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 
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */



import java.util.Scanner;

/**
 *
 * @author Pieter
 */
public class G {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder("");

        int tests = sc.nextInt();

        for(int t = 0; t < tests; t++) {
            int n = sc.nextInt();
            
            
            if(n <= 3) {
                sb.append("-1\n");
            } else {
                if(n == 4) {
                    sb.append("2 4 1 3\n");
                } else {
                    int num = n;
                    
                    while(num >= 1) {
                        sb.append(num + " ");
                        num -= 2;
                    }
                                       
                    if(n%2==0) {
                        sb.append("5 1 3 ");
                        num = 7;
                    } else {
                        sb.append("4 2 ");
                        num = 6;
                    }
                    
                    while(num<=n) {
                        sb.append(num + " ");
                        num+=2;
                    }
                    
                    sb.append("\n");
                }
            }
            //numbers 1, 2, n-1, n.
            //place them so that difference is between 2 and 4 always
            //11-9-7-5-3-1-4-2-6-8-10
            //10-8-6-4-2-5-1-3-7-9      
            //5-3-1-4-2
            //6-4-2-5-1-3
        }

        System.out.println(sb);
    }
}
