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=[[0]*2 for i in range(N)]
for i in range(N):
  X[i]=list(map(int,input().split()))

r2max=0
for i in range(N):
  for j in range(i+1):
    for k in range(j+1):
      if i>j and j>k:
        x=(X[i])
        y=(X[j])
        z=(X[k])
        M=[x[0]-y[0],y[0]-z[0],x[1]-y[1],y[1]-z[1],z[0]-x[0],z[1]-x[1]]
        a=M[0]*M[3]-M[1]*M[2]
        b=-M[0]*M[1]-M[2]*M[3]
        c=-M[0]*M[4]-M[2]*M[5]
        d=-M[4]*M[1]-M[5]*M[3]
        if a!=0 and b>0 and c>0 and d>0:
          xyl=x[0]**2+x[1]**2-(y[0]**2+y[1]**2)
          yzl=y[0]**2+y[1]**2-(z[0]**2+z[1]**2)
          A=(M[3]*xyl-M[2]*yzl)/(2*a)
          B=(-M[1]*xyl+M[0]*yzl)/(2*a)
          r2=(x[0]-A)**2+(x[1]-B)**2
          if r2>r2max:
            r2max=r2
for i in range(N):
  for j in range(i+1):
    r2=(X[i][0]-X[j][0])**2+(X[i][1]-X[j][1])**2
    r2=r2/4
    if r2>r2max:
      r2max=r2
import math
print(math.sqrt(r2max))