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 C {

	public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

	public static void main(String[] args) throws IOException {
		// br = new BufferedReader(new FileReader(".in"));
		// out = new PrintWriter(new FileWriter(".out"));
		int n = Integer.parseInt(br.readLine());
		int[][] copy = {
			{8, 9, 1, 13},
			{3, 12, 7, 5},
			{0, 2, 4, 11},
			{6, 10, 15, 14}
		};
		
		int bias = 0;
		
		int[][] ans = new int[n][n];
		
		for (int i = 0; i < n; i+=4) {
			for (int j = 0; j < n; j+=4) {
				for (int k = i; k < i+4; k++) {
					for (int l = j; l < j+4; l++) {
						ans[k][l] = copy[k-i][l-j]+bias;
					}
				}
				
				bias += 16;
			}	
		}
		
		for (int[] x: ans) {
			for (int y: x) out.print(y + " ");
			out.println();
		}
		
		out.close();
	}

}