Problem:
Score : 600 points

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

2 \leq N \leq 50

0 \leq x_i \leq 1000

0 \leq y_i \leq 1000

The given N points are all different.

The values in input are all integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in Ruby (2.3.3) (judge verdict: Accepted)

# 外接円の中心と半径の自乗
def circumcenter(a,b,c)
  x = (a-b)*c.abs2 + (b-c)*a.abs2 + (c-a)*b.abs2
  y = (a-b)*c.conj + (b-c)*a.conj + (c-a)*b.conj
  z = x / y
  r = (a-z).abs2
  [z,r]
end

# 二点の中心と中心からの距離の自乗
def bisector(a,b)
  z = (a+b) / 2
  r = ((a-b)/2).abs2
  [z,r]
end

# main
n = gets.to_i
a = Array.new(n){ gets.split.map &:to_f }.map{|b| Complex(*b)}
ans = [Float::INFINITY]
EPS = 1e-6
chmin = -> z,r { ans[0] = [ans[0], r].min if a.all?{|v| (v-z).abs2 <= r + EPS}}

# 2点を含む最小円を全探索
a.combination(2) do |s,t|
  z,r = bisector(s,t)
  chmin[z,r]
end

# 3点の外接円を全探索
a.combination(3) do |s,t,u|
  z,r = circumcenter(s,t,u)
  chmin[z,r]
end

puts Math.sqrt(ans[0])