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.Vector;

// Author- Prashant Gupta

public class E {
    public static void main(String[] args) throws IOException {
        // write your code here
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
//        Scanner sc = new Scanner(System.in);
        Reader sc = new Reader();
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            if (n == 2 || n == 3) {
                out.println(-1);
            } else {
                if (n % 2 == 0) {
                    for (int i = n - 1; i > 0; i -= 2) {
                        out.print(i + " ");
                    }
                    out.print("4 2 ");
                    for (int i = 6; i <= n; i += 2) {
                        out.print(i + " ");
                    }
                } else {
                    for (int i = n; i > 0; i -= 2) {
                        out.print(i + " ");
                    }
                    out.print("4 2 ");
                    for (int i = 6; i <= n; i += 2) {
                        out.print(i + " ");
                    }
                }
                out.println();
            }
        }
        out.close();
    }

    /*-------------------------------------------------------------------------------------*/



    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long power(long x, long y) {
        long res = 1;
        while (x > 0) {
            if (y % 2 == 0) {
                x *= x;
                y /= 2;
            } else {
                res *= x;
                y--;
            }
        }
        return res;
    }

    public static long lcm(long x, long y) {
        return (x * y) / gcd(x, y);
    }

    public static int lowerBound(Vector<Integer> v, int e) {
        int start = 0, end = v.size() - 1, ind = -1;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (v.get(mid) == e) {
                ind = mid;
                break;
            } else if (v.get(mid) < e) {
                ind = mid + 1;
                start = mid + 1;
            } else {
                end = mid - 1;
            }
        }
        return ind;
    }

    // Fast I/p

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}
