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:
n = int(input())
points = []
centers = []
INF = 1e100
ans = INF

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __rmul__(self, other):
        return Point(self.x * other, self.y * other)

    def __mul__(self, other):
        return Point(self.x * other, self.y * other)

    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)
        
    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)

    def __truediv__(self, other):
        return Point(self.x / other, self.y / other)

    def sqdist(self, other):
        return (self.x - other.x) ** 2 + (self.y - other.y) ** 2

    def dist(self, other):
        return self.sqdist(other) ** 0.5

    def cross(self, other):
        return self.x * other.y - self.y * other.x

    def dot(self, other):
        return self.x * other.x + self.y * other.y

def three(A, B, C):
    a = B.sqdist(C)
    b = C.sqdist(A)
    c = A.sqdist(B)

    U = (a*(b+c-a)*A + b*(c+a-b)*B + c*(a + b - c)*C) / (a*(b+c-a) + b*(c+a-b) + c*(a + b - c) )
    return U

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

for i in range(n):
    for j in range(i+1, n):
        for k in range(j+1, n):
            if (points[j] - points[i]).cross(points[k] - points[i]) == 0:continue
            centers.append(three(points[i], points[j], points[k]))

for i in range(n):
    for j in range(i+1, n):
        centers.append((points[i] + points[j]) / 2)

for center in centers:
    r = 0
    for i in range(n):
        r = max(r, center.dist(points[i]))
    ans = min(ans, r)
    
print(ans)