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.*;

public class SpecialPermutation {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int testCases = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for (int t = 0; t < testCases; t++) {
            int n = sc.nextInt();
            if (n < 4) {
                sb.append("-1").append("\n");
                continue;
            }
            Deque<Integer> q = new ArrayDeque<>();
            q.add(3);
            q.add(1);
            q.add(4);
            q.add(2);
            int turn = 0;
            for (int i = 5; i <= n; i++) {
                if (turn == 0) {
                    q.addFirst(i);
                } else {
                    q.addLast(i);
                }
                turn = turn ^ 1;
            }
            while (q.size() > 0) {
                sb.append(q.removeFirst() + " ");
            }
            sb.append("\n");
        }
        System.out.print(sb);
    }
}