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 _1352G {
        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.print("-1");
                else {
                    int maxEven=-1;
                    if(n%2==0)
                        maxEven=n;
                    else
                        maxEven=n-1;

                    int put=2;
                    for(int i=0;i<(n/2)/2;i++) {
                        System.out.print(put+ " ");
                        put += 4;
                    }
                    System.out.print(maxEven+ " ");
                    if((n/2)%2!=0)
                        maxEven-=2;
                    else
                        maxEven-=4;
                    for(int i=maxEven;i>=4;i-=4)
                        System.out.print(i+ " ");
                    int maxOdd=(n%2==0)?n-1:n;
                    put=1;
                    for(int i=0;i<((n+1)/2)/2;i++){
                        System.out.print(put + " ");
                        put+=4;
                    }
                    System.out.print(maxOdd+ " ");
                    if(((n+1)/2)%2!=0)
                        maxOdd-=2;
                    else
                        maxOdd-=4;
                    for(int i=maxOdd;i>=3;i-=4)
                        System.out.print(i + " ");
                }
                System.out.println();
            }
        }
    }
