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.*;

public class G {

    void solve() throws IOException {
        in = new InputReader("__std");
        out = new OutputWriter("__std");

        int testCount = in.readInt();
        for (int test = 1; test <= testCount; ++test) {
            int n = in.readInt();
            if (n < 4) {
                out.println(-1);
            } else {
                for (int p = 2; p <= n; p += 2) {
                    out.print(p + " ");
                }
                int a = n - n % 2 - 3;
                out.print(a);
                if (n % 2 > 0) {
                    out.print(" " + (a + 4));
                }
                out.print(" " + (a + 2));
                for (int p = a - 2; p > 0; p -= 2) {
                    out.print(" " + p);
                }
                out.println();
            }
        }

        exit();
    }

    void exit() {
        out.close();
        //System.err.println((System.currentTimeMillis() - startTime) + " ms");
        System.exit(0);
    }

    InputReader in;
    OutputWriter out;

    //long startTime = System.currentTimeMillis();

    public static void main(String[] args) throws IOException {
        new G().solve();
    }

    class InputReader {

        private InputStream stream;

        private byte[] buffer = new byte[1024];
        private int pos, len;

        private int cur;

        private StringBuilder sb = new StringBuilder(32);

        InputReader(String name) throws IOException {
            if (name.equals("__std")) {
                stream = System.in;
            } else {
                stream = new FileInputStream(name);
            }
            cur = read();
        }

        private int read() throws IOException {
            if (len == -1) {
                throw new EOFException();
            }
            if (pos >= len) {
                pos = 0;
                len = stream.read(buffer);
                if (len == -1) return -1;
            }
            return buffer[pos++] & 0xff;
        }

        boolean whitespace() {
            return cur == ' ' || cur == '\t' || cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eol() {
            return cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eof() {
            return cur == -1;
        }

        byte readByte() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            byte res = (byte) cur;
            cur = read();
            return res;
        }

        char readChar() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            char res = (char) cur;
            cur = read();
            return res;
        }

        int readInt() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            int res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        long readLong() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
            }
            long res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        double readDouble() throws IOException {
            return Double.parseDouble(readToken());
        }

        String readToken() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!whitespace()) {
                sb.append((char) cur);
                cur = read();
            }
            return sb.toString();
        }

        String readLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!eol()) {
                sb.append((char) cur);
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
            return sb.toString();
        }

        void skipLine() throws IOException {
            if (eof()) {
                throw new EOFException();
            }
            while (!eol()) {
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
        }
    }

    class OutputWriter {

        private PrintWriter writer;

        OutputWriter(String name) throws IOException {
            if (name.equals("__std")) {
                writer = new PrintWriter(System.out);
            } else {
                writer = new PrintWriter(name);
            }
        }

        void print(String format, Object ... args) {
            writer.print(new Formatter(Locale.US).format(format, args));
        }

        void println(String format, Object ... args) {
            writer.println(new Formatter(Locale.US).format(format, args));
        }

        void print(Object value) {
            writer.print(value);
        }

        void println(Object value) {
            writer.println(value);
        }

        void println() {
            writer.println();
        }

        void printArray(int[] a) {
            boolean first = true;
            for (int v : a) {
                if (!first) {
                    writer.print(' ');
                } else {
                    first = false;
                }
                writer.print(v);
            }
            writer.println();
        }

        void printArray(int[][] a) {
            for (int[] v : a) {
                printArray(v);
            }
        }

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

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