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:
//make sure to make new file!
import java.io.*;
import java.util.*;

public class CMC19{
   
   public static void main(String[] args)throws IOException{
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter out = new PrintWriter(System.out);
      
      int n = Integer.parseInt(f.readLine());
      int n4 = n/4;
      int[][] answer = new int[n][n];
      
      for(int k = 0; k < n4; k++){
         for(int j = 0; j < n4; j++){
            int start = (k*n4+j)*16;
            int count = 0;
            for(int x = k*4; x < k*4 + 4; x++){
               for(int y = j*4; y < j*4 + 4; y++){
                  answer[x][y] = start + count;
                  count++;
               }
             }
         }
      }
      
      for(int k = 0; k < n; k++){
         for(int j = 0; j < n; j++){
            out.print(answer[k][j] + " ");
         }
         out.println();
      } 
      
      
      
      
      out.close();
   }
   
      
}