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.util.*;
import java.io.*;
 
public class Solution{
	static PrintWriter out=new PrintWriter(System.out);
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String[] input=br.readLine().trim().split(" ");
		
		int n = Integer.parseInt(input[0]);
		printMagicGrid(n);
		
		out.flush();
		out.close();
	}
	public static void printMagicGrid(int n)
	{
	    int num = 0;
	    int[][] ans = new int[n][n];
	    for(int row = 0; row < n; row += 4)
	    {
	        for(int col = 0; col < n; col += 4)
	        {
	            for(int i = row; i < row + 4; i++)
	            {
	                for(int j = col; j < col + 4; j++)
	                {
	                    ans[i][j] = num;
	                    num++;
	                }
	            }
	        }
	    }
	    
	    for(int i = 0; i < n; i++){
	        for(int j = 0; j < n; j++){
	            out.print(ans[i][j] + " ");
	        }
	        out.println();
	    }
	}
	
}