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 Python (3.8.2) (judge verdict: Wrong Answer)

#三分探索を使うよ
N = int(input())
x_lis = []
y_lis = []

for i in range(N):
  num_x, num_y = map(int, input().split())
  x_lis.append(num_x)
  y_lis.append(num_y)

max_x = max(x_lis)
min_x = min(x_lis)
max_y = max(y_lis)
min_y = min(y_lis)

x_left = min_x
x_right = max_x
y_left = min_y
y_right = max_y

def dist(x,lis):
  return [abs(x-i) for i in lis]

#凸関数は、横軸：xの位置、縦軸：各点との距離のうち最大のもの
for i in range(500):
  a = (2*x_left+x_right)/3
  b = (x_left+2*x_right)/3
  dist_a = dist(a,x_lis)
  dist_b = dist(b,x_lis)
  dist_left = dist(x_left,x_lis)
  dist_right = dist(x_right,x_lis)
  if max(dist_right) <= max(dist_left):
    x_left = a
  elif max(dist_left) <= max(dist_right):
    x_right = b
  else:
    x_left = a

#凸関数は、横軸：xの位置、縦軸：各点との距離のうち最大のもの
for i in range(500):
  c = (2*y_left+y_right)/3
  d = (y_left+2*y_right)/3
  dist_c = dist(c,y_lis)
  dist_d = dist(d,y_lis)  
  dist_left = dist(y_left,y_lis)
  dist_right = dist(y_right,y_lis)
  if max(dist_right) <= max(dist_left):
    y_left = c
  elif max(dist_left) <= max(dist_right):
    y_right = d
  else:
    y_left = c

r_lis = [((x_left-i)**2+(y_left-j)**2)**0.5 for i,j in zip(x_lis,y_lis)]
print(max(r_lis))