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

def check(a,b,r):
    if r<0:r=0
    res=[0,0,0]
    flg=True
    for i in range(N):
        tmp=(X[i]-a)**2+(Y[i]-b)**2
        if tmp>r**2:
            flg=False
        if tmp>res[0]:
            res=[tmp,X[i],Y[i]]
    res[0]=flg
    return res

x_ave,y_ave=sum(X)/N,sum(Y)/N
MIN=10**(-12)
r=1500
r_diff=r/2
k=0.5
d=999/1000


#print(x_ave,y_ave)
while r_diff>MIN:
    tmpres = check(x_ave,y_ave,r)
    #print(r,x_ave,y_ave)
    if tmpres[0]:
        r-=r_diff
    else:
        r+=r_diff
    x_ave+=(tmpres[1]-x_ave)*k
    y_ave+=(tmpres[2]-y_ave)*k
    r_diff=r_diff*d
    k=k*d

print(r)