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.math.BigInteger;
import java.util.*;
  
public class Main {
	static final long MOD = 998244353;
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner();
        int N = sc.nextInt();
        int[][] grid = new int[250][250];
        int[][] base = {{8,9,1,13},{3,12,7,5},{0,2,4,11},{6,10,15,14}};
        grid[0][0] = 0;
        int power = 1;
        int num = 1;
        while (power < 250) {
        	for (int row = 0; row < power; row++) {
        		grid[row][power] = num;
        		num++;
        	}
        	
        	for (int col = 0; col < power; col++) {
        		grid[power][col] = num;
        		num++;
        	}
        	
        	grid[power][power] = num;
        	num++;
        	power++;
        }
        int[][] ans = new int[N][N];
        for (int i = 0; i < N/4; i++) {
        	for (int j = 0; j < N/4; j++) {
        		for (int a = 0; a < 4; a++) {
        			for (int b = 0; b < 4; b++) {
        				ans[4*i+a][4*j+b] = 16*grid[i][j] + base[a][b];
        			}
        		}
        	}
        }
        StringBuilder print = new StringBuilder();
        for (int i = 0; i < N; i++) {
        	for (int j = 0; j < N; j++) {
        		print.append(ans[i][j] + " ");
        	}
        	print.append("\n");
        }
        System.out.print(print);
    }
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
}

class Node {
	public int n;
	public HashSet<Node> children;
	
	public Node(int n) {
		this.n = n;
		children = new HashSet<Node>();
	}
	
	public void addChild(Node node) {
		children.add(node);
	}
	
	public void removeChild(Node node) {
		children.remove(node);
	}
}