USACO 2015 December Contest, Silver

Problem 1. Switching on the Lights

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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.

OUTPUT FORMAT (file lightson.out):

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


3 6
1 1 1 2
2 1 2 2
1 1 1 3
2 3 3 1
1 3 1 2
1 3 2 1



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.

Problem credits: Austin Bannister and Brian Dean

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