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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;

public class MagicGrid {

    private static long MOD = 1000000007;

    // begin of solution
    public static void main(String[] args) throws IOException {
        AmitScan sc = new AmitScan();
        AmitPrint pr = new AmitPrint();
        int n = sc.si();
        int[][] a = new int[n][n];
        int k = 0;
        for (int i = 0; i < n / 2; i++) {
            for (int j = 0; j < n / 2; j++) {
                a[i][j] = k;
                a[i][j + n / 2] = k + 1;
                a[i + n / 2][j] = k + 2;
                a[i + n / 2][j + n / 2] = k + 3;
                k += 4;
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++)
                pr.p(a[i][j] + " ");
            pr.pl("");
        }
        pr.close();
    }
    // end of solution

    static class AmitScan {
        private byte[] buf = new byte[1024]; // Buffer of Bytes
        private int index;
        private InputStream in;
        private int total;

        AmitScan() {
            in = System.in;
        }

        private int scan() throws IOException // Scan method used to scan buf
        {
            if (total < 0)
                throw new InputMismatchException();
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0)
                    return -1;
            }
            return buf[index++];
        }

        String s() throws IOException {
            StringBuilder sb = new StringBuilder();
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            while (!isWhiteSpace(n)) {
                sb.append((char) n);
                n = scan();
            }
            return sb.toString();
        }

        int si() throws IOException {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) // Removing starting whitespaces
                n = scan();
            int neg = 1;
            if (n == '-') // If Negative Sign encounters
            {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            return neg * integer;
        }

        long sl() throws IOException {
            long integer = 0;
            int n = scan();
            while (isWhiteSpace(n))
                n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                } else
                    throw new InputMismatchException();
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            return n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1;
        }
    }

    static class AmitPrint {
        private final BufferedWriter bw;

        AmitPrint() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        private void p(Object object) throws IOException {
            bw.append("").append(String.valueOf(object));
        }

        void pl(Object object) throws IOException {
            p(object);
            bw.append("\n");
        }

        void close() throws IOException {
            bw.close();
        }

        void f() throws IOException {
            bw.flush();
        }
    }
}