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.awt.*;
import java.io.*;
import java.util.*;

public class Solution {
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        int t=sc.nextInt();
        while (t-->0){
                int n=sc.nextInt();
                if (n==5){
                    System.out.println(3+" "+5+" "+1+" "+4+" "+2);
                    continue;
                }
                ArrayList<Integer> odd=new ArrayList<>(),ev=new ArrayList<>();
                for (int i=1;i<=n;i+=2){
                    odd.add(i);
                }
                for (int i=2;i<=n;i+=2){
                    ev.add(i);
                }
                if (odd.size()<2){
                    System.out.println(-1);
                    continue;
                }else {
                    int pop1=odd.remove(odd.size()-1);
                    int pop2=odd.remove(odd.size()-1);
                    odd.add(pop1);odd.add(pop2);
                    int x=pop2-3;
                    if (x<1){
                        x=pop2+3;
                        if (x>n){
                            System.out.println(-1);
                            continue;
                        }
                    }
                        int i=-1;
                        for (int j=0;j<ev.size();j++){
                            if (ev.get(j)==x){
                                i=j;
                                break;
                            }
                        }
                        int eve[]=new int[ev.size()];
                        for (int j=0;j<ev.size();j++){
                            if (j<=i)continue;
                            eve[j]=ev.get(j);
                        }
                        int l=0;
                        int xr=x-2;
                        for (;x>=2;x-=4){
                            eve[l++]=x;
                        }
                        l=i;
                        for (;xr>=2 && eve[l]==0;xr-=4){
                            eve[l--]=xr;
                        }
                        int c=0;
                        int ans[]=new int[n];
                        for (int y:odd)ans[c++]=y;
                        for (int y:eve)ans[c++]=y;
                        if (ok(ans)){
                            StringBuilder sb=new StringBuilder();
                            for (i=0;i<n;i++)sb.append(ans[i]+" ");
                            System.out.println(sb);
                        }else {
                            System.out.println(-1);
                        }


                }
        }
    }
    static boolean ok(int a[]){
        for (int i=0;i<a.length-1;i++){
            if (Math.abs(a[i]-a[i+1])<2 || Math.abs(a[i]-a[i+1])>4)return false;
        }
        return true;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
