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
n = int(input())
tx,ty = 0,0
x,y = [],[]

for i in range(n):
  tx,ty = map(int,input().split())
  x.append(tx)
  y.append(ty)


cx = 0
cy = 0
rad = 0
jud = 0
diffr = 0
maxdist = 0
sx,sy = [],[]


# 任意2点間の距離を算出し最大距離を出す。
for i in range(n-1):
  for j in range(i+1,n):
    if rad < math.sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j])):
      rad = math.sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]))
      cx = (x[i]+x[j])/2
      cy = (y[i]+y[j])/2

if rad >= max([math.sqrt((cx-x[i])*(cx-x[i])+(cy-y[i])*(cy-y[i])) for i in range(n)])*2:
  jud = 1
#

if jud == 1:
  rad = rad/2
else:
  p,sx,sy = n,x,y
  rad = 800
  for i in range(0,p-2):
    for j in range(i+1,p-1):
      for k in range(j+1,p):
        a = sx[i]
        b = sy[i]
        c = sx[j]
        d = sy[j]
        e = sx[k]
        f = sy[k]
        aa = 2*(c-a)
        bb = 2*(d-b)
        cc = c*c-a*a+d*d-b*b
        dd = 2*(e-a)
        ee = 2*(f-b)
        ff = e*e-a*a+f*f-b*b
        z = bb*dd-aa*ee
        if z != 0:
          cx = (bb*ff-cc*ee)/z
          cy = (cc*dd-aa*ff)/z
          maxdist = max([math.sqrt((cx-sx[m])*(cx-sx[m])+(cy-sy[m])*(cy-sy[m])) for m in range(p)])
          diffr = math.sqrt((cx-a)*(cx-a)+(cy-b)*(cy-b))
          if maxdist <= diffr and diffr < rad:
            rad = diffr

print(rad)