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 ConstantPalindromeSum {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

		int t = Integer.parseInt(br.readLine());

		while (--t >= 0) {
			String[] line = br.readLine().split(" ");
			int n = Integer.parseInt(line[0]), k = Integer.parseInt(line[1]);
			line = br.readLine().split(" ");
			int[] a = new int[n];
			for (int i = 0; i < n; ++i) {
				a[i] = Integer.parseInt(line[i]);
			}
			int half = n >> 1;
			int max = k << 1;

			int[] sums = new int[max];
			int[] count = new int[max];
			for (int i = 0; i < half; ++i) {
				int l = a[i], r = a[a.length-i-1];
				++count[l+r-2];
				if (l < r) {
					++sums[l-1];
					--sums[r+k-1];
				} else {
					--sums[l+k-1];
					++sums[r-1];
				}
			}
			for (int i = 1; i < max; ++i) {
				sums[i] += sums[i-1];
			}
			int min = n;
			for (int x = 0; x < max - 1; ++x) {
				int cost = n - count[x] - sums[x];
				if (cost < min) {
					min = cost;
				}
			}

			bw.write(Integer.toString(min));
			bw.newLine();
		}

		br.close();
		bw.close();
	}
}