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 SpecialPermutation{
    StringTokenizer st;
    BufferedReader br;
    public void run() throws Exception{
        br = new BufferedReader(new InputStreamReader(System.in));
        int t = in();
        while(t-- > 0){
            int n = in(), l = 0, r = n-1, e = 1, tp;
            if(n < 4){
                System.out.println(-1);
                continue;
            }
            int[] arr = new int[n];
            int m = n%2 == 0 ? (n/2)-1 : (n/2)+1;
            while(l <= r){
                arr[l++] = e++;
                if(l > r) break;
                arr[r--] = e++;
            }
            if(n%2 == 0){
                tp = arr[m];
                arr[m] = arr[m-1];
                arr[m-1] = tp;
            }
            else{
                tp = arr[m];
                arr[m] = arr[m+1];
                arr[m+1] = tp;
            }
            for(int el: arr)
                System.out.print(el + " ");
            System.out.print("\n");
        }
    }
    Integer in() throws Exception{
        return Integer.parseInt(nextToken());
    }
    String nextToken() throws Exception{
        if(st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    public static void main(String[] args) throws Exception{
        new SpecialPermutation().run();
    }
}