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:
//package constantpalindromesum;

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

public class constantpalindromesum {
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(fin.readLine());
		StringBuilder fout = new StringBuilder();
		while(t-- > 0) {
			StringTokenizer st = new StringTokenizer(fin.readLine());
			int n = Integer.parseInt(st.nextToken());
			int k = Integer.parseInt(st.nextToken());
			st = new StringTokenizer(fin.readLine());
			int[] nums = new int[n];
			for(int i = 0; i < n; i++) {
				nums[i] = Integer.parseInt(st.nextToken());
			}
			int[] pfx = new int[k * 2 + 1];
			for(int i = 0; i < n / 2; i++) {
				int a = nums[i];
				int b = nums[n - 1 - i];
				int min = Math.min(a, b) + 1;
				int max = Math.max(a, b) + k;
				pfx[0] += 2;
				pfx[min - 1] -= 2;
				pfx[min - 1] += 1;
				pfx[max] -= 1;
				pfx[max] += 2;
				pfx[a + b - 1] -= 1;
				pfx[a + b] += 1;
//				for(int j : pfx) {
//					System.out.print(j + " ");
//				}
//				System.out.println();
			}
			int min = Integer.MAX_VALUE;
			for(int i = 1; i < pfx.length; i++) {
				//System.out.print(pfx[i - 1] + " ");
				min = Math.min(min, pfx[i - 1]);
				pfx[i] += pfx[i - 1];
			}
			fout.append(min).append("\n");
		}
		System.out.print(fout);
	}
}