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())
x = []
y = []
import math
for i in range(n):
    xi,yi = map(int, input().split( ))
    x.append(xi)
    y.append(yi)
if n==2:
    x.append(x[0]+10**(-8))
    y.append(y[0]+10**(-8))
import itertools
def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
    """
    3点を通る円の中心と半径を取得
    """
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d==0:
        return ((0,0),10**10)
    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 = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
    return (x, y), r
ans = 10**10
e = 10**(-8)
for i,j,k in itertools.product(range(n),range(n),range(n)):
    if i!=j and i!=k and j!=k:
        x1, y1, x2, y2, x3, y3 = x[i],y[i],x[j],y[j],x[k],y[k]
        (xc,yc),r = get_circle_center_and_radius(x1, y1, x2, y2, x3, y3)
        flag = True
        for l in range(n):
            if (x[l]-xc)**2 + (y[l]-yc)**2>r**2*(1+e):
                flag = False
                break
        if flag:
            ans = min(ans,r)


for i,j in itertools.product(range(n),range(n)):
    xc = (x[i]+x[j])/2
    yc = (y[i]+y[j])/2
    r = (x[i]-xc)**2 + (y[i]-yc)**2
    flag = True
    for l in range(n):
        if (x[l]-xc)**2 + (y[l]-yc)**2>r*(1+e):
            
            flag = False
            break
    
    if flag:
        ans = min(ans,r**(1/2))
print(ans)