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 

// Magic. Do not touch.
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {
    static int mod=(int)(1e9+7);
    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        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 String next(){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 long l(){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 int i(){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 double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanIntIndexArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i()-1;}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
        public void shuffle(long [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); long temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
        public int swapIntegers(int a,int b){return a;} //Call it like this: a=swapIntegers(b,b=a)
    }
    public static void main(String[] args) throws IOException {

        FastReader fr = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);

     /*
inputCopy
6
10
2
4
6
7
13
outputCopy
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
     */
        //Press Ctrl+Win+Alt+L for reformatting indentation

        int t = fr.i();

        for (int ti = 0; ti < t; ++ti) {
            int n=fr.i();
            if(n<4)
            {
                pw.println(-1);
                continue;
            }
            List<Integer> ans=new ArrayList<>();
            for(int ni=n;ni>=1;--ni)
                if(ni%2!=0)
                    ans.add(ni);
            ans.add(4);
            ans.add(2);
            for(int ni=6;ni<=n;ni+=2)
                ans.add(ni);
            for(int i:ans)pw.print(i+" ");
            pw.println();
        }
        pw.flush();
        pw.close();
    }

}