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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;

public class MagicGrid_C_CF_Manthan {
static PrintWriter pw =new PrintWriter(System.out);
public static void main(String[] args) throws Exception{
	BufferedReader bf= new BufferedReader(new InputStreamReader(System.in));
	int n=Integer.parseInt(bf.readLine());
	int[][] grid=new int[n][n];
	int num=0;
	for(int i=0;i<n/2;i++) {
		for(int j=0;j<n/2;j++) {
			grid[i][j]=num<<2;
			grid[i+n/2][j]=(num<<2)+1;
			grid[i][j+n/2]=(num<<2)+2;
			grid[i+n/2][j+n/2]=(num<<2)+3;
			num++;
		}
	}
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)
			pw.print(grid[i][j]+" ");
		pw.println();
	}
	pw.flush();
}
static int xor(int[] row) {
	int ans=0;
	for(int num:row)
		ans^=num;
	return ans;
}
}