## Problem 1. Angry Cows

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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 with sufficient force to detonate the hay bales in close proximity to her landing site, which in turn might set of a chain reaction that causes additional hay bales to explode. The goal is to use a single cow to start a chain reaction that detonates all the hay bales.

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 with power $R$ landing at position $x$, this will causes a blast of "radius $R$", engulfing all hay bales within the range $x-R \ldots x+R$. These hay bales then themselves explode (all simultaneously), each with a blast radius of $R-1$. Any not-yet-exploded bales caught in these blasts then all explode (all simultaneously) with blast radius $R-2$, and so on.

Please determine the minimum amount of power $R$ with which a single cow may be launched so that, if it lands at an appropriate location, it will cause subsequent detonation of every single hay bale in the scene.

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

The first line of input contains $N$ ($2 \leq N \leq 50,000$). 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 minimum power $R$ with which a cow must be launched in order to detonate all the hay bales. Answers should be rounded and printed to exactly 1 decimal point.

#### SAMPLE INPUT:

5
8
10
3
11
1


#### SAMPLE OUTPUT:

3.0


In this example, a cow launched with power 3 at, say, location 5, will cause immediate detonation of hay bales at positions 3 and 8. These then explode (simultaneously) each with blast radius 2, engulfing bales at positions 1 and 10, which next explode (simultaneously) with blast radius 1, engulfing the final bale at position 11, which finally explodes with blast radius 0.

Problem credits: Brian Dean

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