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.PrintWriter;
import java.util.Scanner;

public class SpecialPermutation {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int t = Integer.parseInt(in.nextLine());

        while (t-- > 0) {
            solve(in, out);
        }

        in.close();
        out.close();
    }

    public static void solve(Scanner in, PrintWriter out) {
        int n = in.nextInt();
        if( n < 4 ){
            out.println(-1);
        }else {
            for (int i = n; i >= 1 ; i--) if(i % 2 != 0) out.print(i + " ");

            out.print(4 + " " + 2 + " ");

            for (int i = 6; i <= n; i++) {
                if(i % 2 == 0) out.print(i + " ");
            }
            out.println();
        }
    }
}
