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.BufferedWriter;
import java.io.File;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Scanner;

public class G1352 {
	public static void main(String[] args) throws IOException{
		Scanner scanner = new Scanner(System.in);
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		int cases = scanner.nextInt();
		for(int i = 0; i < cases; i++) {
			int n = scanner.nextInt();
			int mod = (n + 1) % 2;
			int[] per = new int[n];
			if(n > 3) {
				for(int j = 0; j < (n + 1) / 2 ; j++)
					per[j] = n - j * 2 - mod;
				per[(n + 1 )/ 2] = 4;
				per[(n + 1 )/ 2 + 1] = 2;
				for(int j = (n + 1 )/ 2 + 2; j < n; j++)
					per[j] = (j - (n + 1) / 2 + 1) * 2 ;
				for(int j: per)
					log.write("" + j + " ");
			}
			else
				log.write("-1");
			log.write("\n");
		}
		log.flush();
	}
}
