Print the chessboard

You are given a chessboard of size $n\times n$. It is filled with numbers from $1$ to $n^2$ in the following way: the first $ceil(n^2/2)$ numbers from $1$ to $ceil(n^2/2)$ are written in the cells with an even sum of coordinates from left to right from top to bottom. The rest of the $n^2-ceil(n^2/2)$ numbers from $ceil(n^2/2)+1$ to $n^2$ are written in the cells with an odd sum of coordinates from left to right from top to bottom.

The operation $ceil(x/y)$ means division $x$ by $y$ rounded up.

Input

One integer $n(1\le n\le 9)$.

Output

Print the matrix — the chessboard in the given manner. Watch for alignment!

Examples