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.*;
import java.util.*;

/*
* @author: Ramanqul
* */
public class Main {
    private static boolean USE_TEST_CASES = true;


    private static List<Integer> dfs(int start, List<Integer>[] adj) {
        boolean v[] = new boolean[adj.length+1];

        List<Integer> res = new ArrayList<>();

        Stack<Integer> st = new Stack<>();

        st.push(start);

        while (!st.isEmpty()) {
            int x = st.pop();
            if (!v[x]) {
                res.add(x);
                boolean allVisited = true;
                for (int e: adj[x]) {
                    if (!v[e]) {
                        st.push(e);
                        allVisited = false;
                    }
                }

                if (allVisited) {
                    break;
                }

                v[x] = true;
            } else {
                break;
            }
        }

        return res;
    }

    private static void solve(MyScanner in, PrintWriter out) {
        int n = in.nextInt();

        List<Integer>[] adj= new ArrayList[n+1];

        for (int i=1;i<=n;i++) {
            if (adj[i] == null) {
                adj[i] = new ArrayList<>();
            }

            for (int j=2;j<=4;j++) {
                if (i-j > 0) {
                    adj[i].add(i-j);
                }
            }

            for (int j=2;j<=4;j++) {
                if (i+j<=n) {
                    adj[i].add(i+j);
                }
            }
        }

        for (int start=1;start<=n;start++) {
            List<Integer> ans = dfs(start, adj);
            if (ans.size() != n) {
                continue;
            } else {
                for (int x: ans) {
                    out.print(x + " ");
                }
                out.println();

                return;
            }
        }

        out.println(-1);
    }

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = 1;

        if (USE_TEST_CASES) {
            t = sc.nextInt();
        }

        for (int i=0;i<t;i++) {
            solve(sc, out);
        }
        out.close();
    }

    private static class Pair<A,B> {
        public A first;
        public B second;
        public Pair(A first, B second) {
            this.first = first;
            this.second = second;
        }
    }

    private static class Triple<A,B,C> {
        public A first;
        public B second;
        public C third;

        public Triple(A first, B second, C third) {
            this.first = first;
            this.second = second;
            this.third = third;
        }
    }

    private static class _ {
        public static void readArray(MyScanner in, int a[], int n) {
            for (int i=0;i<n;i++) {
                a[i] = in.nextInt();
            }
        }

        public static Pair<Integer, Integer>[] readIntPairs(MyScanner in, int n) {
            Pair[] pairs = new Pair[n];
            for (int i=0;i<n;i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                pairs[i] = new Pair<Integer, Integer>(x, y);
            }

            return pairs;
        }


        public static long gcd(long a, long b) {
            if (a == 0) {
                return b;
            }

            return gcd(b%a, a);
        }

        public static long lcm(long a, long b) {
            return (a * b) / gcd(a,b);
        }
    }

    private static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public MyScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        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;
        }

    }
}