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:
    // No sorceries shall previal. //
         
    import java.util.Scanner; 
    import java.io.PrintWriter;
    import java.util.*;
    import java.util.Arrays;
     
    public class InVoker {
    		
    	public static void main(String args[]) {
    		
    		Scanner inp = new Scanner(System.in);
    		PrintWriter out= new PrintWriter(System.out);
    		
    		int n=inp.nextInt();
    		int a[][]=new int[n][n];
    		
    		
    		int x = 0;
    		for (int i = 0; i < n; i += 4) 
    		{
    		  for (int j = 0; j < n; j += 4) 
    		  {
    			for (int ii = 0; ii < 4; ii++)
    		    {
    		      for (int jj = 0; jj < 4; jj++)
    		      {
    		        a[i + ii][j + jj] = x++;
    		      }
    		    }
    		  }
    		}
    		
    		for(int i=0;i<n;i++)
    		{
    			for(int j=0;j<n;j++)
    			{
    				out.print(a[i][j]+" ");
    			}
    			out.println();
    		}
    		out.close();
    		inp.close();
    					
    }
    		
}