Description

Slavko wants to fill an $n \times n$ matrix with $n^2$ distinct positive integers such that:

• The average of the $n$ numbers in each row is an integer that appears in that row.
• The average of the $n$ numbers in each column is an integer that appears in that column.
• For any element $a_{i,j}$ in the matrix, $1 \le a_{i,j} \le 10^9$.

Please help him find any feasible solution.

Input Format

One line with one integer $n$.

Output Format

This problem uses Special Judge.

If there is no solution, output -1.

Otherwise, output $n$ lines, each containing $n$ integers, representing any matrix that meets the requirements.

3 

1 2 3
4 5 6
7 8 9 

2 

-1 

Hint

Sample 1 Explanation

The row averages are $2,5,8$, and each is an integer in its corresponding row.

The column averages are $4,5,6$, and each is an integer in its corresponding column.

Constraints

For $100\%$ of the testdata, $1 \le n \le 100$.

Notes

Translated from COCI2016-2017 CONTEST #2 T4 Prosječni。

Translated by ChatGPT 5