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:
from itertools import combinations
INFTY = 10**4
epsilon = 1e-10
def dist(x,y):
    return ((x[0]-y[0])**2+(x[1]-y[1])**2)**0.5
def cross(x,y):
    return x[0]*y[1]-x[1]*y[0]
def dot(x,y):
    return x[0]*y[0]+x[1]*y[1]
N = int(input())
X = [list(map(int,input().split())) for _ in range(N)]
rmin = INFTY
for z in combinations(range(N),3):
    i,j,k = z
    x0,y0 = X[i]
    x1,y1 = X[j]
    x2,y2 = X[k]
    r = max(dist(X[i],X[j]),dist(X[j],X[k]),dist(X[k],X[i]))/2
    if r==dist(X[i],X[j])/2:
        x = (x0+x1)/2
        y = (y0+y1)/2
    elif r==dist(X[j],X[k])/2:
        x = (x1+x2)/2
        y = (y1+y2)/2
    else:
        x = (x2+x0)/2
        y = (y2+y0)/2
    a = cross([x1-x0,y1-y0],[x2-x0,y2-y0])
    if a==0:continue
    if dot([x1-x0,y1-y0],[x2-x0,y2-y0])>=0 and dot([x0-x1,y0-y1],[x2-x1,y2-y1])>=0 and dot([x1-x2,y1-y2],[x0-x2,y0-y2])>=0:
        s = ((x1-x0)**2+(y1-y0)**2-(x0+x1-2*x2)**2-(y0+y1-2*y2)**2)/8
        s = s/(x0*y1-x1*y0-x2*y1+x2*y0-x0*y2+x1*y2)
        x = (x0+x1)/2+s*(y1-y0)
        y = (y0+y1)/2+s*(x0-x1)
        r = dist([x,y],[x0,y0])
    flag = 0
    for i in range(N):
        if dist([x,y],X[i])<=r+epsilon:
            continue
        else:
            flag = 1
            break
    if flag==0:
        rmin = min(rmin,r)
if rmin==INFTY:
    rmin = 0
    for i in range(N-1):
        for j in range(i+1,N):
            rmin = max(rmin,dist(X[i],X[j]))
    print(rmin/2)
else:
    print(rmin)