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 Ishu
{
    static Scanner scan = new Scanner(System.in);
    static BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out)); 
    static void tc() throws Exception
    {
    int n = scan.nextInt();
    int[][] a = new int[n][n];
    int i,j;
    int cnt = 0;
    for(i=0;i<n;i+=4)
        for(j=0;j<n;j+=4, cnt += 16)
            {
            int sr = i;
            int sc = j;
            
            int[][] cr = new int[4][4];
            int l,r;
            
            int cc = cnt;
            for(l=0;l<4;++l)
                for(r=0;r<4;++r,++cc)
                    cr[l][r] = cc;
                    
            int[] temp = new int[4];    
            for(l=0;l<4;++l)
                {
                int idx = 0;
                int amt = l;
                for(r=amt;r<4;++r)  
                    temp[idx++] = cr[l][r];
                for(r=0;r<amt;++r)    
                    temp[idx++] = cr[l][r];
                    
                for(r=0;r<4;++r)    
                    cr[l][r] = temp[r];
                }
                
            for(l=0;l<4;++l)  
                for(r=0;r<4;++r)  
                    a[sr + l][sc + r] = cr[l][r];
            }
    for(i=0;i<n;++i)
        {
        for(j=0;j<n;++j)
            output.write(a[i][j] + " ");
        output.write("\n");
        }
    output.flush();
    }
    public static void main(String[] args) throws Exception
    {
    int t = 1;
    //t = scan.nextInt();
    while(t-- > 0)
        tc();
    }
}