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.*;
import java.io.*;
public class f {
	static final FS sc = new FS();
	static final PrintWriter pw = new PrintWriter(System.out);
	
	static final int max = 500;
	
	static int n;
	static int[] arr, idx;
	static ArrayList<Integer> steps;
	public static void main(String[] args) {
		int t = sc.nextInt();
		scan : for(int tt = 1; tt <= t; ++tt) {
			n = sc.nextInt();
			num[] nums = new num[n];
			for(int i = 0; i < n; ++i) {
				int in = sc.nextInt();
				nums[i] = new num(in, i);
			}
			
			Arrays.sort(nums);
			if(solve(nums)) continue scan;
			else {
				// then switch the first two things that are the same value
				for(int i = 0; i < n - 1; ++i) {
					if(nums[i].val == nums[i + 1].val) {
						// switch these two
						num num1 = new num(nums[i].val, nums[i].idx);
						num num2 = new num(nums[i + 1].val, nums[i + 1].idx);
						
						nums[i] = new num(num2.val, num2.idx);
						nums[i + 1] = new num(num1.val, num1.idx);
						
						solve(nums);
						continue scan;
					}
				}
			}
			
			pw.println(-1);
		}
		pw.flush();
	}
	static boolean solve(num[] nums) {
		arr = new int[n + 1];
		for(int i = 0; i < n; ++i) arr[nums[i].idx + 1] = i + 1;
		idx = new int[n + 1];
		for(int i = 1; i <= n; ++i) idx[arr[i]] = i;
		
		steps = new ArrayList<>();
		for(int a = 1; a <= n - 2; ++a) {
			int i = idx[a];
			
			// move this thing
			while(i >= a + 2) {
				// do a cyclic shift
				shift(i - 2);
				i -= 2;
			}
			
			// we in a weird spot
			if(i >= a + 1) {
				shift(i - 1);
				shift(i - 1);
			}
		}
		
		if(arr[n - 1] < arr[n]) {
			// weGood; print
			pw.println(steps.size());
			for(int a : steps) pw.print(a + " ");
			pw.println();
			return true;
		}
		
		return false;
	}
	static void shift(int i) {
		int temp = arr[i + 2];
		arr[i + 2] = arr[i + 1];
		arr[i + 1] = arr[i];
		arr[i] = temp;
		
		for(int j = i; j <= i + 2; ++j) {
			idx[arr[j]] = j;
		}
		
		steps.add(i);
	}
	static class num implements Comparable<num>{
		int val, idx;
		num(int vv, int ii){
			val = vv;
			idx = ii;
		}
		public int compareTo(num in) {
			if(val != in.val) return Integer.compare(val, in.val);
			return Integer.compare(idx, in.idx);
		}
	}
	static class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while(!st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch(Exception e) {}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}