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.math.BigInteger; 
import java.util.*;
import java.math.*; 

//Mann Shah [ DAIICT ].
//fast io

public class Main {
	static long mod = (long) (1e9+7);
	static long mm = (long)(1e9+6);
	static long N = (long)(2*1e5);
	static InputReader in;
    static PrintWriter out;
    static Debugger deb;
    
    
    public static int lower_bound(long[] a,int k) { // no. of elements less than k in array.
    		int first = 0,last = a.length,mid;
        while (first < last) {
            mid = first + ((last - first) >> 1); 
            if (a[mid] < k)  //lower bound. for upper use <= ( n - first)
                first = mid + 1; 
            else 
                last = mid;
        }
    		return first;
    }
    
    public static int gcd(int a, int b){ 
	    if (a == 0) 
	        return b;  
	    return gcd(b % a, a);  
    } 
    
    public static long power(long x, long y, long p) 
    { 
        long res = 1;      
        x = x % p;  
       if (x == 0) return 0; 
        while (y > 0) { 
            if((y & 1)==1) 
                res = (res * x) % p;
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }     
    
    	public static void main(String args[] ) throws NumberFormatException, IOException  {
			
		in = new InputReader(System.in);
	    out = new PrintWriter(System.out);
	    deb = new Debugger();
	    
	    int T = in.nextInt();
	    while(T-->0) {
	    		int n = in.nextInt();	
	    		
	    		if(n<=3) {
	    			out.println("-1");
	    		}
	    		else {
	    			LinkedList<Integer> q = new LinkedList();
	    			q.add(3);q.add(1);q.add(4);q.add(2);
	    			
	    			for(int i=5;i<=n;i+=2) {
	    				q.add(i);
	    			}
	    			for(int i=6;i<=n;i+=2) {
	    				q.addFirst(i);
	    			}
	    			
	    			for(int i=0;i<q.size();i++) {
	    				out.print(q.get(i)+" ");
	    			}
	    			out.println("");
	    		}
 	    		
	    }
	    
	    	
	    
	    out.close();
	}
		
/* TC space



 */	
		static class InputReader
	    {
	        private final InputStream stream;
	        private final byte[] buf = new byte[8192];
	        private int curChar, snumChars;
	        private SpaceCharFilter filter;

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

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

	        public int nextInt()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                int sgn = 1;
	                if (c == '-')
	                {
	                        sgn = -1;
	                        c = snext();
	                }
	                int res = 0;
	                do
	                {
	                        if (c < '0' || c > '9')
	                                throw new InputMismatchException();
	                        res *= 10;
	                        res += c - '0';
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

	        public long nextLong()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                int sgn = 1;
	                if (c == '-')
	                {
	                        sgn = -1;
	                        c = snext();
	                }
	                long res = 0;
	                do
	                {
	                        if (c < '0' || c > '9')
	                                throw new InputMismatchException();
	                        res *= 10;
	                        res += c - '0';
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

	        public int[] nextIntArray(int n)
	        {
	                int a[] = new int[n];
	                for (int i = 0; i < n; i++)
	                {
	                        a[i] = nextInt();
	                }
	                return a;
	        }

	        public long[] nextLongArray(int n)
	        {
	                long a[] = new long[n];
	                for (int i = 0; i < n; i++)
	                {
	                        a[i] = nextLong();
	                }
	                return a;
	        }
	        
	        public ArrayList<Integer> nextArrayList(int n){
	        			ArrayList<Integer> x = new ArrayList<Integer>();
	        			for(int i=0;i<n;i++) {
	        				int v = in.nextInt();
	        				x.add(v);
	        			}
	        			return x;
	        }

	        public String readString()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res.toString();
	        }

	        public String nextLine()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                        c = snext();
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isEndOfLine(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;
	        }

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

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

	    }
		
		static class Debugger{
			public void n(int x) {
				out.println(x);
			}
			
			public void a(int[] a) {
		        StringBuilder sb = new StringBuilder();
		        for(int i=0;i<a.length;i++) {
		        		sb.append(a[i]+" ");
		        }
		        out.println(sb.toString());
			}
		}
		
}


 class Pair { 
    int x; 
    int y; 
    // Constructor 
    public Pair(int x, int y) 
    { 
        this.x = x; 
        this.y = y; 
    } 
	@Override
	public boolean equals(Object o) {
	    if (this == o) return true;
	    if (!(o instanceof Pair)) return false;
	    Pair p = (Pair) o;
	    return x == p.x && y == p.y;
	}	
	@Override
	public int hashCode() {
		return (""+x+"-"+y).hashCode();
	}
	
} 

//        (p1,p2) -> p1.x-p2.x Using lembda function...
 
//        Arrays.sort(arr, new Comparator<Pair>() { 
//            @Override public int compare(Pair p1, Pair p2) 
//            { 
//                return p1.x - p2.x; 
//            } 
//        }); 
