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 sqrt 
n= int(input())
xy=[[int(i) for i in input().split()] for _ in range(n)]
def d(x, y):
    return sqrt((x[0] - y[0]) ** 2 + (x[1] - y[1]) ** 2)
def nai(x, y, z):
    c,b,a = sorted([d(x, y), d(y, z), d(z, x)])
    co = (b**2 + c**2 - a**2)/(2*b*c)
    if co<0: return a/2
    si = sqrt(1-co**2)
    return a/si/2

if n==2:
    print(d(xy[0],xy[1])/2)
else:
    ans=0
    for i in range(n):
        for j in range(i+1, n):
            for k in range(j+1, n):
                ans = max(ans,nai(xy[i],xy[j],xy[k]))
    print(ans)