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.io.PrintWriter;
import java.util.*;

public class A{
    static void solve(){
        int n=readInt();
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n ; j++) {
                write(j%2+j/2*4+i%2*2+i/2*n*2);
            }
            writeln("");
        }
    }
    static PrintWriter pw=new PrintWriter(System.out);
    static BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st=new StringTokenizer(""," ");
    public static void main(String... args){
        solve();
        pw.flush();
    }
    static String read() {
        try {
            if(st.hasMoreTokens())
                return st.nextToken();
            st=new StringTokenizer(bf.readLine()," ");
            if(st.hasMoreTokens())
                return st.nextToken();
        }
        catch (IOException e){e.printStackTrace();}
        return "";
    }
    static int readInt(){
        return Integer.parseInt(read());
    }
    static long readLong(){
        return Long.parseLong(read());
    }
    static <T> void write(T s) {
        pw.write(String.valueOf(s)+" ");
    }
    static <T> void writeln(T s) {
        pw.write(String.valueOf(s)+"\n");
    }
}