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 Main {
    static int inf = (int) 1e9 + 7;

    static void add(HashMap<Integer, Integer> one, int two) {
        if (!one.containsKey(two)) one.put(two, 0);
        one.put(two, one.get(two) + 1);
    }

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int n = nextInt();
        int a[][] = new int [n][n];
        int num = 0;
        for(int i = 0;i < n/ 4;i++) {
            for(int j = 0;j < n / 4;j++) {
                for(int i1 = 0;i1 < 4;i1++) {
                    for(int j1 = 0;j1 < 4;j1++) {
                        a[i * 4 + i1][j * 4 + j1] = num;
                        num++;
                    }
                }
            }
        }
        for(int i = 0;i < n;i++) {
            for(int j = 0;j < n;j++) pw.print(a[i][j] + " ");
            pw.println();
        }
        pw.close();
    }

    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");
    static PrintWriter pw;

    static String next() throws IOException {
        while (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}