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: Wrong Answer)

n = gets.chomp.to_i
x = []
y = []
dis1 = 0
dis_index1 = 0
dis2 = 0
dis_index2 = 0
x[0], y[0] = gets.chomp.split(' ').map{|i| i.to_i }
(n - 1).times{|i|
  ii = i + 1
  x[ii], y[ii] = gets.chomp.split(' ').map{|iii| iii.to_i }
  dis = (x[0] - x[ii]) ** 2 + (y[0] - y[ii]) ** 2
  if dis > dis1
    dis1 = dis
    dis_index1 = ii
  end
}

n.times{|i|
  dis = (x[dis_index1] - x[i]) ** 2 + (y[dis_index1] - y[i]) ** 2
  if dis > dis2
    dis2 = dis
    dis_index2 = i
  end
}

dis3 = 0
dis_index3 = 0
n.times{|i|
  dis = (x[dis_index2] - x[i]) ** 2 + (y[dis_index2] - y[i]) ** 2
  if dis > dis3
    dis3 = dis
    dis_index3 = i
  end
}

puts Math.sqrt(dis3) / 2.0