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)

from numpy.linalg import det
from numpy.linalg import solve
import numpy as np
import math


def find_cross_point(x1, y1, x2, y2, x3, y3):
    A = np.array([[x2-x1, y2-y1], [x3-x2, y3-y2]])
    B = np.array([(x2**2+y2**2-x1**2-y1**2)/2, (x3**2+y3**2-x2**1-y2**1)/2])
    if det(A) == 0:
        return (float("inf"), float("inf"))
    C = solve(A, B)
    return C


N = int(input())
ans = 10**10
plots = []


for i in range(N):
    x, y = map(int, input().split())
    plots.append((x, y))


# 2点の間が直線になる時
for i in range(N):
    for j in range(i+1, N):
        sub = 0
        m_x, m_y = (plots[i][0]+plots[j][0])/2, (plots[i][1]+plots[j][1])/2
        for k in range(N):
            sub = max(sub, math.hypot(m_x-plots[k][0], m_y-plots[k][1]))
        ans = min(ans, sub)


# 3点を円が通る時
for i in range(N):
    for j in range(i+1, N):
        for k in range(j+1, N):
            sub = 0
            x1, y1 = plots[i]
            x2, y2 = plots[j]
            x3, y3 = plots[k]
            mx, my = find_cross_point(x1, y1, x2, y2, x3, y3)
            for k in range(N):
                sub = max(sub, math.hypot(m_x-plots[k][0], m_y-plots[k][1]))
            ans = min(ans, sub)
print(ans)