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.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;


public class Main {
    static String[][][] ans = new String[101][101][101];
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int num = in.nextInt();
        while (num-- != 0) {
            int x = in.nextInt();
            System.out.println(fun(x));

        }
    }

    static String fun (int x) {
        if (x <= 3) return "-1";
        if (x == 4) return "3 1 4 2";
        StringBuffer bf = new StringBuffer("3 1 4 2 ");
        for (int i = 5; i <= x ; i++) {
            if (i % 2 == 1) { bf.insert(0, i + " "); }
            else { bf.append(i + " "); }

        }
        return bf.toString();
    }
}
class D {
    int x ;
    int y ;
    int z ;
    String data;
    public D (int x, int y, int z, String d) {
        this.x = x;
        this .y = y;
        this.z = z;
        this.data = d;
    }
}
