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 (3.4.3) (judge verdict: Wrong Answer)

import math

def f(a,b,x,y):
    ans=math.sqrt( (a-x)*(a-x) + (b-y)*(b-y) )
    return ans

n=int(input())
x=[]
y=[]
for i in range(n):
    u,v=map(int,input().split())
    x.append(u)
    y.append(v)

radius=20000
for i in range(n):
    for j in range(i+1,n):
        a=(x[i]+x[j])/2
        b=(y[i]+y[j])/2
        r=f(x[i],y[i],x[j],y[j])/2
        ff=1
        for k in range(n):
            if f(a,b,x[k],y[k])>r:
                ff=0
                break
        if ff:
            radius=min(r,radius)
print("%0.12f"%radius)