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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class main {
	
	public static ArrayList<Long> list=new ArrayList<Long>();
	
	public static List<Integer> cnt,pref;
	
	
	
    private static final Scanner scanner = new Scanner(System.in);

	public static void main(String[] args) {
		
		int t=scanner.nextInt();
	    while(t>0) {
	    	
	    	int n=scanner.nextInt();
	    	int k=scanner.nextInt();
	    	pref = new ArrayList<Integer>(Collections.nCopies(2*k+10, 0));
	    	 cnt = new ArrayList<Integer>(Collections.nCopies(2*k+10, 0));
	    	List<Integer> ai=new ArrayList<Integer>();
	    	for(int i =0;i<n;i++) {
	    		int a=scanner.nextInt();
	    		ai.add(a);
	    	}
	    	for(int i=0;i<n/2;i++) {
	    		int x=ai.get(i)+ai.get(n-i-1);
	    		cnt.set(x, cnt.get(x)+1);
	    		
	    		int l=Math.min(ai.get(i), ai.get(n-i-1))+1;
	    		int h=Math.max(ai.get(i), ai.get(n-i-1))+k;
	    		
	    		
	    		
	    		pref.set(l,pref.get(l)+1);
	    		pref.set(h+1, pref.get(h+1)-1);
	    		
	    	}
	    	int sum=0;
	    	for(int i=0;i<2*k+10;i++) {
	    		sum+=pref.get(i);
	    		
	    		pref.set(i,sum);
	    	}
	    	int mini=n;
	    	for(int i=2;i<2*k+1;i++) {
	    		
	    		int cn=(pref.get(i)-cnt.get(i))+(n/2-pref.get(i))*2;
	    		
	    		mini=Math.min(cn, mini);
	    	}
	    	System.out.println(mini);
	    	
	    	 t--;
	    
	    	
	    }
	    
	    	
	    	
	    	
		

}
}