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:
import math
from itertools import combinations
n = int(input())
xy = [list(map(int,input().split())) for i in range(n)]
def enc(i,j,k):
  a,b = i
  c,d = j
  e,f = k
  aa = a*a
  bb = b*b
  cc = c*c
  dd = d*d
  ee = e*e
  ff = f*f
  if (2*(e-a)*(b-d)-2*(c-a)*(b-f)) == 0:
    ymax = max(b,d,f)
    ymin = min(b,d,f)
    xmax = max(a,c,e)
    xmin = min(a,c,e)
    (px,py) = ((xmax-xmin)/2,(ymax-ymin)/2)
    r = math.hypot(xmax-xmin,ymax-ymin)/2
  else:
    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 = math.hypot(px-a, py-b)
  return (r,px,py)
def judge(r,px,py):
  ls = [math.hypot(px-x,py-y) for x,y in xy]
  if max(ls) <= r+10**-7:
    return True
  else:
    return False
ans = 10**18
for i,j in combinations(xy,2):
  x1,y1 = i
  x2,y2 = j
  px = (x1+x2)/2
  py = (y1+y2)/2
  r = math.hypot(x1-x2,y1-y2)/2
  if judge(r,px,py):
    ans = min(ans,r)
for i,j,k in combinations(xy,3):
  r,px,py = enc(i,j,k)
  if judge(r,px,py):
    ans = min(ans,r)
print(ans)