Island Hopping

The nation of Islandia can be represented as an $N \times N$ grid. Let $(i, j)$ denote the square at the $i$-th row from the top and the $j$-th column from the left. A cell $(i, j)$ is labelled $1$ if it is land and $0$ if it is water. Any two cells of the grid which share a side, and are both land are said to belong to the same island. Islandia holds two contests a year, the first at $(x_a, y_a