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 dis(x1,y1,x2,y2):
    return ((x1-x2)**2+(y1-y2)**2)**0.5
N = int(input())
xy = []
rmax = 2000
r = 1000
rmin = 0
eps = 10e-10
for i in range(N):
    x,y = map(int,input().split())
    xy.append((x,y))
for i in range(50):
    intersections = []
    for i in range(N):
        xi,yi = xy[i]
        for j in range(N):
           if i < j:
               xj,yj = xy[j]
               xc = (xi+xj)/2
               yc = (yi+yj)/2
               dc = dis(xc,yc,xi,yi)
               if r > dc:
                   d = (r**2-dc**2)**0.5
                   intersections.append((xc+(yc-yi)*d/dc,yc-(xc-xi)*d/dc))
                   intersections.append((xc-(yc-yi)*d/dc,yc+(xc-xi)*d/dc))
    ans = False
    for x,y in intersections:
        for i in range(N):
            xi,yi = xy[i]
            if dis(x,y,xi,yi) > r+eps:
                break
        else:
            ans = True
    if ans:
        rmax = r
    else:
        rmin = r
    r = (rmax+rmin)/2
print(r)