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.io.IOException;

import java.util.*;
//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;

//import sun.net.www.content.audio.wav;



    
   public  class Codeforces {
        
        public static long mod = (long)Math.pow(10, 9)+7 ;
        public static double epsilon=0.00000000008854;//value of epsilon
        public static InputReader sc = new InputReader(System.in);
        public static PrintWriter pw = new PrintWriter(System.out);
        public static int firstNode(int a,HashMap<Integer,Integer> p){
            if(p.containsKey(a)){
                p.put(a, firstNode(p.get(a), p));
            }
            else return a;
            return p.get(a);
        }
        public static void Union(int a,int b,HashMap<Integer,Integer> p){
            //int a=firstNode(a1, p);
            //int b=firstNode(b1, p);
            /*if(a!=b){
                if(r[a]<r[b]){
                    p[a]=b;
                }
                else if(r[a]>r[b]){
                    p[b]=a;
                }
                else{
                    r[b]++;
                    p[a]=b;
                }
            }*/
            a=firstNode(a, p);
            b=firstNode(b, p);
            if(a!=b)
            p.put(a, b);//if no rank than 
        }
        public static ArrayList<ArrayList <Integer>> GetGraph(int n,int m){
            ArrayList<ArrayList <Integer>> a=new ArrayList<>();
            for(int i=0;i<n;i++){
                a.add(new ArrayList<>());
            }
            for(int i=0;i<m;i++){
                int u=sc.nextInt()-1;
                int v=sc.nextInt()-1;
                a.get(u).add(v);
                a.get(v).add(u);
            } 
            return a;
        }
        public static void dfs(char a[][],int vis[][],int x,int y){
            int n=a.length;
            int m=a[0].length;
            if(x<0||x>=n||y<0||y>=m){
                return;
            }
            if(vis[x][y]==1)
            return;
            if(a[x][y]=='G'||a[x][y]=='.'){
                vis[x][y]=1;
                dfs(a, vis, x+1, y);
                dfs(a, vis, x-1, y);
                dfs(a, vis, x, y+1);
                dfs(a, vis, x, y-1);
            }
        }
        public static void main(String[] args) {
            // code starts..
           int q=sc.nextInt();
           while(q-->0){
              int n=sc.nextInt();
              if(n==1){
                  pw.println(1);
              }
              else if(n<4){
                  pw.println(-1);
              }
              else if(n%2==0){
                  for(int i=2;i<=n;i+=2){
                      pw.print(i+" ");
                  }
                  pw.print((n-3)+" "+(n-1)+" ");
                  for(int i=n-5;i>0;i-=2){
                      pw.print(i+" ");
                  }
                  pw.print("\n");
              }
              else {
                for(int i=2;i<=n;i+=2){
                    pw.print(i+" ");
                }
                pw.print((n-4)+" "+(n)+" "+(n-2)+" ");
                for(int i=n-6;i>0;i-=2){
                    pw.print(i+" ");

                }
                pw.print("\n");
            }
            
           }
            // Code ends...
            pw.flush();
            pw.close();
        }
       
        public static Comparator<Integer[]> column(int i){
            return 
            new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    return o1[i].compareTo(o2[i]);//for ascending
                    //return o2[i].compareTo(o1[i]);//for descending
                }
            };
        }
        public static String reverseString(String s){
            StringBuilder input1 = new StringBuilder(); 
            input1.append(s);  
            input1 = input1.reverse();
            return input1.toString();
        }
        public static int[] scanArray(int n){
            int a[]=new int [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
    
            return a;
        }
        public static long[] scanLongArray(int n){
            long a[]=new long [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
    
            return a;
        }
        public static String [] scanStrings(int n){
            String a[]=new String [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLine();
    
            return a;
        }
        
    }
    
    class InputReader {
    
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;
    
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
    
            public int snext() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
    
            public int nextInt() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
                return a;
            }
    
            public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
            }
    
            public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
            }
    
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
    
            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }
    
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
        class SegmentTree{
            int s[],n;
            SegmentTree(int a[]){
                n=a.length;
                int l=(int)Math.ceil(Math.log(n)/Math.log(2));
                l=2*(int)Math.pow(2,l)-1;
                s=new int[l];
                createSegmentTreeUtil(a, 0, 0, a.length-1);
            }
            
            int createSegmentTreeUtil(int a[],int root,int l,int r){
                if(l==r)
                s[root]=a[l];
                else
                s[root]= Compare(createSegmentTreeUtil(a, 2*root+1, l, (l+r)/2), createSegmentTreeUtil(a,2*root+2, (l+r)/2+1,r));
                return s[root];
            }
            int getValue(int gl,int gr){
                return getValueUtil(0, 0, n-1, gl, gr);
            }
            int getValueUtil(int root,int l,int r,int gl,int gr){
                if(l>=gl&&r<=gr){
                    return s[root];
                }
                if(l>gr||r<gl){
                    return 0;
                }
                return Compare(getValueUtil(2*root+1, l, (l+r)/2, gl, gr), getValueUtil(2*root+2, (l+r)/2+1, r, gl, gr));
            }
            void update(int value,int index){
                updateUtil(value, index,0,0,n-1);
            }
            int updateUtil(int p,int k,int root,int l,int r){
                if(l==r&&l==k){
                    return s[root]=p;
                }
                else if(l>k||r<k)
                return s[root];
                else{
                    return s[root]=Compare(updateUtil(p, k, 2*root+1, l, (l+r)/2), updateUtil(p, k, 2*root+2,(l+r)/2+1,r ));
                }
            }
            int Compare(int a,int b){
                return Math.max(a, b);
            }
        }
        