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())
XY = [tuple(map(int,input().split())) for _ in range(N)]

def f(x,y):
  mx = 0
  for x1,y1 in XY:
    if ((x1-x)**2+(y1-y)**2)**0.5 > mx:
      mx = ((x1-x)**2+(y1-y)**2)**0.5
  return mx

def g(x):
  l = 0.0
  r = 1000.0
  for i in range(80):
    c1 = (l*2+r)/3
    c2 = (l+r*2)/3
    if f(x,c1) > f(x,c2):
      l = c1
    else:
      r = c2
  return f(x,l)

l = 0.0
r = 1000.0
for i in range(80):
  c1 = (l*2+r)/3
  c2 = (l+r*2)/3
  if g(c1) > g(c2):
    l = c1
  else:
    r = c2

print(g(l))