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 itertools
N = int(input())
XY = sorted([tuple(int(_) for _ in input().split()) for _ in range(N)])


def calc(a, b, c, d, e, f):
    if (e - a) * (b - d) == (c - a) * (b - f):
        vx = max([a, c, e]) - min([a, c, e])
        vy = max([b, d, f]) - min([b, d, f])
        return (vx**2 + vy**2) / 4, (max([a, c, e]) + min([a, c, e])) / 2, (
            max([b, d, f]) + min([b, d, f])) / 2
    Py = ((e - a) * (a**2 + b**2 - c**2 - d**2) -
          (c - a) * (a**2 + b**2 - e**2 - f**2)) / (2 * (e - a) * (b - d) - 2 *
                                                    (c - a) * (b - f))
    if c - a:
        Px = (2 * (b - d) * Py - a**2 - b**2 + c**2 + d**2) / (2 * (c - a))
    else:
        Px = (2 * (b - f) * Py - a**2 - b**2 + e**2 + f**2) / (2 * (e - a))
    R2 = ((Px - a)**2 + (Py - b)**2)
    return R2, Px, Py


# ps = [(x, y), ...]: ソートされた座標list
def cross(a, b, c):
    return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0])


def convex_hull(ps):
    qs = []
    n = len(ps)
    for p in ps:
        while len(qs) > 1 and cross(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    t = len(qs)
    for i in range(n - 2, -1, -1):
        p = ps[i]
        while len(qs) > t and cross(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    return qs


XY = convex_hull(XY)
N = len(XY)

ans = -1
if N == 2:
    a, b = XY[0]
    c, d = XY[1]
    print(((a - c)**2 + (b - d)**2)**0.5 / 2)
    exit()
for i, j, k in itertools.combinations(range(N), 3):
    a, b = XY[i]
    c, d = XY[j]
    e, f = XY[k]
    r2, x, y = calc(a, b, c, d, e, f)
    if r2 > ans:
        ans, ansx, ansy = r2, x, y
print(ans**0.5)