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.*;

public class Main {
    FastScanner in;
    PrintWriter out;
    private static final int MODULO = 998244353;

    public static void main(String[] args) {
        (new Main()).run();
    }

    void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            in.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int[][] baseMatrix = {
            {8, 9, 1, 13},
            {3, 12, 7, 5},
            {0, 2, 4, 11},
            {6, 10, 15, 14},
        };
        int n = in.nextInt();
        int[][] result = new int[n][n];
        for (int i = 0; i < n; i += 4) {
            for (int j = 0; j < n; j += 4) {
                for (int k = 0; k < 4; k++) {
                    for (int l = 0; l < 4; l++) {
                        result[i + k][j + l] = baseMatrix[k][l] + 4 * (i * n / 4 + j);
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                out.print(result[i][j]);
                out.write(' ');
            }
            out.println();
        }
    }


    private static class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String line = bufferedReader.readLine();
                if (line == null) {
                    return null;
                }
                stringTokenizer = new StringTokenizer(line);
            }
            return stringTokenizer.nextToken();
        }

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

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        void close() throws IOException {
            bufferedReader.close();
            ;
        }
    }
}