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 Hello {
    static class FastReader {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        public FastReader() {
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        final int grid = scan.nextInt();
        int temp = 0;
        int array[][] = new int[grid][grid];
        StringBuilder stringBuilder = new StringBuilder();

        for (int i = 0; i < grid / 2; i++) {
            for (int j = 0; j < grid / 2; j++) {
                array[i][j] = 4 * temp + 1;
                array[i][j + (grid / 2)] = 4 * temp + 2;
                array[i + grid / 2][j] = 4 * temp + 3;
                array[i + grid / 2][j + (grid / 2)] = 4 * temp;
                temp++;
            }
        }

        for (int i = 0; i < grid; i++) {
            for (int j = 0; j < grid; j++) {
                stringBuilder.append(array[i][j]).append(' ');
            }
            stringBuilder.append('\n');
        }

        System.out.println(stringBuilder);
    }
}