Static PACMAN

In a static version of the game PAC-MAN, our hero doesn't have to eat any Pac-Dots and instead it is sufficient to traverse a square matrix of dimensions $N$ x $N$. The matrix is lying in a cartesian plane and is composed of $N+1$ horizontal wires equally spaced by $1$ units and $N+1$ vertical wires equally spaced by $1$ units. The intersection of wires form small squares(cells) of area $1$ squar