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:
import math


def main():
    N = int(input())
    points = []
    for i in range(N):
        x, y = [int(s) for s in input().split()]
        points.append((x, y))

    l = 0
    r = 1000
    for i in range(80):
        c1 = (l * 2 + r) / 3
        c2 = (l + r * 2) / 3
        if g(points, c1) > g(points, c2):
            l = c1
        else:
            r = c2
    print(g(points, l))


def g(points, x):
    l = 0
    r = 1000
    for i in range(80):
        c1 = (l * 2 + r) / 3
        c2 = (l + r * 2) / 3
        if f(points, x, c1) > f(points, x, c2):
            l = c1
        else:
            r = c2
    return f(points, x, l)


def f(points, x, y):
    max_distance = 0
    for i in range(len(points)):
        d = distance(x, y, float(points[i][0]), float(points[i][1]))
        if d > max_distance:
            max_distance = d

    return max_distance


def distance(x1, y1, x2, y2):
    return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)


if __name__ == "__main__":
    main()