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())
x=[0 for i in range(N)]
y=[0 for i in range(N)]
p=[]
for i in range(N):
    x[i],y[i]=map(int,input().split())
    p.append((x[i],y[i]))
def dist(p,q):
    a,b=p
    c,d=q
    return math.sqrt((a-c)**2+(b-d)**2)
def check(R):
    Q=[]
    for i in range(N):
        for j in range(i+1,N):
            d=dist(p[i],p[j])/2
            if R<d:
                return False
            h=math.sqrt(R*R-d*d)
            #print(d,h,R)
            nx,ny=(x[j]-x[i],y[j]-y[i])
            nr=math.sqrt(nx**2+ny**2)
            dx,dy=h*nx/nr,h*ny/nr
            mx,my=(x[i]+x[j])/2,(y[i]+y[j])/2
            #print(mx,my)
            #print(dx,dy)
            Q.append((mx+dy,my-dx))
            Q.append((mx-dy,my+dx))
    #print(Q,R)
    for pa in Q:
        flag=1
        for i in range(N):
            #print(pa,i,dist(pa,p[i]),R)
            if dist(pa,p[i])>R+9e-7:
                flag=0
                break
        if flag==1:
            return True
    return False

low=0
high=2000
for line in range(50):
    mid=(low+high)/2
    if check(mid):
        high=mid
    else:
        low=mid
print(mid)