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:
from math import hypot
N = int(input())
XY = [tuple(map(int,input().split())) for i in range(N)]

if N == 2:
    d = hypot(XY[0][0]-XY[1][0], XY[0][1]-XY[1][1])
    print(d/2)
    exit()

def center(a,b,c,d,e,f):
    aa = a * a
    bb = b * b
    cc = c * c
    dd = d * d
    ee = e * e
    ff = f * f
    py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))
    px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a)) \
        if (c == a) else (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))
    r = hypot(px - a, py - b)
    return (r,px,py)

eps = 10**-10
ans = float('inf')
for i in range(N-2):
    x1,y1 = XY[i]
    for j in range(i+1,N-1):
        x2,y2 = XY[j]
        for k in range(j+1,N):
            x3,y3 = XY[k]
            try:
                r,px,py = center(x1,y1,x2,y2,x3,y3)
            except ZeroDivisionError:
                continue
            for x,y in XY:
                d = hypot(px-x, py-y)
                if d <= r+eps:
                    continue
                break
            else:
                ans = min(ans,r)
for i in range(N-1):
    for j in range(i+1,N):
        x1,y1 = XY[i]
        x2,y2 = XY[j]
        x = (x1+x2)/2
        y = (y1+y2)/2
        r = hypot(x1-x, y1-y)
        for x3,y3 in XY:
            d = hypot(x-x3,y-y3)
            if d <= r+eps:
                continue
            break
        else:
            ans = min(ans,r)

print(ans)