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:
//package manthan19;
import java.io.*;
import java.util.*;

public class C {
	static int n;
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		n = sc.nextInt();
		int[][] a = new int[n][n];
		for(int i = 0; i < n; i++)
			for(int j = 0; j < n; j++) {
				int m4 = f(i, j);
				int x = g(i % (n / 2), j % (n / 2));
				a[i][j] = x * 4 + m4;
			}
		/*for(int i = 0; i < n; i++) {
			int xor = 0;
			for(int j = 0; j < n; j++)
				xor ^= a[i][j];
			if(xor != 0)
				out.println(i + " "+ xor);
		}
		for(int j = 0; j < n; j++) {
			int xor = 0;
			for(int i = 0; i < n; i++)
				xor ^= a[i][j];
			if(xor != 0)
				out.println(j + "J" + xor);
		}*/
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < n; j++)
				out.print(a[i][j] + " ");
			out.println();
		}
		out.close();
	}
	static int g(int i, int j) {
		return i * n / 2 + j;
	}
	static int f(int i, int j) {
		int ans = 0;
		if(i >= n / 2)
			ans += 2;
		if(j >= n / 2)
			ans++;
		return ans;
	}
	public static PrintWriter out  = new PrintWriter(new BufferedOutputStream(System.out));
	public static class MyScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		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;
		}
	}
}