Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

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 only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in JAVA):

Solution:
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.min;

//javac Solution2.java
//python interactive_runner.py python.exe testing_tool.py 0 -- java Solution2
//change name before submit

public class Solution2 {

	public static void main(String args[]) {
		Scanner input = new Scanner(System.in);
		int T = input.nextInt();
		for (int i = 1; i <= T; i++) {
			int a = input.nextInt();
			int k = input.nextInt();
			int[] array = new int[k * 2 + 2];
			int [] aa = new int[a];
			for (int ii = 0; ii < a; ii++) {
				aa[ii] = input.nextInt();
			}
			for (int ii = 0; ii < a / 2; ii++) {
				int b = aa[ii];
				int c = aa[a - ii - 1];
				array[2] = array[2] + 2;
				array[min(b, c) + 1] = array[min(b, c) + 1] - 1;
				array[b + c] = array[b + c] - 1;
				array[b + c + 1] = array[b + c + 1] + 1;
				array[max(b, c) + k + 1] = array[max(b, c) + k + 1] + 1;
			}
			int res = array[2];
			int pom = array[2];
			for (int ii = 3; ii <= k * 2; ii++) {
				pom = pom + array[ii];
				if (pom < res) {
					res = pom;
				}
			}
			System.out.println(res);
		}
	}
}