Problem Statement

You are given a positive integer $N$.

Fill each square of a grid with $N$ rows and $N$ columns by writing a positive integer not greater than $N^2$ so that all of the following conditions are satisfied.

• Two positive integers written in horizontally or vertically adjacent squares never sum to a prime number.
• Every positive integer not greater than $N^2$ is written in one of the squares.

Under the Constraints of this problem, it can be proved that such a way to fill the grid always exists.

Constraints

• $3\leq N\leq 1000$

Input

The input is given from Standard Input in the following format:

N

Output

Print a way to fill the grid under the conditions in the following format, where $A_{ij}$ is the positive integer at the $i$-th row and $j$-th column:

A_{11} \ldots A_{1N}
\vdots
A_{N1} \ldots A_{NN}

If there are multiple ways to fill the grid under the conditions, any of them will be accepted.