Problem Statement

We have an $N \times N$ grid. Let $(i,j)$ denote the square at the $i$-th row from the top and $j$-th column from the left in this grid. Find one way to write an integer on every square to satisfy the conditions below.

• Each integer between $1$ and $N^2$ is written exactly once.
• For every pair of integers $i,j\, (1 \leq i,j \leq N)$, the square $(i,j)$ satisfies the following.
• Among the squares horizontally, vertically, or diagonally adjacent to $(i,j)$ (there are at most eight of them), let $a$ and $b$ be the number of squares with integers larger than and smaller than that of $(i,j)$, respectively. Then, $a \neq b$ holds.

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

Constraints

• $2 \leq N \leq 500$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print a way to write integers to satisfy the conditions, in the following format:

x_{1,1} \ldots x_{1,N}
\vdots
x_{N,1} \ldots x_{N,N}

Here, $x_{i,j}$ is the integer to write on the square $(i,j)$. If multiple solutions exist, any of them will be accepted.