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 sys

def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))  #空白あり

N = I()
xy = [LI() for i in range(N)]

# 円の中心の半径は、ある2点の中点か、ある3点の外心かである

ans = []

def distance(A,B):  # 2点間の距離
    x1,y1 = A
    x2,y2 = B
    return ((x1-x2)**2+(y1-y2)**2)**.5

for i in range(N-1):
    for j in range(i+1,N):
        x1,y1 = xy[i]
        x2,y2 = xy[j]
        x,y = (x1+x2)/2,(y1+y2)/2
        r = distance((x,y),(x1,y1))
        for k in range(N):
            if k == i or k == j:
                continue
            else:
                if distance(xy[k],(x,y)) > r+10**-8:
                    break
        else:
            ans.append(r)

def gaishin(A,B,C):  # 3点の外心
    x1,y1 = A
    x2,y2 = B
    x3,y3 = C
    a = 2*((x2-x1)*(y3-y1)-(x3-x1)*(y2-y1))
    b = x2**2-x1**2+y2**2-y1**2
    c = x3**2-x1**2+y3**2-y1**2
    if a == 0:
        return (0,float('inf'))  # 適当な値
    else:
        x = ((y3-y1)*b-(y2-y1)*c)/a
        y = (-(x3-x1)*b+(x2-x1)*c)/a
    return (x,y)

for i in range(N-2):
    for j in range(i+1,N-1):
        for k in range(j+1,N):
            x,y = gaishin(xy[i],xy[j],xy[k])
            if y == float('inf'):
                continue
            else:
                r = distance((x,y),xy[i])
                for l in range(N):
                    if l == i or l == j or l == k:
                        continue
                    else:
                        if distance(xy[l],(x,y)) > r+10**-8:
                            break
                else:
                    ans.append(r)

print(min(ans))