A magic square is a special $N \times N$ matrix: it is composed of the numbers $1, 2, 3, \dots, N \times N$, and the sum of the numbers in each row, each column, and both diagonals are the same.

When $N$ is odd, we can construct a magic square using the following method:

First, write $1$ in the middle of the first row.

After that, fill in each number $K$ ($K = 2, 3, \dots, N \times N$) in increasing order according to the following rules:

1. If $(K-1)$ is in the first row but not in the last column, then $K$ is placed in the last row, in the column to the right of $(K-1)$.
2. If $(K-1)$ is in the last column but not in the first row, then $K$ is placed in the first column, in the row above $(K-1)$.
3. If $(K-1)$ is in the last row and the last column, then $K$ is placed directly below $(K-1)$.
4. If $(K-1)$ is neither in the first row nor in the last column, and the cell to the upper-right of $(K-1)$ is not yet filled, then $K$ is placed in the upper-right of $(K-1)$; otherwise, $K$ is placed directly below $(K-1)$.

Given $N$, please construct the $N \times N$ magic square using the method described above.

Input

The input consists of a single line containing an integer $N$, representing the size of the magic square.

Output

The output contains $N$ lines, each containing $N$ integers, representing the $N \times N$ magic square constructed by the method above. Adjacent integers in a row are separated by a single space.

Examples

Input 1

3

Output 1

8 1 6
3 5 7
4 9 2

Input 2

5

Output 2

17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9

Constraints

For $100\%$ of the data, $1 \le N \le 39$ and $N$ is odd.