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.*;
import java.math.*;

 
 public class Main	{
   static class Pair implements Comparable<Pair>{
   int a;
   int b;
   public Pair(int x,int y){a=x;b=y;}
   public Pair(){}
   public int compareTo(Pair p){
	 return p.a - a;
   }



 }
static class TrieNode{
  TrieNode[]child;
  int w;
  boolean term;
  TrieNode(){
    child = new TrieNode[26];  
  }
}
  public static long gcd(long a,long b)
  {
    if(a<b)

      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  static long lcm(long a,long b) {
	  return a*b / gcd(a,b);
  }
  //static long ans = 0;
  static long mod = (long)(1e9+7);///998244353;
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

static long pow(long x,long y){
    if(y == 0)return 1;
    if(y==1)return x;
    long a = pow(x,y/2);
    a = (a*a)%mod;
    if(y%2==0){
        return a;
    }
    return (a*x)%mod;
}

static long mxx;
static int mxN = (int)(3e5+5);
static long[]fact,inv_fact;
static long my_inv(long a) {
	return pow(a,mod-2);
}
static long bin(int a,int b) {
	if(a < b || a<0 || b<0)return 0;
    return ((fact[a]*inv_fact[a-b])%mod * inv_fact[b])%mod;
}
static ArrayList<ArrayList<Integer>>adj;
static boolean[]vis;
static long[]dis;
static long val;
static void dfs(int sv,int cur) {
	if(vis[sv]) {
	//	dis[sv] = cur;
		val = cur-dis[sv];
		return;
	}
	vis[sv] = true;
	dis[sv]=cur;
	for(int x:adj.get(sv)) {
		     
			dfs(x,cur+1);
		
	}
	
}

 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int tc = s.nextInt();
        mxx = (long)(1e18+5);
//       fact=new long[mxN];
//       inv_fact = new long[mxN];
//       fact[0]=inv_fact[0]=1L;
//       for(int i=1;i<mxN;i++) {
//    	   fact[i] = (i*fact[i-1])%mod;
//    	   inv_fact[i] = my_inv(fact[i]);
//       }
        while(tc-->0){
        	int n = s.nextInt();
        	int[]ans = new int[n+1];
        	if(n <= 3)out.println("-1");
        	else {
        		int st = n+1;
        		int i = 1;
        		while(st > 2) {
        			ans[i++] = st-2;
        		    st -=2;
        		}
        		ans[i++] = st+3;st +=3;
        		if(st > 4)
        		{
        			ans[i++] = st-4;
        			st-=4;
        			if(i <= n) {
        				ans[i++] = st+2;st+=2;
        			}
        			if(i<=n) {
        				ans[i++] = st+4;st+=4;
        			}
        		}
        		else if(st > 2){
        			ans[i++] = st-2;
        			st-=2;
        			if(i <= n) {
        				ans[i++] = st+4;
        				st+=4;
        			}
        		}
        		while(i <= n) {
        			ans[i++] = st+2;
        			st += 2;
        		}
        		for(i=1;i<=n;i++)out.print(ans[i]+" ");
        		out.println();
        	}
        }
        	
           
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}
