Find the Gap
Description
You are given $n$ points in the 3D space. Please find two parallel planes such that all the $n$ points are inside the gap of the two parallel planes, and the length of the gap is minimized.
The first line of the input contains a single integer $n$ ($1 \leq n \leq 50$), denoting the number of points.
Each of the following $n$ lines contains three integers $x_i$, $y_i$ and $z_i$ ($1 \leq x_i,y_i,z_i \leq 10\,000$), describing a point $(x_i,y_i,z_i)$. It is guaranteed that all the $n$ points are pairwise distinct.
Print a single line containing a single real number: the minimum possible length of the gap with an absolute or relative error of at most $10^{-9}$.
Precisely speaking, assume that your answer is $a$ and the jury's answer is $b$. Your answer will be considered correct if and only if $\frac{|a - b|}{\max\{1, |b|\}} \le 10^{-9}$.
Input
The first line of the input contains a single integer $n$ ($1 \leq n \leq 50$), denoting the number of points.
Each of the following $n$ lines contains three integers $x_i$, $y_i$ and $z_i$ ($1 \leq x_i,y_i,z_i \leq 10\,000$), describing a point $(x_i,y_i,z_i)$. It is guaranteed that all the $n$ points are pairwise distinct.
Output
Print a single line containing a single real number: the minimum possible length of the gap with an absolute or relative error of at most $10^{-9}$.
Precisely speaking, assume that your answer is $a$ and the jury's answer is $b$. Your answer will be considered correct if and only if $\frac{|a - b|}{\max\{1, |b|\}} \le 10^{-9}$.
8
1 1 1
1 1 2
1 2 1
1 2 2
2 1 1
2 1 2
2 2 1
2 2 2
5
1 1 1
1 2 1
1 1 2
1 2 2
2 1 1
1.000000000000000
0.707106781186548