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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.StringTokenizer;
import java.io.File;
import java.io.*;
import java.util.*;

public class Main {

    // static final File ip = new File("input.txt");
    // static final File op = new File("output.txt");
    // static {
    //     try {
    //         System.setOut(new PrintStream(op));
    //         System.setIn(new FileInputStream(ip));
    //     } catch (Exception e) {
    //     }
    // }
   
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int test = sc.nextInt();
        while(test-- != 0)
        {
            int n = sc.nextInt();
            if(n==2)
            {
                System.out.println("-1");
                continue;
            }
            int[][] mat = new int[n][n];
            int temp = 1;
            int x=0,y=0;
            boolean check = true;
            for(int i=0;i<n;i++)
            {
                for(int j=0;j<n;j++)
                {
                    if(temp > n*n)
                    {
                       x = i;
                       y = j;
                       check = false;
                       break;
                    }
                    mat[i][j] = temp;
                    temp+=2;
                }
                if(check == false)
                break;
            }
            // System.out.println(x+" "+y);
            check = true;
            temp = 2;
            for(int i=x;i<=x;i++)
            {
                for(int j=y;j<n;j++)
                {
                    if(temp > n*n)
                    {
                       x = i;
                       y = j;
                       check = false;
                       break;
                    }
                    mat[i][j] = temp;
                    temp+=2;
                }
                if(check == false)
                break;
            }
            check = true;
            for(int i=x+1;i<n;i++)
            {
                for(int j=0;j<n;j++)
                {
                    if(temp > n*n)
                    {
                       x = i;
                       y = j;
                       check = false;
                       break;
                    }
                    mat[i][j] = temp;
                    temp+=2;
                }
                if(check == false)
                break;
            }
            for(int i=0;i<n;i++)
            {
                for(int j=0;j<n;j++)
                {
                    System.out.print(mat[i][j]+" ");   
                }
                System.out.println();
            }
        }
    }

    public static int countSetBits(long number) {
        int count = 0;
        while (number > 0) {
            ++count;
            number &= number - 1;
        }
        return count;
    }

    private static <T> void swap(T[] array, int i, int j) {
        if (i != j) {
            T tmp = array[i];
            array[i] = array[j];
            array[j] = tmp;
        }
    }

    private static long getSum(int[] array) {
        long sum = 0;
        for (int value : array) {
            sum += value;
        }

        return sum;
    }

    private static boolean isPrime(int x) {
        if (x < 2)
            return false;
        for (int d = 2; d * d <= x; ++d) {
            if (x % d == 0)
                return false;
        }

        return true;
    }

    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n];
        used[0] = used[1] = true;

        int size = 0;
        for (int i = 2; i < n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j < n; j += i) {
                    used[j] = true;
                }
            }
        }

        int[] primes = new int[size];
        for (int i = 0, cur = 0; i < n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }

        return primes;
    }

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    static void shuffleArray(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    static void shuffleList(ArrayList<Long> arr) {
        int n = arr.size();
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr.get(i);
            int randomPos = i + rnd.nextInt(n - i);
            arr.set(i, arr.get(randomPos));
            arr.set(randomPos, tmp);
        }
    }

    static void shuffleArrayL(long[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public boolean hasNext() {
            return false;
        }

        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;
        }
    }
}