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.io.*;
import java.math.*;
import java.util.*;


// @author : Dinosparton 

public class test {
	 
	   static class Pair{ 
		   long x;
		   long y;
		   
		   Pair(long x,long y){ 
			   this.x = x;
			   this.y = y;
			   
		   }
	   }
	  
	   static class Compare { 
		   
		     void compare(Pair arr[], int n) 
		    { 
		        // Comparator to sort the pair according to second element 
		        Arrays.sort(arr, new Comparator<Pair>() { 
		            @Override public int compare(Pair p1, Pair p2) 
		            { 
		            	if(p1.x!=p2.x) {
		                return (int)(p1.x - p2.x); 
		            	}
		            	else { 
		            		return (int)(p1.y - p2.y);
		            	}
		            } 
		        }); 
		  
//		        for (int i = 0; i < n; i++) { 
//		            System.out.print(arr[i].x + " " + arr[i].y + " "); 
//		        } 
//		        System.out.println(); 
		    } 
		} 
	 
	   static class Scanner {
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public Scanner()
	        {
	            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;
	        }
	    }
	
	  static void swap (int a[],int i,int j) { 
		  
		  int temp = a[i];
		  a[i] = a[j];
		  a[j] = temp;
	  }
	   public static void main(String args[]) throws Exception { 
		
		   Scanner sc = new Scanner();
		   StringBuffer res = new StringBuffer();
		   
		   int tc = sc.nextInt();
		   
		   while(tc-->0) { 
			
			int n = sc.nextInt();
			
			if(n==2 || n==3) { 
				System.out.println(-1);
				continue;
			}
			else if(n==4) { 
				System.out.println(2+" "+4+" "+1+" "+3);
				continue;
			}
			int ans[] = new int[n];
			
			int p = 0;
			
			for(int i=1;i<=n;i += 2) {  
				ans[p] = i;
				p++;
			}
			
			for(int j= n - (n%2);j>=2;j-=2) { 
				ans[p] = j;
				p++;
			}
			
			if(n%2!=0) { 
				
				int i = (n+1)/2;
				
				swap(ans,i,i+1);
			}
			else { 
				
				int i = n/2;
				swap(ans,i+1,i+2);
				swap(ans,i,i+1);
				
			}
			
			for(int i=0;i<n;i++) { 
				System.out.print(ans[i]+" ");
			}
			System.out.println();
		   }
			System.out.println(res);
		  
	   }
}  




