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 PYTHON3):

Solution:
def main():
    def f(n):
        if n == 1:
            return [[1]]
        it = iter(range((n - 4) * n + 5, n * n + 1) if n & 2 else range(n * n, 0, -1))
        res = [[next(it) for _ in range(n)]]
        for row in f(n - 2):
            res.append([next(it)] + row)
        res.append([next(it) for _ in range(n)])
        for row in res[1:-1]:
            row.append(next(it))
        return res

    for l in f(int(input())):
        print(*l)


if __name__ == '__main__':
    main()