## USACO 2016 January Contest, Bronze

## Problem 2. Angry Cows

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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.

#### INPUT FORMAT (file angry.in):

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 $0 \ldots 1,000,000,000$).#### OUTPUT FORMAT (file angry.out):

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

6 8 5 6 13 3 4

#### SAMPLE OUTPUT:

5

In this example, launching a cow onto the hay bale at position 5 will cause the bales at positions 4 and 6 to explode, each with blast radius 2. These explosions in turn cause the bales at positions 3 and 8 to explode, each with blast radius 3. However, these final explosions are not strong enough to reach the bale at position 13.

Problem credits: Brian Dean