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 
/*
ID: davidzh8
PROG: subset
LANG: JAVA
 */

import java.io.*;
import java.util.*;
import java.lang.*;

public class specialpermutation {
    //Start Stub
    static long startTime = System.nanoTime();
    //Globals Go Here

    //Globals End
    public static void main(String[] args) throws IOException {
        FastScanner sc = new FastScanner("specialpermutation.in", true);
        FastWriter pw = new FastWriter("specialpermutation.out", true);
        int tcs= sc.ni();
        while(tcs-->0){
            int N= sc.ni();
            if(N<4) System.out.println(-1);
            else{
                ArrayDeque<Integer> dq= new ArrayDeque<>();
                dq.addLast(3); dq.addLast(1); dq.addLast(4); dq.addLast(2);
                for (int i = 5; i <= N; i++) {
                    if(i%2==1) dq.addLast(i);
                    else dq.addFirst(i);
                }
                while(!dq.isEmpty()) System.out.print(dq.poll()+" ");
                System.out.println();
            }
        }





        /* End Stub */
        long endTime = System.nanoTime();
        //System.out.println("Execution Time: " + (endTime - startTime) / 1e9 + " s");
        pw.close();
    }


    static class Edge implements Comparable<Edge> {
        int w;
        int a;
        int b;

        public Edge(int w, int a, int b) {
            this.w = w;
            this.a = a;
            this.b = b;

        }

        public int compareTo(Edge obj) {
            if (obj.w == w) {
                if (obj.a == a) {
                    return b - obj.b;
                }
                return a - obj.a;
            } else return w - obj.w;
        }
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair obj) {
            if (obj.a == a) {
                return b - obj.b;
            } else return a - obj.a;
        }
    }

    static class SegmentTree {
        public long[] arr;
        public long[] tree;
        public int N;

        //Zero initialization
        public SegmentTree(int n) {
            N = n;
            arr = new long[N];
            tree = new long[4 * N + 1];
        }

        public long query(int treeIndex, int lo, int hi, int i, int j) {
            // query for arr[i..j]
            if (lo > j || hi < i)
                return 0;
            if (i <= lo && j >= hi)
                return tree[treeIndex];
            int mid = lo + (hi - lo) / 2;

            if (i > mid)
                return query(2 * treeIndex + 2, mid + 1, hi, i, j);
            else if (j <= mid)
                return query(2 * treeIndex + 1, lo, mid, i, j);

            long leftQuery = query(2 * treeIndex + 1, lo, mid, i, mid);
            long rightQuery = query(2 * treeIndex + 2, mid + 1, hi, mid + 1, j);

            // merge query results
            return merge(leftQuery, rightQuery);
        }

        public void update(int treeIndex, int lo, int hi, int arrIndex, long val) {
            if (lo == hi) {
                tree[treeIndex] = val;
                arr[arrIndex] = val;
                return;
            }

            int mid = lo + (hi - lo) / 2;

            if (arrIndex > mid)
                update(2 * treeIndex + 2, mid + 1, hi, arrIndex, val);
            else if (arrIndex <= mid)
                update(2 * treeIndex + 1, lo, mid, arrIndex, val);

            // merge updates
            tree[treeIndex] = merge(tree[2 * treeIndex + 1], tree[2 * treeIndex + 2]);
        }

        public long merge(long a, long b) {
            return (a + b);
        }
    }

    static class djset {
        int N;
        int[] parent;

        // Creates a disjoint set of size n (0, 1, ..., n-1)
        public djset(int n) {
            parent = new int[n];
            N = n;
            for (int i = 0; i < n; i++)
                parent[i] = i;
        }

        public int find(int v) {

            // I am the club president!!! (root of the tree)
            if (parent[v] == v) return v;

            // Find my parent's root.
            int res = find(parent[v]);

            // Attach me directly to the root of my tree.
            parent[v] = res;
            return res;
        }

        public boolean union(int v1, int v2) {

            // Find respective roots.
            int rootv1 = find(v1);
            int rootv2 = find(v2);

            // No union done, v1, v2 already together.
            if (rootv1 == rootv2) return false;

            // Attach tree of v2 to tree of v1.
            parent[rootv2] = rootv1;
            return true;
        }


    }

    static class FastScanner {
        public BufferedReader br;
        public StringTokenizer st;
        public InputStream is;

        public FastScanner(String name, boolean debug) throws IOException {
            if (debug) {
                is = System.in;
            } else {
                is = new FileInputStream(name);
            }
            br = new BufferedReader(new InputStreamReader(is), 32768);
            st = null;
        }


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

        public int ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

        public double nd() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return str;
        }
    }

    static class FastWriter {
        public PrintWriter pw;

        public FastWriter(String name, boolean debug) throws IOException {
            if (debug) {
                pw = new PrintWriter(System.out);
            } else {
                pw = new PrintWriter(new BufferedWriter(new FileWriter(new File(name))));
            }
        }

        public void println(Object text) {
            pw.println(text);
        }

        public void print(Object text) {
            pw.print(text);
        }

        public void close() {
            pw.close();
        }

        public void flush() {
            pw.flush();
        }
    }

}
