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:
def solve():
    from sys import stdin
    f_i = stdin
    
    N = int(f_i.readline())
    
    points = []
    for i in range(N):
        x, y = map(int, f_i.readline().split())
        points.append(x + y * 1j)
    
    from itertools import combinations
    radiuses = []
    
    for p1, p2 in combinations(points, 2):
        c = (p1 + p2) / 2
        r = abs(p1 - c)
        for p in points:
            if abs(p - c) > r:
                break
        else:
            radiuses.append(r)
    
    if radiuses:
        return min(radiuses)
    
    def circumcircle(a, b, c):
        n = (a - b) * abs(c) ** 2 + (b - c) * abs(a) ** 2 + (c - a) * abs(b) ** 2
        d = (a - b) * c.conjugate() + (b - c) * a.conjugate() + (c - a) * b.conjugate()
        return n / d # center of circumcircle
    
    err = 10 ** -7
    for p1, p2, p3 in combinations(points, 3):
        z1 = p3 - p1
        z2 = p2 - p1
        if z1.real * z2.imag == z1.imag * z2.real:
            continue
        
        c = circumcircle(p1, p2, p3)
        r = abs(p1 - c)
        for p in points:
            #if abs(p - c) > r:
            if abs(p - c) - r > err:
                break
        else:
            radiuses.append(r)
    
    return min(radiuses)

print(solve())