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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
from math import sqrt
input = sys.stdin.readline
N = int(input())
p = []
for _ in range(N):
  p.append(tuple(map(int, input().split())))

def dist(x, y, u, v):
  return sqrt((x - u) ** 2 + (y - v) ** 2)

p.sort(key = lambda x: x[1])
y = (p[N // 2][1] + p[N // 2 - 1][1]) / 2
if N % 2:
  y = p[N // 2][1]
p.sort(key = lambda x: x[0])
x = (p[N // 2][0] + p[N // 2 - 1][0]) / 2
if N % 2:
  x = p[N // 2][0]
res = 0
for t in p:
  u = t[0]
  v = t[1]
  res = max(res, dist(x, y, u, v))
print(res)