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:
EPS = 10**(-10)

N = int(input())
points = [list(map(float,input().split())) for _ in range(N)]

def dist(p0,p1):
    x0,y0 = p0
    x1,y1 = p1
    return ((x1-x0)**2+(y1-y0)**2)**0.5

def canMakeRectangle(p0,p1,p2):
    x0,y0 = p0
    x1,y1 = p1
    x2,y2 = p2
    if abs((y1-y0)*(x2-x0)-(y2-y0)*(x1-x0))<EPS:
        return False
    else:
        return True

def circumcircle(p0,p1,p2):
    x0,y0 = p0
    x1,y1 = p1
    x2,y2 = p2
    l0,l1,l2 = dist(p1,p2),dist(p2,p0),dist(p0,p1)
    r = l0*l1*l2/(((l0+l1+l2)*(-l0+l1+l2)*(l0-l1+l2)*(l0+l1-l2))**0.5)
    a = ((l0**2)*(l1**2+l2**2-l0**2)*x0+(l1**2)*(l2**2+l0**2-l1**2)*x1+(l2**2)*(l0**2+l1**2-l2**2)*x2)/((l0**2)*(l1**2+l2**2-l0**2)+(l1**2)*(l2**2+l0**2-l1**2)+(l2**2)*(l0**2+l1**2-l2**2))
    b = ((l0**2)*(l1**2+l2**2-l0**2)*y0+(l1**2)*(l2**2+l0**2-l1**2)*y1+(l2**2)*(l0**2+l1**2-l2**2)*y2)/((l0**2)*(l1**2+l2**2-l0**2)+(l1**2)*(l2**2+l0**2-l1**2)+(l2**2)*(l0**2+l1**2-l2**2))
    return r,a,b

def circle(p0,p1):
    x0,y0 = p0
    x1,y1 = p1
    r = dist(p0,p1)/2
    a = (x1-x0)/2+x0
    b = (y1-y0)/2+y0
    return r,a,b

def check(c,P):
    r,a,b = c
    for p in P:
        if dist((a,b),p) > r+EPS:
            return False
    return True

ans = float('inf')

for i in range(N-2):
    for j in range(i+1,N-1):
        for k in range(j+1,N):
            if canMakeRectangle(points[i],points[j],points[k]):
                r,a,b = circumcircle(points[i],points[j],points[k])
                if check((r,a,b),points):
                    ans = min(ans,r)

for i in range(N-1):
    for j in range(i+1,N):
        r,a,b = circle(points[i],points[j])
        if check((r,a,b),points):
            ans = min(ans,r)

print(ans)