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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

public class SpecialPermutation {

    public static final int MOD_VALUE = 1000000007;

    public static void main(String[] args) {

        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);

        int t = in.readInt();

        while (t--!=0){
            int n = in.readInt();

            if(n<=3){
                out.printLine(-1);
            }
            else {
                int sum = 0;
                while(n>7){
                    out.print(2+sum+" ");
                    out.print(4+sum+" ");
                    out.print(1+sum+" ");
                    out.print(3+sum+" ");
                    n-=4;
                    sum+=4;
                }
                if(n==7){
                    out.print(3+sum+" ");
                    out.print(7+sum+" ");
                    out.print(4+sum+" ");
                    out.print(6+sum+" ");
                    out.print(2+sum+" ");
                    out.print(5+sum+" ");
                    out.print(1+sum+" ");
                }
                if(n==6){
                    out.print(3+sum+" ");
                    out.print(6+sum+" ");
                    out.print(4+sum+" ");
                    out.print(1+sum+" ");
                    out.print(5+sum+" ");
                    out.print(2+sum+" ");
                }
                if(n==5){
                    out.print(2+sum+" ");
                    out.print(4+sum+" ");
                    out.print(1+sum+" ");
                    out.print(3+sum+" ");
                    out.print(5+sum+" ");
                    n-=5;
                    sum+=5;
                }
                if(n==4){
                    out.print(2+sum+" ");
                    out.print(4+sum+" ");
                    out.print(1+sum+" ");
                    out.print(3+sum+" ");
                    n-=4;
                    sum+=4;
                }
                out.printLine();
            }
        }

        out.flush();
    }

    static class InputReader {

        private InputStream                 stream;
        private byte[]                      buf = new byte[1024];
        private int                         curChar;
        private int                         numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) { throw new InputMismatchException(); }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) { return -1; }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) { c = read(); }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') { throw new InputMismatchException(); }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) { c = read(); }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') { throw new InputMismatchException(); }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) { c = read(); }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) { return filter.isSpaceChar(c); }
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) { writer.print(' '); }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

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

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

    }

    static class IOUtils {

        public static int[] readIntegerArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readInt();
            }
            return array;
        }

        public static long[] readLongArray(InputReader in, int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readLong();
            }
            return array;
        }

        public static Set<Integer> readIntegerSet(InputReader in, int size) {
            Set<Integer> set = new HashSet<Integer>();
            for (int i = 0; i < size; i++) {
                set.add(in.readInt());
            }
            return set;
        }
    }

}
