USACO Silver 2016 January - Build Gates

The official solution stores the farm in a $2005 \times 2005$ boolean array with the origin at $(1002, 1002)$, but this is not sufficient. Since each fence segment is doubled, the maximum distance in each direction could be $2000$ units, causing an input such as $1000$ $\texttt{N}$s to go out of bounds. To not go out of bounds, an array of size $4003 \times 4003$ should be used: $1$ unit for the origin position, $2000$ units in each direction from the origin and $1$ more unit in each direction to ensure that the farm includes area beyond the fence.