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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main{
	
	
	
	
	   public static void main(String[] args) {
	      MyScanner sc = new MyScanner();
	      out = new PrintWriter(new BufferedOutputStream(System.out));
	      
	      int testcase = sc.nextInt();
	      for( int t=1 ; t<=testcase ; ++t ) {
	    	  int n = sc.nextInt();
	    	  if( n%4!=0 ) {
	    		  System.out.println("NO");
	    		  continue;
	    	  }
	    	  System.out.println("YES");
	    	  int arr[] = new int[n];
	    	  int odd=1,even=2,ind=1,oddInd=n-1,evenInd=0;
	    	  while( ind<=n/4 ) {
	    		  arr[evenInd++] = even;
	    		  arr[oddInd--] = odd;
	    		  odd += 2;
	    		  even += 2;
	    		  ++ind;
	    	  }
	    	  ind=1;
	    	  odd += 2;
	    	  while( ind<=n/4 ) {
	    		  arr[evenInd++] = even;
	    		  arr[oddInd--] = odd;
	    		  odd += 2;
	    		  even += 2;
	    		  ++ind;
	    	  }
	    	  for( int i=0 ; i<n ; ++i ) {
	    		  System.out.print(arr[i]+" ");
	    	  }
	    	  System.out.println();
	      }

	      out.close();
	   }

	     

	   //-----------PrintWriter for faster output---------------------------------
	   public static PrintWriter out;
	      
	   //-----------MyScanner class for faster input----------
	   public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }

	   }
	   //--------------------------------------------------------
	}