Bessie the cow has designed what she thinks will be the next big hit video game:
"Angry Cows". The premise, which she believes is completely original, is that
the player shoots a cow with a slingshot into a one-dimensional scene
consisting of a set of hay bales located at various points on a number line; the
cow lands on a hay bale with sufficient force to cause the bale to explode,
which in turn might set of a chain reaction that causes additional nearby hay
bales to explode. The goal is to use a single cow to start a chain reaction
that detonates as many hay bales as possible.

There are \(N\) hay bales located at distinct integer positions
\(x_1, x_2, \ldots, x_N\) on the number line. If a cow is launched onto a hay
bale at position \(x\), this hay bale explodes with a "blast radius" of 1, meaning
that any other hay bales within 1 unit of distance are also engulfed by the
explosion. These neighboring bales then themselves explode (all simultaneously),
each with a blast radius of 2, so these explosions may engulf additional
yet-unexploded bales up to 2 units of distance away. In the next time step,
these bales also explode (all simultaneously) with blast radius 3. In general,
at time \(t\) a set of hay bales will explode, each with blast radius \(t\). Bales
engulfed by these explosions will themselves explode at time \(t+1\) with blast
radius \(t+1\), and so on.

Please determine the maximum number of hay bales that can explode if a single
cow is launched onto the best possible hay bale to start a chain reaction.

Problem credits: Brian Dean

Problem credits: Brian Dean

The first line of input contains \(N\) (\(1 \leq N \leq 100\)). The remaining \(N\)
lines all contain integers \(x_1 \ldots x_N\) (each in the range
\(0 \ldots 1,000,000,000\)).

Please output the maximum number of hay bales that a single cow can cause to
explode.

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출처 올림피아드 > USACO > 2015-2016 > January > Bronze