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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Comparator;

public class d {
    static BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
   // static Scanner s=new Scanner(System.in);
    public static void main(String[] args) throws IOException {
        StringBuilder sb = new StringBuilder();
      String[] s1=s();
      int n=i(s1[0]);
      int pre=0;
      int val=-1;int k=0;
      int[] [] a=new int[4][4];
      for(int i=0;i<4;i++){
          for(int j=0;j<4;j++){
              a[i][j]=k++;
          }
      }
      int[][] ans=new int[n][n];

        int x=0;
      for(int i=0;i<n;i+=4){
          for(int j=0;j<n;j+=4){
               for(int l=0;l<4;l++){
                   for(int m=0;m<4;m++){
                       ans[i+l][j+m]=x++;
                   }
               }
          }//sb.append("\n");
      }
      for(int i=0;i<n;i++){
          for(int j=0;j<n;j++){
              sb.append(ans[i][j]+" ");
          }sb.append("\n");
      }

        System.out.println(sb.toString());
    }

    static String[] s() throws IOException {

        return s.readLine().trim().split("\\s+");
    }

    static int i(String ss) {
        return Integer.parseInt(ss);
    }
    static long l(String ss) {
        return Long.parseLong(ss);
    }
}

class anyname implements Comparator<anyname>{
    public anyname(){}
    int val;
    public anyname(int val){
        this.val=val;
    }
    @Override
    public int compare(anyname a1,anyname a2){
        return a2.val-a1.val;
    }
}