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 
// Working program with FastReader 
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class G_Special_Permutation{
    public static void main(String[] args) {
       FastReader sc=new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int test = sc.nextInt();
        for(int t=0;t<test;t++){
            int n =sc.nextInt();
            if(n<=3)out.println(-1);
            else if(n==4)out.println("3 1 4 2");
            else{
                int[] array = new int[n];
                int i = 1;
                // int k =0;
                // for(int k=0;k<n;k++){
                //     if(i<n){
                //         array[k] = i;
                //         i++;
                //     }

                // } 
                int k = 0;
                while(i<=n){
                    array[k] = i;
                    i+=2;
                    k++;
                }
                i-=2;
                i-=3;
                array[k] = i;
                k++;
                if(i+4<=n){
                    i+=4;
                    array[k] = i;
                    k++;
                    i-=2;
                    array[k]= i;
                    k++;
                    i-=4;
                }
                else{
                    i+=2;
                    array[k] = i;
                    k++;
                    i-=4;
                }
                while(i>1){
                    array[k] = i;
                    i-=2;
                    k++;
                }
                for(i =0;i<n;i++){
                    out.print(array[i]+" ");
                }
                out.println();

            }
            
        }
        out.close();
    }
    
    public static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 

        public FastReader() 
        { 
            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; 
        } 
}
}
