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 
/*package whatever //do not write package name here */
import java.util.*;
import java.io.*;

public final class GFG {
	public static void main (String[] args) {
	    Scanner sc = new Scanner(System.in);
	    int t = sc.nextInt();
	    while(t-->0) {
	        int n = sc.nextInt();
	        if(n<=3) {
	            System.out.println(-1);
	            continue;
	        }
	        if(n==4) {
	            System.out.println("3 1 4 2");
	        }
	        else {
	            int even = n/2;
	            int odd = n-even;
	            int[] o = new int[odd];
	            int[] e = new int[even];
	            for(int i = 0; i<even; i++)
    	            e[i] = i*2+2;
    	        for(int i = 0; i<odd; i++)
        	        o[i] = i*2+1;
        	    if(odd==even) {
            	    int t1 = o[odd-1];
            	    int t2 = o[odd-2];
            	    o[odd-2] = t1;
            	    o[odd-1] = t2;
            	    for(int i: e)
                	    System.out.print(i + " ");
                	for(int i = odd-1; i>=0; i--)
                    	System.out.print(o[i] + " ");
        	    }
        	    else {
        	        int t1 = e[even-1];
        	        int t2 = e[even-2];
        	        e[even-1] = t2;
        	        e[even-2] = t1;
        	        for(int i: o) 
            	        System.out.print(i + " ");
            	    for(int i = even-1; i>=0; i--)
                	    System.out.print(e[i] + " ");
        	    }
                System.out.println();
	        }
	    }
	}
}