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.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

public class MagicGrid {
    
    public static void main(String[] args) throws NumberFormatException, IOException
    {
        new MagicGrid().run();
    }

    public void run() throws NumberFormatException, IOException
    {
    	Scanner file = new Scanner(System.in);
    	int N = file.nextInt();
    	int[][] ints = new int[N][N];
    	int x = 0;
    	for(int i = 0;i<ints.length;i+=4)
    	{
    		for(int j = 0;j<ints.length;j+=4)
    		{
    			for(int k = 0;k<4;k++)
    			{
    				for(int l = 0;l<4;l++)
    				{
    					ints[i+k][j+l] = x++;
    				}
    			}
    		}
    	}
    	PrintWriter out = new PrintWriter(System.out);
    	for(int i = 0;i<ints.length;i++){
    		for(int j = 0;j<ints.length;j++)
    		{
    			out.print(ints[i][j]+" ");
    		}
    		out.println();
    	}
    	out.flush();
    	out.close();
    }
}