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. \InputFile One integer $n~(1 \le n \le 9)$. \OutputFile Print the matrix --- the chessboard in the given manner. Watch for alignment!