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.util.*;
import java.io.*;

/*
*/

public class Main{
    //
    public static void nl(Object o){System.out.println(o);}
    public static void l(Object o){System.out.print(o);}
    public static void arp(int[] o){for(int i=0;i<o.length;i++) System.out.print(o[i]+" ");}
    public static void arpnl(int[] o){for(int i=0;i<o.length;i++) System.out.println(o[i]);}
    //
    static int MOD=1000000007;
    //
    public static void main(String[] args) throws IOException{
        // long sttm=System.currentTimeMillis();
        FastReader sc=new FastReader();
        OutputStream out=new BufferedOutputStream(System.out);
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            ArrayList<Integer> arrl=new ArrayList<Integer>();
            arrl.add(2);arrl.add(4);arrl.add(1);arrl.add(3);
            for(int i=5;i<=n;i++){
                if(i%2==0){
                    arrl.add(i);
                }
                else{
                    arrl.add(0,i);
                }
            }
            if(n>=4){
                Iterator<Integer> it=arrl.iterator();
                while(it.hasNext()){
                    l(it.next()+" ");
                }
                nl(" ");
            }
            else{
                nl("-1");
            }
        }
        out.flush();
    }


    // public static String decToBin(long val){
    //     String res="";
    //     while(val>0){
    //         long rem=val%2;val/=2;
    //         // res+=Integer.t
    //     }
    //     return res;
    // }

    public static boolean dfsCycle(ArrayList<Integer>[] arrl,int[] vis,int st,int pr){
        vis[st]=1;
        int cupr=st;
        for(int elm:arrl[st]){
            if(vis[elm]==1 && elm!=pr){
                return true;
            }
            else if(vis[elm]==0 && dfsCycle(arrl, vis, elm, cupr)){
                return true;
            }
        }
        vis[st]=2;
        return false;
    }



    public static long powMOD(long n,long k){                 //n-pow(k)
        if(k==1){
            return n%MOD;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2)%MOD;
        if(k%2==0)return ((val%MOD)*(val%MOD))%MOD;
        else return (((val*val)%MOD)*n)%MOD;
    }

    public static long pow(long n,long k){                 //n-pow(k)
        if(k==1){
            return n;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2);
        if(k%2==0)return ((val)*(val));
        else return (((val*val))*n);
    }


    public static HashMap<Integer,Integer> lcm(int num){
        ArrayList<Integer> arrl=new ArrayList<Integer>();
        HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
        while(num%2==0){

            if(!map.containsKey(2)){
                arrl.add(2);
                map.put(2, 1);
            }
            else{
                map.put(2,map.get(2)+1);
            }
            num/=2;
        }
        for(int i=3;i*i<=num;i+=2){
            while(num%i==0){
                if(!map.containsKey(i)){
                    arrl.add(i);
                    map.put(i, 1);
                }
                else{
                    map.put(i,map.get(i)+1);
                }
                num/=i;
            }
        }
        if(num>2){
            if(!map.containsKey(num)){
                arrl.add(num);
                map.put(num, 1);
            }
            else{
                map.put(num,map.get(num)+1);
            }
        }
        return map;
    }


    static long m=998244353l;
    static long modInverse(long a,long m)
    {
        long m0 = m;
        long y = 0l, x = 1l;

        if (m == 1)
            return 0l;

        while (a > 1)
        {

            long q = a / m;

            long t = m;

            m = a % m;
            a = t;
            t = y;

            y = x - q * y;
            x = t;
        }
        if (x < 0)
            x += m0;

        return x;
    }


    public static int num_fact(int num){
        ArrayList<Integer> arr=new ArrayList<Integer>();
        int cnt=0;
        for(int i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                }
                else{
                    cnt+=2;
                }
            }
        }
        return cnt;
    }


    public static void sort_inc(int[][] arr,int col){        //change dimention if req
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(final int[] entry1,final int[] entry2) {
                if (entry1[col] > entry2[col])              //this is for inc
                    return 1;
                else if(entry1[col]==entry2[col])
                    return 0;
                else
                    return -1;
            }
        });
    }


    public static boolean prime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }


    static long gcd(long a, long b)
	{
	if (b == 0)
		return a;
	return gcd(b, a % b);
    }

    public static long lcmOfTwo(int a,int b){
        return a*b/gcd(a,b);
    }

}


class FastReader{
    BufferedReader br;
    StringTokenizer st;

    public FastReader(){
        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;
    }
}