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 CF1343D extends PrintWriter {
	CF1343D() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1343D o = new CF1343D(); o.main(); o.flush();
	}

	void main() {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			int[] aa = new int[n];
			for (int i = 0; i < n; i++)
				aa[i] = sc.nextInt();
			int[] dd = new int[k + k + 1 + 1];
			for (int i = 0, j = n - 1; i < j; i++, j--) {
				int a = aa[i], b = aa[j];
				int l, r;
				l = a + b + 1; r = k + Math.max(a, b);
				if (l <= r) {
					dd[l]++;
					dd[r + 1]--;
				}
				l = r + 1; r = k + k;
				if (l <= r) {
					dd[l] += 2;
					dd[r + 1] -= 2;
				}
				l = 1 + Math.min(a, b); r = a + b - 1;
				if (l <= r) {
					dd[l]++;
					dd[r + 1]--;
				}
				r = l - 1; l = 1 + 1;
				if (l <= r) {
					dd[l] += 2;
					dd[r + 1] -= 2;
				}
			}
			int ans = n;
			for (int a = 1 + 1; a <= k + k; a++)
				ans = Math.min(ans, dd[a] += dd[a - 1]);
			println(ans);
		}
	}
}