Problem: Let us define a magic grid to be a square matrix of integers of size n × n, satisfying the following conditions. 

  * All integers from 0 to (n^2 - 1) inclusive appear in the matrix exactly once. 
  * [Bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all elements in a row or a column must be the same for each row and column. 



You are given an integer n which is a multiple of 4. Construct a magic grid of size n × n.

Input

The only line of input contains an integer n (4 ≤ n ≤ 1000). It is guaranteed that n is a multiple of 4.

Output

Print a magic grid, i.e. n lines, the i-th of which contains n space-separated integers, representing the i-th row of the grid.

If there are multiple answers, print any. We can show that an answer always exists.

Examples

Input


4


Output


8 9 1 13
3 12 7 5
0 2 4 11
6 10 15 14

Input


8


Output


19 55 11 39 32 36 4 52
51 7 35 31 12 48 28 20
43 23 59 15 0 8 16 44
3 47 27 63 24 40 60 56
34 38 6 54 17 53 9 37
14 50 30 22 49 5 33 29
2 10 18 46 41 21 57 13
26 42 62 58 1 45 25 61

Note

In the first example, XOR of each row and each column is 13.

In the second example, XOR of each row and each column is 60.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int a[][]=new int[n][n];
            int x=0;
            for(int i=0;i<n/2;i++)
            {
                for(int j=0;j<n/2;j++)
                {
                    a[i][j]=x*4;
                    x++;
                }
            }
            x=0;
            for(int i=n/2;i<n;i++)
            {
                for(int j=0;j<n/2;j++)
                {
                    a[i][j]=x*4;
                    x++;
                }
            }
            x=0;
            for(int i=0;i<n/2;i++)
            {
                for(int j=n/2;j<n;j++)
                {
                    a[i][j]=x*4;
                    x++;
                }
            }
            x=0;
            for(int i=n/2;i<n;i++)
            {
                for(int j=n/2;j<n;j++)
                {
                    a[i][j]=x*4;
                    x++;
                }
            }
            for(int i=0;i<n;i++)
            {
                for(int j=0;j<n;j++)
                {
                    if(i<n/2 && j<n/2)
                    {
                        out.print(a[i][j]+" ");
                    }
                    else if(i<n/2 && j>=n/2)
                    {
                        out.print((a[i][j]+1)+" ");
                    }
                    else if(i>=n/2 && j<n/2)
                    {
                        out.print((a[i][j]+2)+" ");
                    }
                    else
                    {
                        out.print((a[i][j]+3)+" ");
                    }
                }
                out.println();
            }
        }
        out.close();
    }
    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;
        }
    }
}