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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class SpecialPermutation {

	//2d arraylist adj list
	//ArrayList<ArrayList<Integer>> adj = new ArrayList<ArrayList<Integer>>();
	//for (int i = 0; i < n; i++)adj.add(new ArrayList<Integer>());
	/*
	 -Binary search
	 int lo = 0;
	 int hi = highest val possible;
	 while (lo <= hi){
	 int mid = (lo+hi)/2;
	 
	 if (check){
	 
	 	}else {
	 	
	 	}
	 }
	 */
		
		
		
	//Custom Comparators
	/*
	 //ArrayList<comp> a = new ArrayList<comp>();
	 //long [] a = new new long [n];
	 
	 class comp implements Comparable<comp> {

		public int a, b;

		public comp(int a, int b) {
			this.a = b;
			this.a = b;
		}

		public int compareTo(comp other) {
		//sort by 1 criteria
		 //return Integer.compare(this.a. other.a);
		  
		  //sort by 2 criteria
			//if (this.a != other.a) {
			//	return Integer.compare(this.a, other.a);
			//} else {
				return Integer.compare(other.b, this.b);
			//}
		}
	}
	 */
		
		
		
	//MultiSet
	/*
	 static void add(int x){
		if(multiset.containsKey(x)){
			multiset.put(x, multiset.get(x) + 1);
		} else {
			multiset.put(x, 1);
		}
	}

	static void remove(int x){
		multiset.put(x, multiset.get(x) - 1);
		if(multiset.get(x) == 0){
			multiset.remove(x);
		}
	}
	 */
	 
		
	//DFS and other related items
	//ArrayList<ArrayList<Integer>> adj = new ArrayList<ArrayList<Integer>>();
	//for (int i = 0; i < n; i++)adj.add(new ArrayList<Integer>());
	//boolean [] visited = new boolean [n];
	/*
	 static void dfs(int node) {
			if (visited[node]) return;
			
			nodes++;
			visited[node] = true;
			for (int neighbor : adj.get(node)) {
				dfs(neighbor);
			}
	 */
	 

		
	//Floodfill
	/*
	 static void floodfill(int r, int c, char curC) {
		if (r < x || r >= 0 || c < y || c >= 0) {
			return;
		} 
		if(visited[r][c] || grid[r][c] != curC) {
			return;
		}
		visited[r][c] = true;
		size++;
		
		floodfill(r+1, c, curC);
		floodfill(r-1, c, curC);
		floodfill(r, c+1, curC);
		floodfill(r, c-1, curC);
	}
	 */
		
		
	//2 pointers
	/*
	 int l = 0, r = 0, cur = 0, ans = 0;
			while (l < n && r < n) {
				while (r < n) {
					r++;
					if ((check condition)) {
						r--;
						break;
					}
				}

				l++;
			}
	 */
		public static void main(String[] args) throws IOException {
			BufferedReader read = new BufferedReader(new InputStreamReader(System.in));//new FileReader("cowdance.in")
			 PrintWriter out = new PrintWriter(System.out);//new FileWriter("cowdance.out")
			 StringTokenizer st = new StringTokenizer(read.readLine());
			 int t = Integer.parseInt(st.nextToken());
			 
			 for (int ie = 0; ie < t; ie++) {
			 st = new StringTokenizer(read.readLine());
			 int n = Integer.parseInt(st.nextToken());//Long.parseLong(st.nextToken());
			 int i = 0;
			 if (n%2 == 0)
				 i = n-1;
			 else
				 i = n;
			 if (n >= 4) {
			 for (; i > 0; i-= 2) {
				 out.print(i+" ");
			 }
			 out.print(4+" "+2+" ");
			 for (int j = 6; j <= n; j+=2) {
				 out.print(j+" ");
			 }
			 out.println();
			 }else 
				 out.println(-1);
			 
			 }
			 out.close();
	}

}
