A1018.Switching on the Lights--Silver

Farmer John has recently built an enormous barn consisting of an $N \times N$
grid of rooms ($2 \leq N \leq 100$), numbered from $(1,1)$ up to $(N,N)$.
Being somewhat afraid of the dark, Bessie the cow wants to turn on the lights
in as many rooms as possible.
Bessie starts in room $(1,1)$, the only room that is initially lit. In some
rooms, she will find light switches that she can use to toggle the lights in
other rooms; for example there might be a switch in room $(1,1)$ that toggles
the lights in room $(1,2)$. Bessie can only travel through lit rooms, and she
can only move from a room $(x,y)$ to its four adjacent neighbors $(x-1,y)$,
$(x+1,y)$, $(x,y-1)$ and $(x,y+1)$ (or possibly fewer neighbors if this room
is on the boundary of the grid).
Please determine the maximum number of rooms Bessie can illuminate.

The first line of input contains integers $N$ and $M$ ($1 \leq M \leq 20,000$).
The next $M$ lines each describe a single light switch with four integers $x$,
$y$, $a$, $b$, that a switch in room $(x,y)$ can be used to toggle the lights
in room $(a,b)$. Multiple switches may exist in any room, and multiple
switches may toggle the lights of any room.

A single line giving the maximum number of rooms Bessie can illuminate.

Here, Bessie can use the switch in $(1,1)$ to turn on lights in $(1,2)$ and
$(1,3)$. She can then walk to $(1,3)$ and turn on the lights in $(2,1)$, from
which she can turn on the lights in $(2,2)$. The switch in $(2,3)$ is
inaccessible to her, being in an unlit room. She can therefore illuminate at
most 5 rooms.