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 itertools
import math

def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d == 0:
        return 0, 0, 0
    x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
    y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / (-d)
    r = (x - x1) ** 2 + (y - y1) ** 2
    return x, y, r

def get_circle_center_and_radius_two(x1, y1, x2, y2):
    x = (x1 + x2) / 2
    y = (y1 + y2) / 2
    r = (x - x1) ** 2 + (y - y1) ** 2
    return x, y, r

def check_if_all_included(x, y, r, points, v):
    for point in points:
        if point in v:
            continue
        
        dist = (x - point[0]) ** 2 + (y - point[1]) ** 2
        if dist > r:
            break
    else:
        return True
    
    return False
            

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

r_min = 1000000
    
for v in itertools.combinations(points, 2):
    x1, y1, x2, y2 = v[0][0], v[0][1], v[1][0], v[1][1]
    x, y, r = get_circle_center_and_radius_two(x1, y1, x2, y2)
    if check_if_all_included(x, y, r, points, v) and r < r_min:
        r_min = r
    
for v in itertools.combinations(points, 3):
    x1, y1, x2, y2, x3, y3 = v[0][0], v[0][1], v[1][0], v[1][1], v[2][0], v[2][1]
    x, y, r = get_circle_center_and_radius(x1, y1, x2, y2, x3, y3)
    if r == 0:
        continue
    
    if check_if_all_included(x, y, r, points, v) and r < r_min:
        r_min = r

print(math.sqrt(r_min))