Magic Odd Square

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

inputFormat

Input

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

outputFormat

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

样例

1

1

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