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.lang.reflect.Array;
import java.util.*;

public class CodingLegacy {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Palindrome solver = new Palindrome();

        int t = 1;
        t = in.nextInt();

        for (int i = 0; i < t; i++) {
            solver.solve(i + 1, in, out);
        }

        out.close();
    }

    static class Palindrome {
        static long mod = 1000000007;
        static long maxX = (long) 1e18;
        static long mod2 = 998244353;

        void solve(int testNumber, ScanReader in, PrintWriter out) {
            ArrayList<Integer> aa = new ArrayList<>();
            int p = 1;
            int n = in.nextInt();
            int[] a = new int[n];

            if(n < 4) {
                out.println("-1");
                return;
            }

            if(n%4 == 0) {
                a[0] = 2;a[1] = 4;a[2] = 1;a[3] = 3;

                for(int i = 4;i<n;i += 4) {
                    a[i] = a[i - 4] + 4 ;a[ i + 1] = a[i + 1 - 4] + 4;a[i + 2] = a[i +2 - 4] + 4;a[i + 3] = a[i + 3 - 4] + 4;
                }

                for(int i = 0;i<n;i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            } else if(n%4 == 1) {
                a[0] = 2;a[1] = 4;a[2] = 1;a[3] = 3;

                for(int i = 4;i<n-1;i += 4) {
                    a[i] = a[i - 4] + 4 ;a[ i + 1] = a[i + 1 - 4] + 4;a[i + 2] = a[i +2 - 4] + 4;a[i + 3] = a[i + 3 - 4] + 4;
                }

                a[n-2] = n;
                a[n - 1] = n-2;

                for(int i = 0;i<n;i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            } else if (n%4 == 2) {
                a[0] = 2;a[1] = 4;a[2] = 1;a[3] = 3;

                for(int i = 4;i<n-2;i += 4) {
                    a[i] = a[i - 4] + 4 ;a[ i + 1] = a[i + 1 - 4] + 4;a[i + 2] = a[i +2 - 4] + 4;a[i + 3] = a[i + 3 - 4] + 4;
                }

                a[n-3] = n -1;
                a[n - 2] = n-3;
                a[n-1] = n;

                for(int i = 0;i<n;i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            } else {
                a[0] = 2;a[1] = 4;a[2] = 1;a[3] = 3;

                for(int i = 4;i<n-3;i += 4) {
                    a[i] = a[i - 4] + 4 ;a[ i + 1] = a[i + 1 - 4] + 4;a[i + 2] = a[i +2 - 4] + 4;a[i + 3] = a[i + 3 - 4] + 4;
                }

                a[n - 4] = n -2;
                a[n-3] = n ;
                a[n - 2] = n-4;
                a[n-1] = n-1;

                for(int i = 0;i<n;i++) {
                    out.print(a[i] + " ");
                }
                out.println();
            }
        }
    }

    static class ScanReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public ScanReader(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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            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 nextLong() {
            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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            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);
        }
    }
}