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 F {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        int n = Integer.parseInt(reader.readLine());
        int[][] array = new int[n][n];
        array[0][0] = 8;
        array[0][1] = 9;
        array[0][2] = 1;
        array[0][3] = 13;
        array[1][0] = 3;
        array[1][1] = 12;
        array[1][2] = 7;
        array[1][3] = 5;
        array[2][0] = 0;
        array[2][1] = 2;
        array[2][2] = 4;
        array[2][3] = 11;
        array[3][0] = 6;
        array[3][1] = 10;
        array[3][2] = 15;
        array[3][3] = 14;
        int add = 16;
        for(int i = 0; i < n; i += 4){
            for(int j = 0; j < n; j += 4){
                if(i == 0 && j == 0){
                    continue;
                }
                array[i][j] = 8 + add;
                array[i][j + 1] = 9 + add;
                array[i][2 + j] = 1 + add;
                array[i][3 + j] = 13+ add;
                array[i + 1][j] = 3+ add;
                array[i + 1][1 + j] = 12+ add;
                array[i + 1][2 + j] = 7+ add;
                array[i + 1][3 + j] = 5+ add;
                array[i + 2][j] = 0+ add;
                array[i + 2][1 + j] = 2+ add;
                array[i + 2][2 + j] = 4+ add;
                array[i + 2][3 + j] = 11+ add;
                array[i + 3][j] = 6+ add;
                array[i + 3][1 + j] = 10+ add;
                array[i + 3][2 + j] = 15+ add;
                array[i + 3][3 + j] = 14+ add;
                add += 16;
            }
        }
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < n; ++j){
                writer.print(array[i][j] + " ");
            }
            writer.println("");
        }
        writer.close();
    }
}