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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.logging.Level;
import java.util.logging.Logger;
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 * @author shubhamsaxena
 * Solution is at the Top
 */
public class Header {

    private final long MOD = 998244353L;

    private void solve() {
        int t = inpi();
        while (t-- > 0) {
            int n = inpi();
            if (n < 4) out.println(-1);
            else {
                switch (n % 4) {
                    case 0:
                        printOrder(n);
                        break;
                    case 1:
                        printOrder(n - 1);
                        out.print(n);
                        break;
                    case 2:
                        printOrder(n - 6);
                        out.print((n - 4) + " " + (n - 1) + " " + (n - 5) + " " + (n - 3) + " " + (n) + " " + (n - 2));
                        break;
                    case 3:
                        printOrder(n - 7);
                        out.print((n - 5) + " " + (n - 2) + " " + (n - 6) + " " + (n - 4) + " " + (n - 1) + " " + (n - 3) + " " + (n));
                        break;
                }
                out.println();
            }
        }
    }

    private void printOrder(int n) {
        //n%4 == 0 always
        for (int i = 1; i <= n; i += 4) {
            out.print((i + 1) + " " + (i + 3) + " " + (i) + " " + (i + 2) + " ");
        }
    }

    public boolean isPrime(long n) {
        return BigInteger.valueOf(n).isProbablePrime(5);
    }

    public boolean[] sieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        for (int p = 2; p <= n; p++) {
            if (prime[p]) {

            }
        }
        return prime;
    }

    InputStream obj;
    PrintWriter out;
    String check = "";

    public static void main(String[] args) {
        new Thread(null, () -> {
            try {
                new Header().main1();
            } catch (IOException ex) {
                Logger.getLogger(Header.class.getName()).log(Level.SEVERE, null, ex);
                throw new RuntimeException();
            }
        }, "1", 1 << 26).start();

    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }

    private byte[] inbuffer = new byte[1024];
    private int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) {
            return -1;
        }
        return inbuffer[ptrbuffer++];
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    String inps() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    int inpi() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long inpl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    float inpf() {
        return Float.parseFloat(inps());
    }

    double inpd() {
        return Double.parseDouble(inps());
    }

    char inpc() {
        return (char) skip();
    }

    int[] inpia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpi();
        }
        return a;
    }

    long[] inpla(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpl();
        }
        return a;
    }

    String[] inpsa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = inps();
        }
        return a;
    }

    double[][] inpdm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpd();
            }
        }
        return a;
    }

    int[][] inpim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpi();
            }
        }
        return a;
    }
}