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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Submit {
    public static void main(String argsp[]) throws IOException{
        process();
    }
    public static void process() throws IOException{
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(in.readLine());
        for(int t=0;t<T;t++){
            int n=Integer.parseInt(in.readLine());
            if(n<4)
                System.out.println("-1");
            else if(n==4)
                System.out.println("3 1 4 2");
            else{
                int x;
                if(n%2==0)
                    x=n;
                else
                    x=n-1;
                for(int i=x;i>0;i-=2)
                    System.out.print(i+" ");
                System.out.print("5 1 3 ");
                x=7;
                for(int i=x;i<=n;i+=2)
                    System.out.print(i+" ");
                System.out.println();
            }
        }
    }
}
