Problem: We will consider the numbers a and b as adjacent if they differ by exactly one, that is, |a-b|=1.

We will consider cells of a square matrix n × n as adjacent if they have a common side, that is, for cell (r, c) cells (r, c-1), (r, c+1), (r-1, c) and (r+1, c) are adjacent to it.

For a given number n, construct a square matrix n × n such that: 

  * Each integer from 1 to n^2 occurs in this matrix exactly once; 
  * If (r_1, c_1) and (r_2, c_2) are adjacent cells, then the numbers written in them must not be adjacent. 

Input

The first line contains one integer t (1 ≤ t ≤ 100). Then t test cases follow.

Each test case is characterized by one integer n (1 ≤ n ≤ 100).

Output

For each test case, output: 

  * -1, if the required matrix does not exist; 
  * the required matrix, otherwise (any such matrix if many of them exist). 



The matrix should be outputted as n lines, where each line contains n integers.

Example

Input


3
1
2
3


Output


1
-1
2 9 7
4 6 3
1 8 5

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;

public class cf
{
    static PrintWriter out;
    static long MOD = 1000000007;
    static FastReader scan;

    /*-------- I/O using short named function ---------*/
    public static String ns(){return scan.next();}
    public static int ni(){return scan.nextInt();}
    public static long nl(){return scan.nextLong();}
    public static double nd(){return scan.nextDouble();}
    public static String nln(){return scan.nextLine();}
    public static void p(Object o){out.print(o);}
    public static void ps(Object o){out.print(o + " ");}
    public static void pn(Object o){out.println(o);}
    /*-------- for output of an array ---------------------*/
    static void iPA(int arr []){
        StringBuilder output = new StringBuilder();
        for(int i=0; i<arr.length; i++)output.append(arr[i] + " ");out.println(output);
    }
    static void lPA(long arr []){
        StringBuilder output = new StringBuilder();
        for(int i=0; i<arr.length; i++)output.append(arr[i] + " ");out.println(output);
    }
    static void sPA(String arr []){
        StringBuilder output = new StringBuilder();
        for(int i=0; i<arr.length; i++)output.append(arr[i] + " ");out.println(output);
    }
    static void dPA(double arr []){
        StringBuilder output = new StringBuilder();
        for(int i=0; i<arr.length; i++)output.append(arr[i] + " ");out.println(output);
    }
    /*-------------- for input in an array ---------------------*/
    static void iIA(int arr[]){
        for(int i=0; i<arr.length; i++)arr[i] = ni();
    }
    static void lIA(long arr[]){
        for(int i=0; i<arr.length; i++)arr[i] = nl();
    }
    static void sIA(String arr[]){
        for(int i=0; i<arr.length; i++)arr[i] = ns();
    }
    static void dIA(double arr[]){
        for(int i=0; i<arr.length; i++)arr[i] = nd();
    }
    /*------------ for taking input faster ----------------*/
    static 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;
        }
    }

    // Method to check if x is power of 2
    static boolean isPowerOfTwo (int x) { return x!=0 && ((x&(x-1)) == 0);}
    //Method to return lcm of two numbers
    static int gcd(int a, int b){return a==0?b:gcd(b % a, a); }
    //Method to count digit of a number
    static int countDigit(long n){return (int)Math.floor(Math.log10(n) + 1);}

    //Method for sorting
    static void ruffle_sort(int[] a) {
        //shandom_ruffle
        Random r=new Random();
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=r.nextInt(n);
            int temp=a[i];
            a[i]=a[oi];
            a[oi]=temp;
        }
        //sort
        Arrays.sort(a);
    }
    //Method for checking if a number is prime or not
    static boolean isPrime(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    public static void main (String[] args) throws java.lang.Exception
    {
        OutputStream outputStream =System.out;
        out =new PrintWriter(outputStream);
        scan =new FastReader();
        //for fast output sometimes
        StringBuilder sb = new StringBuilder();
        int t = ni();

        while(t--!=0){
            int n=ni();
            if(n==1)
                pn("1");
            else if(n==2)
                pn("-1");
            else{
                int k=1;
                for(int i=0;i<n;i++){
                    for(int j=0;j<n;j++){
                        ps(k+" ");
                        k=k+2;
                        if(k>n*n)
                            k=2;
                    }
                    pn("");
                }
            }
        }
        out.flush();
        out.close();
    }


}