {
				int i = 0;
				while (i < n && aa[i] != a)
					i++;
				while (i + 2 <= a) {
					qu[cnt++] = i;
					aa[i] = aa[i + 2]; aa[i + 2] = aa[i + 1]; aa[i + 1] = a;
					i++;
				}
				if (i + 1 == a) {
					qu[cnt++] = i - 1;
					aa[i] = aa[i - 1]; aa[i - 1] = aa[i + 1]; aa[i + 1] = a;
					i++;
				}
			}
			println(cnt);
			for (int h = 0; h < cnt; h++)
				print(qu[h] + 1 + " ");
			println();
		}
	}
}