A949.Icy Perimeter--Silver

Farmer John is going into the ice cream business! He has built a machine that
produces blobs of ice cream but unfortunately in somewhat irregular shapes,
and he is hoping to optimize the machine to make the shapes produced as output
more reasonable.
The configuration of ice cream output by the machine can be described using an
$N \times N$ grid ($1 \leq N \leq 1000$) as follows: