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 {
    public static int n;
    public static boolean check(int[][] arr) {
        TreeSet<Integer> set = new TreeSet<>();
        boolean[] marked = new boolean[n * n];
        for (int i = 0; i < n; i++) {
            int a = arr[i][0];
            int b = arr[0][i];
            for (int j = 1; j < n; j++) {
                a ^= arr[i][j];
                b ^= arr[j][i];
            }
            set.add(a);
            set.add(b);
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                marked[arr[i][j]] = true;
            }
        }
        int cnt = 0;
        for (boolean flag : marked) {
            if (flag) cnt++;
        }
        return set.size() == 1 && cnt == n * n;
    }
    public static void main(String[] args) {
        PrintWriter pw = new PrintWriter(System.out);
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        int[][] matrix = new int[n][n];
        matrix[0][0] = 8;
        matrix[0][1] = 9;
        matrix[0][2] = 1;
        matrix[0][3] = 13;
        matrix[1][0] = 3;
        matrix[1][1] = 12;
        matrix[1][2] = 7;
        matrix[1][3] = 5;
        matrix[2][0] = 0;
        matrix[2][1] = 2;
        matrix[2][2] = 4;
        matrix[2][3] = 11;
        matrix[3][0] = 6;
        matrix[3][1] = 10;
        matrix[3][2] = 15;
        matrix[3][3] = 14;
        int curr = (16 * (n / 4));
        for (int i = 0; i < n; i += 4) {
            for (int j = 0; j < n; j += 4) {
                if (i == 0 && j == 0) continue;
                if (j == 0) {
                    for (int k = i; k < i + 4; k++) {
                        for (int l = j; l < j + 4; l++) {
                            matrix[k][l] = matrix[k - 4][l] + curr;
                        }
                    }
                } else {
                    for (int k = i; k < i + 4; k++) {
                        for (int l = j; l < j + 4; l++) {
                            matrix[k][l] = matrix[k][l - 4] + 16;
                        }
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                pw.print(matrix[i][j] + " ");
            }
            pw.println();
        }
        pw.flush();
    }
}