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.*;

import static java.lang.Math.*;

public class Main {

    public static void main(String[] args) throws IOException{
        Scanner scan = new Scanner(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int n = scan.nextInt();

        int[][] a = new int[n][n];

        int cnt = 0;
        for (int i = 0; i < n / 2; i++) {
            for (int j = 0; j < n / 2; j++) {
                a[i][j] = 4 * cnt;
                a[i + n / 2][j] = 4 * cnt + 1;
                a[i][j + n / 2] = 4 * cnt + 2;
                a[i + n / 2][j + n / 2] = 4 * cnt + 3;
                cnt++;
            }
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                out.write(a[i][j] + " ");
            }
            out.write("\n");
        }
        out.close();
    }
}