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 _ in range(n)]
sgm=pow(10,-7)
def func(c):
    allp=[]
    for i in range(n-1):
        for j in range(i+1,n):
            xi,yi=xy[i]
            xj,yj=xy[j]
            dx=xi-xj
            dy=yi-yj
            d=((xi-xj)**2+(yi-yj)**2)**0.5
            if c**2-(d/2)**2<0:return False
            h=(c**2-(d/2)**2)**0.5
            mx,my=(xi+xj)/2,(yi+yj)/2
            if dx==0:
                allp.append([mx-h,my])
                allp.append([mx+h,my])
            elif dy==0:
                allp.append([mx,my-h])
                allp.append([mx,my+h])
            else:
                dx,dy=dy,-dx
                dh=(dy**2+dx**2)**0.5
                dx*=h/dh
                dy*=h/dh
                allp.append([mx+dx,my+dy])
                allp.append([mx-dx,my-dy])
    for px,py in allp:
        flg=True
        for x,y in xy:
            if ((px-x)**2+(py-y)**2)**0.5>c+sgm:
                flg=False
                break
        if flg:
            return True
    return False

r=2*max([abs(x) for x,y in xy])+max([abs(y) for x,y in xy])
l,r=0,r
for i in range(400):
    c=(l+r)/2
    if func(c):
        l,r=l,c
    else:
        l,r=c,r
print(c)
#print(c**2)