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=[list(map(int,input().split())) for i in range(N)]
from itertools import combinations
a=9999
def f(X,Y,R2,a):
    if all([(X-x)**2+(Y-y)**2<R2 for x,y in XY]):
        a=min(a,R2**.5)
    return a
for (x1,y1),(x2,y2),(x3,y3) in combinations(XY,3):
    e1=(x2-x3)**2+(y2-y3)**2
    e2=(x3-x1)**2+(y3-y1)**2
    e3=(x1-x2)**2+(y1-y2)**2
    p=e1*(e2+e3-e1)
    q=e2*(e3+e1-e2)
    r=e3*(e1+e2-e3)
    if p+q+r==0:continue
    X=(p*x1+q*x2+r*x3)/(p+q+r)
    Y=(p*y1+q*y2+r*y3)/(p+q+r)
    R2=(X-x1)**2+(Y-y1)**2+10e-9
    a=f(X,Y,R2,a)
for (x1,y1),(x2,y2) in combinations(XY,2):
    X=(x1+x2)/2
    Y=(y1+y2)/2
    R2=(X-x1)**2+(Y-y1)**2+10e-9
    a=f(X,Y,R2,a)
print(a)