Distinct Sums Grid

Create an n \times n grid that fulfills the following requirements:

Each integer 1 \dots n appears n times in the grid.

If we create a set that consists of all sums in rows and columns, there are 2n distinct values.

Input

The only line has an integer n.

Output

Print a grid that fulfills the requirements. You can print any valid solution. If there are no solutions, print IMPOSSIBLE.

Constraints

$1 \le n \le 1000$

Example

Input

5

Output

2 3 1 1 1 
1 5 5 3 3 
2 3 5 2 4 
5 4 5 4 1 
2 3 4 4 2

Explanation: Each integer 1 \dots 5 appears 5 times, and the sums in rows and columns are {8,11,12,14,15,16,17,18,19,20}.