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)

N = int(input())
P =[]
for i in range(N):
    x,y = map(int,input().split())
    P.append([x,y])
import math
def R(p1,p2,p3):
    a,b = p1
    c,d = p2
    e,f = p3

    aa = a * a
    bb = b * b
    cc = c * c
    dd = d * d
    ee = e * e
    ff = f * f
    
    if (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))!=0:
        py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))
        px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a)) if (c == a) else (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))
        
    r = math.hypot(px - a, py - b)
    return px,py,r

ans = float('inf')

def norm(p):
    r = (p[0]**2+p[1]**2)**0.5
    r /= 2
    return r

def xy(p1,p2):
    return (p1[0]+p2[0])/2.0,(p1[1]+p2[1])/2.0

if N >= 3:
    for i in range(N):
        for j in range(i+1,N):
            for k in range(j+1,N):
                p1,p2,p3 = P[i],P[j],P[k]
                v1 = [p2[0]-p1[0],p2[1]-p1[1]]
                v2 = [p3[0]-p1[0],p3[1]-p1[1]]
                v3 =  [p3[0]-p2[0],p3[1]-p2[1]]
                
                if v1[0]*v2[1]==v1[1]*v2[0]:
                    if max(norm(v1),norm(v2),norm(v3))==norm(v1):
                        r = norm(v1)
                        px,py = xy(p1,p2)
                    elif max(norm(v1),norm(v2),norm(v3))==norm(v2):
                        r = norm(v2)
                        px,py = xy(p1,p3)
                    else:
                        r = norm(v3)
                        px,py = xy(p2,p3)
                else:
                    px,py,r = R(p1,p2,p3)
                flag = 0
                for l in range(N):
                    x,y = P[l]
                    if (x-px)**2 + (y-py)**2 > r**2:
                        flag = 1
                if flag == 0:
                    if ans > r:
                        ans = r
                        ansx,ansy = px,py
else:
    r = ((P[0][0]-P[1][0])**2+(P[0][1]-P[1][1])**2)**0.5
    r /= 2
print(ans)