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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.TreeSet;

public class C {
	static void merge(long arr[], int l, int m, int r) 
    { 
        int n1 = m - l + 1; 
        int n2 = r - m; 

        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
        int i = 0, j = 0; 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            int m = (l+r)/2; 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
            merge(arr, l, m, r); 
        } 
    }
	static PrintWriter out = new PrintWriter(System.out);
	public static void main(String[] args) throws IOException {
		try {
		BufferInput in = new BufferInput();
		//StringBuilder sb = new StringBuilder();
		int t = in.nextInt();
		while(t-->0) {
			int n = in.nextInt();
			if(n<4) {
				out.println("-1");
				continue;
			}
			int nn = n;
			if(n%2!=0) {
				while(n>=1) {
					out.print(n+" ");
					n-=2;
				}
			 out.print("4 2 ");
			 for(int i=6;i<nn;i+=2) out.print(i+" ");
			 out.println();
			}
			else {
				n--;
				while(n>=1) {
					out.print(n+" ");
					n-=2;
				}
			 out.print("4 2 ");
			 for(int i=6;i<=nn;i+=2) out.print(i+" ");
			 out.println();
			}
		}
		//System.out.print(sb);
		out.close();
	
		
}catch(Exception e) {}
	
}
//	static class Pair implements Comparable<Pair>
//	{
//	    int x;
//	    int y;
//	 
//	    public Pair(int x, int y)
//	    {
//	        this.x = x;
//	        this.y = y;
//	    }
//	 
//	    @Override
//	    public int compareTo(Pair ob)
//	    {
//	        if(this.x < ob.x)
//	            return -1;
//	        return 1;
//	    }
//	}
	static class Pair{
    	int x;
    	int y;
    	Pair(int x,int y){
    		this.x=x;
    		this.y=y;
    	}
    	@Override
        public int hashCode() {
            final int prime = 31;
           int  result = prime * x + y; 
            return result;
        }
    	
    	 @Override
    	    public boolean equals(Object obj) {
    	        if (this == obj)
    	            return true;
    	        if (obj == null)
    	            return false;
    	        if (getClass() != obj.getClass())
    	            return false;
    	        Pair other = (Pair) obj;
    	        if (x != other.x && y != other.y)
    	            return false;
    	        return true;
    	    }
    	 @Override
    	 public String toString() {
    		 return "{"+String.valueOf(x)+","+String.valueOf(y)+"}";
    	 }
    	
    }
static class BufferInput {
		
		final private int BUFFER_SIZE = 1 << 16;
		
		private DataInputStream din;
		
		private byte[] buffer;
		
		private int bufferPointer, bytesRead;
		
		public BufferInput() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public BufferInput(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];
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}
		
		public String nextString() throws IOException{
			
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			
			StringBuilder builder = new StringBuilder();
			builder.append((char)c);
			c = read();
			while(!Character.isWhitespace(c)){
				builder.append((char)c);
				c = read();
			}
			
			return builder.toString();
		}
		
		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 int[] nextIntArray(int n) throws IOException {
			int arr[] = new int[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextInt();
			}
			return arr;
		}
		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 long[] nextLongArray(int n) throws IOException {
			long arr[] = new long[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextLong();
			}
			return arr;
		}
		
		public char nextChar() throws IOException{
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			return (char) c;	
		}
		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;
		}
		public double[] nextDoubleArray(int n) throws IOException {
			double arr[] = new double[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextDouble();
			}
			return arr;
		}
		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();
		}
	}
}
