Problem: Find an n × n matrix with different numbers from 1 to n2, so the sum in each row, column and both main diagonals are odd.

Input

The only line contains odd integer n (1 ≤ n ≤ 49).

Output

Print n lines with n integers. All the integers should be different and from 1 to n2. The sum in each row, column and both main diagonals should be odd.

Examples

Input

1


Output

1


Input

3


Output

2 1 4
3 5 7
6 9 8

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class MagicSquare {

    public static void main(String[] args) { 
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        if (n % 2 == 0) throw new RuntimeException("n must be odd");

        int[][] magic = new int[n][n];

        int row = n-1;
        int col = n/2;
        magic[row][col] = 1;

        for (int i = 2; i <= n*n; i++) {
            if (magic[(row + 1) % n][(col + 1) % n] == 0) {
                row = (row + 1) % n;
                col = (col + 1) % n;
            }
            else {
                row = (row - 1 + n) % n;
                // don't change col
            }
            magic[row][col] = i;
        }

        // print results
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (magic[i][j] < 10)  System.out.print(" ");  // for alignment
                if (magic[i][j] < 100) System.out.print(" ");  // for alignment
                System.out.print(magic[i][j] + " ");
            }
            System.out.println();
        }

    }
}