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 bisect
import copy
import heapq
import math
import sys
from collections import *
from itertools import accumulate, combinations, permutations, product
# from math import gcd
def input():
    return sys.stdin.readline()[:-1]
def ruiseki(lst):
    return [0]+list(accumulate(lst))
mod=pow(10,9)+7
al=[chr(ord('a') + i) for i in range(26)]
direction=[[1,0],[0,1],[-1,0],[0,-1]]

n=int(input())
xy=[list(map(int,input().split())) for i in range(n)]

mi,ma=0,2000
com=list(combinations(range(n),2))

while ma-mi>10**(-8):
    half=(ma+mi)/2
    lst=[]
    flag=1
    for co in com:
        a,b=co
        ax,ay=xy[a]
        bx,by=xy[b]
        if (ax-bx)**2+(ay-by)**2>(2*half)**2:
            flag=0
        else:
            kyori=((ax-bx)**2+(ay-by)**2)**(0.5)
            h=(half**2-(kyori/2)**2)**(0.5)
            tyuuten=((ax+bx)/2,(ay+by)/2)
            tmp=h/2/kyori
            lst.append((tyuuten[0]+(ay-by)*tmp,tyuuten[1]-(ax-bx)*tmp))
            lst.append((tyuuten[0]-(ay-by)*tmp,tyuuten[1]+(ax-bx)*tmp))
    if flag==0:
        mi=half
        continue
    for co in lst:
        bx,by=co
        flag=1
        for i in range(n):
            ax,ay=xy[i]
            bx,by=co
            if (ax-bx)**2+(ay-by)**2>(2*half)**2:
                flag=0
        if flag==1:
            ma=half
            break
    else:
        mi=half

    # print(ma,mi,half)

print((ma+mi)/2)