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)

require 'pp'

n = gets.chomp!.to_i
points = []

min_x = 99999
max_x = 0
min_y = 99999
max_y = 0

n.times do |i|
    x, y = gets.chomp!.split.map(&:to_i)
    points << [x, y]

    if x < min_x
        min_x = x
    end

    if x > max_x
        max_x = x
    end

    if y < min_y
        min_y = y
    end

    if y > max_y
        max_y = y
    end
end

mid_x = (min_x + max_x).to_f / 2.0
mid_y = (min_y + max_y).to_f / 2.0
diff_x = max_x - min_y
diff_y = max_y - min_y

pp mid_x
pp mid_y

memo_left = Array.new(n, 0.0)
n.times do |i|
    memo_left[i] = Math.sqrt((points[i][0] - mid_x) ** 2 + (points[i][1] - mid_y) ** 2)
end

puts memo_left[-1]