J. Find the Gap
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

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 $$$\frac{|a - b|}{\max\{1, |b|\}} \le 10^{-9}$$$.

Examples
Input
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
Output
1.000000000000000
Input
5
1 1 1
1 2 1
1 1 2
1 2 2
2 1 1
Output
0.707106781186548