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.*;
public class Main {
	public static void main(String[] args) throws IOException 
	{ 
		FastScanner f = new FastScanner(); 
		int t=1;
		t=f.nextInt();
		PrintWriter out=new PrintWriter(System.out);
		for(int tt=0;tt<t;tt++) {
			int n=f.nextInt();
			if (n<4) {
				System.out.println(-1);
				continue;
			}
			int[] four= {2, 4, 1, 3};
			int[] five= {2, 4, 1, 3, 5};
			int[] six= {1, 4, 2, 6, 3, 5};//5 3 6 2 4 1
			int[] seven= {7, 4, 2, 6, 3, 1, 5};//5 1 3 6 2 4 7
			for (int i=0; i<seven.length; i++) seven[i]=8-seven[i];
			if (n%4==0) {
				for (int i=0; i<n; i+=4)
					for (int j=0; j<4; j++) System.out.print(i+four[j]+" ");
				System.out.println();
			}
			if (n%4==1) {
				for (int i=0; i<n-5; i+=4)
					for (int j=0; j<4; j++) System.out.print(i+four[j]+" ");
				for (int i=0; i<5; i++)
					System.out.print(n-5+five[i]+" ");
				System.out.println();
			}
			if (n%4==2) {
				for (int i=0; i<n-6; i+=4)
					for (int j=0; j<4; j++) System.out.print(i+four[j]+" ");
				for (int i=0; i<6; i++)
					System.out.print(n-6+six[i]+" ");
				System.out.println();
			}
			if (n%4==3) {
				for (int i=0; i<n-7; i+=4)
					for (int j=0; j<4; j++) System.out.print(i+four[j]+" ");
				for (int i=0; i<7; i++)
					System.out.print(n-7+seven[i]+" ");
				System.out.println();
			}
		}
		out.close();
	} 
	static void sort(long[] p) {
        ArrayList<Integer> q = new ArrayList<>();
        for (long i: p) q.add((int) i);
        Collections.sort(q);
        for (int i = 0; i < p.length; i++) p[i] = q.get(i);
    }
    
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
} 	
//Some things to notice
//Check for the overflow
//Binary Search
//Bitmask
//runtime error most of the time is due to array index out of range