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.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

public class G {
    public static void main(String args[])
    {
        FastReader Reader=new FastReader(System.in);
        int T=Reader.nextInt();

        for(int m=0;m<T;m++)
        {
            int N=Reader.nextInt();
            if(N<=3)
            {
                System.out.println(-1);
                continue;
            }
            ArrayList<Integer> arr=new ArrayList<>();

            int count=0;
            int j=0;
            if(N%5==0)
            {
                while(j<N)
                {
                    arr.add(count*5+3);
                    arr.add(count*5+1);
                    arr.add(count*5+4);
                    arr.add(count*5+2);
                    arr.add(count*5+5);
                    count++;
                    j+=5;
                }
            }
            else if(N%5==1)
            {
                while(j<N)
                {
                    arr.add(count*5+1);
                    j+=1;
                    if(j%N==0)
                        break;
                    arr.add(count*5+4);
                    arr.add(count*5+2);
                    arr.add(count*5+5);
                    arr.add(count*5+3);
                    j+=4;
                    count++;
                }
            }
            else if(N%5==2)
            {
                while(N-j>7)
                {
                    arr.add(count*5+3);
                    arr.add(count*5+1);
                    arr.add(count*5+4);
                    arr.add(count*5+2);
                    arr.add(count*5+5);
                    count++;
                    j+=5;
                }
                arr.add(count*5+4);
                arr.add(count*5+1);
                arr.add(count*5+3);
                arr.add(count*5+6);
                arr.add(count*5+2);
                arr.add(count*5+5);
                arr.add(count*5+7);
            }
            else if(N%5==3)
            {
                while(N-j>8)
                {
                    arr.add(count*5+3);
                    arr.add(count*5+1);
                    arr.add(count*5+4);
                    arr.add(count*5+2);
                    arr.add(count*5+5);
                    count++;
                    j+=5;
                }
                arr.add(count*5+4);
                arr.add(count*5+2);
                arr.add(count*5+6);
                arr.add(count*5+8);
                arr.add(count*5+5);
                arr.add(count*5+7);
                arr.add(count*5+3);
                arr.add(count*5+1);
            }
            else if(N%5==4)
            {
                while(j<N)
                {
                    arr.add(count*5+3);
                    arr.add(count*5+1);
                    arr.add(count*5+4);
                    arr.add(count*5+2);
                    j+=4;
                    if(j%N==0)
                        break;
                    arr.add(count*5+5);
                    j+=1;
                    count++;
                }

            }
            for(int i=0;i<arr.size();i++)
            {
                System.out.print(arr.get(i)+" ");
            }
            System.out.println();
        }


    }
    public static void sorts(int arr[],int N)
    {
        Integer arr_obj[]=new Integer[N];
        for(int i=0; i<N; ++i){
            arr_obj[i] = new Integer(arr[i]);
        }
        Arrays.sort(arr_obj);
        for(int i=0; i<N; ++i){
            arr[i] = arr_obj[i];
        }
    }
}
class FastReader {
    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar;
    private int pnumChars;
    private FastReader.SpaceCharFilter filter;

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

    public int read() {
        if (pnumChars == -1) {
            throw new InputMismatchException();
        }
        if (curChar >= pnumChars) {
            curChar = 0;
            try {
                pnumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (pnumChars <= 0) {
                return -1;
            }
        }
        return buf[curChar++];
    }

    public String next() {
        return nextString();
    }

    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 == ',') {
                c = read();
            }
            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 String nextString() {
        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 String nextLine() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }


    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null) {
            return filter.isSpaceChar(c);
        }
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);

    }

}