Elephants in a Pond

Some elephants have decided to drink water from a pond. The pond may be considered a grid with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). There are $4N$ elephants and they stand at the perimeter of the pond in such a way that there is exactly one elephant at the top and bottom of each column and at the left and right end of each row. Since elephants can only s