A permutation of length n is an array p=[p_1,p_2,...,p_n], which contains every integer from 1 to n (inclusive) and, moreover, each number appears exactly once. For example, p=[3,1,4,2,5] is a permutation of length 5.

For a given number n (n ≥ 2), find a permutation p in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between 2 and 4, inclusive. Formally, find such permutation p that 2 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ i < n).

Print any such permutation for the given integer n or determine that it does not exist.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.

Each test case is described by a single line containing an integer n (2 ≤ n ≤ 1000).

Output

Print t lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input


6
10
2
4
6
7
13


Output


9 6 10 8 4 7 3 1 5 2 
-1
3 1 4 2 
5 3 6 2 4 1 
5 1 3 6 2 4 7 
13 9 7 11 8 4 1 3 5 2 6 10 12 
import java.util.*;
import java.io.*;

public class spcl{

      
      public static void main(String args[])throws Exception{



              BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

              int t = Integer.parseInt(br.readLine());

              for(int k =0;k<t;k++){


              	 int n = Integer.parseInt(br.readLine());

              	

              	 if(n==2||n==3){
              	 	System.out.println(-1);
              	 	continue;
              	 }
              	 if(n==4){
              	 	System.out.println(2+" "+4+" "+1+" "+3);
              	 	continue;
              	 }
              	 if(n==5){
              	 	       	 	System.out.println(2+" "+4+" "+1+" "+3+" "+5);
              	 	       	 	continue;

              	 }

              	 for(int i =2;i<=n;i+=2){
              	 	System.out.print(i+" ");
              	 }
              	 int last =0;
              	 int secondOdd =0;
              	 if(n%2==0){
              	 	last=n-3;
              	 	secondOdd=last+2;
              	 } else{
              	 	last= n-4;
              	 	secondOdd=n;
              	 }

              	 System.out.print(last+" ");

              	 for(int i = secondOdd;i>=1;i-=2){
              	 	if(i==last){
              	 		continue;
              	 	}
              	 	if(i==1){
              	 		System.out.print(1);
              	 		continue;
              	 	}

              	 	 	 System.out.print(i+" ");


              	 }
              	 System.out.println();


              }


      }
   


}