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.*;
import java.lang.*;
import java.io.IOException;


public class solution{
	static int[]array;
	private static Scanner in = new Scanner(System.in);
	public static void main(String[]args)throws IOException{
		StringBuilder ans = new StringBuilder("");
		int t = in.nextInt();
		while(t-- > 0){
			ans.append(solve()).append("\n");
		}
		System.out.println(ans);
	}
	static StringBuilder solve(){
		StringBuilder ans = new StringBuilder("");
		int n = in.nextInt();
		int tmp = n/2;
		if(tmp%2 !=0){
			ans.append("NO");
			return ans;
		}else{
			ans.append("YES").append("\n");
		}
		array = new int[n];
		int evensum = 0;
		for(int i=0,j=2;i<n/2;i++,j+=2){
			array[i] = j;
			evensum += j;
		}
		int oddsum = 0;
		for(int i=n/2,j=1;i<n-1;i++,j+=2){
			array[i] = j;
			oddsum += j;
		}
		array[n-1] = evensum-oddsum;
		for(int i=0;i<n;i++){
			ans.append(array[i]).append(" ");
		}
		return ans;
	}
}