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.to_i
P = N.times.map { gets.split.map(&:to_i) }

def ternary_search_tree(left, right)
  loop_cnt = 10000

  loop_cnt.times do
    if yield((left * 2 + right) / 3.0) < yield((left + right * 2) / 3.0)
      right = (left + right * 2) / 3.0
    else
      left = (left * 2 + right) / 3.0
    end
  end

  (left + right) / 2.0
end

CX = ternary_search_tree(-10000, 10000) { |n|
  P.map { |x, _| (x - n).abs }.max
}

CY = ternary_search_tree(-10000, 10000) { |n|
  P.map { |_, y| (y - n).abs }.max
}

cy = P.map(&:first).inject(:+) / N.to_f
cx = P.map(&:last).inject(:+) / N.to_f

r = P.map { |x, y| Math.sqrt((x - CX) ** 2 + (y - CY) ** 2) }.max
r2 = P.map { |x, y| Math.sqrt((x - cx) ** 2 + (y - cy) ** 2) }.max

puts [r, r2].min