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: Accepted)

def f_enf_enclose_all_ternary_search(ITER=100):
    from math import hypot
    N = int(input())
    Pos = [[int(i) for i in input().split()] for j in range(N)]

    def f(x, y):
        """N 個の点をすべて囲む円のうち，中心が (x, y) で半径が最小の円の半径"""
        return max(hypot(px - x, py - y) for px, py in Pos)

    def g(x):
        left, right = -1000.0, 1000.0
        for _ in range(ITER):
            m1 = (left * 2 + right) / 3
            m2 = (left + right * 2) / 3
            if f(x, m1) > f(x, m2):
                left = m1
            else:
                right = m2
        return f(x, left)

    left, right = -1000.0, 1000.0
    for _ in range(ITER):
        m1 = (left * 2 + right) / 3
        m2 = (left + right * 2) / 3
        if g(m1) > g(m2):
            left = m1
        else:
            right = m2
    return round(g(left), 10)

print(f_enf_enclose_all_ternary_search())