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.*;
import java.math.BigInteger;
public class GFG {
     public static void main (String[] args)throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		int t=sc.nextInt();
		while (t-->0)
		{
           int n=sc.nextInt();
           if(n==1)
           {
               System.out.println(1);continue;
           }
           if(n==2||n==3){
           System.out.println(-1);continue;}
           int m=n;
           if(n%2==0)
           n--;
           for(int i=n;i>=1;i-=2)
           out.print(i+" ");
           out.print(4+" ");
           out.print(2+" ");
           for(int i=6;i<=m;i+=2)
           out.print(i+" ");
           out.println();
           out.flush();
		}
     }
}