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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;


public class Ar {

	public static void main(String[]args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter pr = new PrintWriter(System.out);
	    int n = Integer.parseInt(br.readLine());
	    for(int i=0 ; i<n ; i++){
	    	int m = Integer.parseInt(br.readLine());
    		int[]x = new int[m];
	    	if(m%4!=0)
	    		pr.println("NO");
	    	else{
	    		pr.println("YES");
	    		int d = 2;
	    		int e = 1;
	    		for(int j=0 ; j<m-1 ;j++){
	    			if(j<m/2){
	    			x[j]=d;
	    			d+=2;
	    			}
	    			else{
	    				x[j]=e;
	    				e+=2;
	    			}
	    		}
	    		x[m-1] = x[m-2] + x[(m/2)-(m/4)];
	    		for(int k=0 ; k<m ; k++){
	    			pr.print(x[k] + " ");
	    		}
	    		pr.println();
	    	}
	    // pr.println(Arrays.toString(x));
	    }
	    pr.flush();
	}
}