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.InputStreamReader;
import java.util.*;

public class ssss {
    public static void main(String[] args){
        try{
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int n=Integer.parseInt(br.readLine());

            int[][] arr=new int[n][n];
            int cur=0;
            for(int i=0;i<n;i+=2){
                for(int j=0;j<n;j+=2){
                    arr[i][j]=cur*4;
                    arr[i+1][j]=cur*4+1;
                    arr[i][j+1]=cur*4+2;
                    arr[i+1][j+1]=cur*4+3;
                    cur+=1;
                }
            }
            for(int i=0;i<n;i++){
                StringBuilder str=new StringBuilder("");
                for(int j=0;j<n;j++){
                    str.append(arr[i][j]+" ");
                }
                System.out.println(str);
            }

        }catch(Exception e){
            System.out.println("KKKK "+e.getMessage());
        }
    }
    static int mod(int a,int b){
        if (a>b){
            return a-b;
        }
        return b-a;
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
}