Horde Chess

Imagine you have a $N\times N$ chessboard. - The horizontal rows are called ranks and are numbered from $1$ to $N$ from **bottom** to **top**. - The vertical columns are called files and are numbered from $1$ to $N$ from **left** to **right**. - A square in the $i^{th}$ rank and $j^{th}$ file is represented as $(i,j)$. A chess pawn present in the square $(i,j)$ can attack on the squares $(i+1,j-1