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 G {
	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		int T = sc.nextInt();
		while (T-- > 0) {
			int N = sc.nextInt();
			
			if (N < 4) {
				System.out.println("-1");
			} else {
				LinkedList<Integer> dq = new LinkedList<>();
				for (int n : new int[] {3, 1, 4, 2}) dq.addLast(n);
				for (int K = 5; K <= N; K++) {
					if (K % 2 == 0) dq.addLast(K);
					else dq.addFirst(K);
				}
				
				for (int n : dq) {
					System.out.print(n + " ");
				}
				System.out.println();
			}
		}
	}
}
