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.*;
import java.util.stream.*;

public class CF640G {
    private static boolean debug = false;

    private static int N;
    private static int[] A;

    private static void solveProblem(InputStream instr) throws Exception {
        InputReader sc = new InputReader(instr);
        int testCount = sc.nextInt();
       /* if (debug) {
            testCount = sc.nextInt();
        }*/

        for (int t = 1; t <= testCount; t++) {
            printDebug("------ " + t + " ------");
            N = sc.nextInt();
            Object result = solveTestCase();
            System.out.println(result);
        }
    }

    private static Object solveTestCase() {
        int[] answers = new int[N];
        int[] order4 = {2, 4, 1, 3};
        int[] order5 = {2, 4, 1, 3, 5};
        int[] order6 = {2, 4, 6, 3, 5, 1};
        int[] order7 = {2, 4, 6, 3, 1, 5, 7};
        if(N < 4){
            return -1;
        }
        int full = N / 4 - 1;
        int reminder = N - full * 4;
        for(int i = 0;  i < full; i++) {
            for (int j = 0; j < 4; j++) {
                answers[i * 4 + j] = 4 * i + order4[j];
            }
        }
        int[] reminderOrder = null;
        if(reminder == 4){
            reminderOrder = order4;
        }else if(reminder == 5){
            reminderOrder = order5;
        }else if(reminder == 6){
            reminderOrder = order6;
        }else{
            reminderOrder = order7;
        }
        for(int i = 0; i < reminderOrder.length; i++){
            answers[4 * full + i] = 4 * full + reminderOrder[i];
        }
        return joinValues(answers, " ");
    }

    private static int[] readInts(InputReader sc, int N) throws Exception {
        int[] arr = new int[N];
        for (int i = 0; i < N; i++) {
            arr[i] = sc.nextInt();
        }
        return arr;
    }

    private static String joinValues(List<? extends Object> list, String delim) {
        return list.stream().map(Object::toString).collect(Collectors.joining(delim));
    }

    private static String joinValues(int[] arr, String delim) {
        List<Object> list = new ArrayList<>();
        for (Object value : arr) {
            list.add(value);
        }
        return list.stream().map(Object::toString).collect(Collectors.joining(delim));
    }

    public static void printDebug(Object str) {
        if (debug) {
            System.out.println("DEBUG: " + str);
        }
    }

    private static final class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[1024];
        private int curChar;
        private int Chars;

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

        private int read() throws Exception {
            if (curChar >= Chars) {
                curChar = 0;
                Chars = stream.read(buf);
                if (Chars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public final int nextInt() throws Exception {
            return (int)nextLong();
        }

        public final long nextLong() throws Exception {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
                if (c == -1)
                    throw new IOException();
            }
            boolean negative = false;
            if (c == '-') {
                negative = true;
                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 negative ? (-res) : (res);
        }

        public final int[] nextIntBrray(int size) throws Exception {
            int[] arr = new int[size];
            for (int i = 0; i < size; i++)
                arr[i] = nextInt();
            return arr;
        }

        public final String next() throws Exception {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public final String nextLine() throws Exception {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = read();
            } while (c != '\n' && c != -1);
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }

    public static void main(String[] args) throws Exception {
        long currTime = System.currentTimeMillis();
        try {
            if (new File("input.in").exists()) {
                debug = true;
            }
        } catch (Throwable ex) {

        }
        if (debug) {
            solveProblem(new FileInputStream(new File("input.in")));
            System.out.println("Time: " + (System.currentTimeMillis() - currTime));
        } else {
            solveProblem(System.in);
        }
    }

}
