Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in PYTHON3):

Solution:
from math import sqrt

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

lower = 0
upper = 10000


def get_cross_point(p1, p2, r):
    x, y = p2
    x -= p1[0]
    y -= p1[1]
    a = (x ** 2 + y ** 2) / 2
    if (x ** 2 + y ** 2) * r ** 2 - a ** 2 < 0:
        return None
    x1 = (a * x + y * sqrt((x ** 2 + y ** 2) * r ** 2 - a ** 2)) / (x ** 2 + y ** 2)
    y1 = (a * y - x * sqrt((x ** 2 + y ** 2) * r ** 2 - a ** 2)) / (x ** 2 + y ** 2)
    x2 = (a * x - y * sqrt((x ** 2 + y ** 2) * r ** 2 - a ** 2)) / (x ** 2 + y ** 2)
    y2 = (a * y + x * sqrt((x ** 2 + y ** 2) * r ** 2 - a ** 2)) / (x ** 2 + y ** 2)
    x1 += p1[0]
    x2 += p1[0]
    y1 += p1[1]
    y2 += p1[1]
    return (x1, y1), (x2, y2)


def square_dist(p0, p1):
    return ((p0[0] - p1[0]) ** 2) + ((p0[1] - p1[1]) ** 2)


def check_all_in_r(p, r):
    for q in points:
        if square_dist(p, q) > (r ** 2) + 0.0000001:
            return False
    return True


def check(r):
    for i in range(n):
        for j in range(i + 1, n):
            cross_points = get_cross_point(points[i], points[j], r)
            if cross_points is None:
                return False
            for p in cross_points:
                if check_all_in_r(p, r):
                    return True

    return False


for _ in range(100):
    middle = (upper + lower) / 2
    if check(middle):
        upper = middle
    else:
        lower = middle
print(middle)