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

#(a,b)(c,d)(e,f)の3点で考える


#同一の点が存在するかの判定(存在する→True/しない→False)
def exist_same_point(a,b,c,d,e,f):
    
    return (a,b)==(c,d) or (c,d)==(e,f) or (e,f)==(a,b)



#3点が一直線上にあるかの判定(ある→True/無い→False)
def three_points_on_a_line(a,b,c,d,e,f):

    dx1 = a-c
    dy1 = b-d
    dx2 = a-e
    dy2 = b-f

    return dx2*dy1 == dx1*dy2



#三角形の外心(1直線上に3点があるor同じ点がある場合はNoneを返す)

def circumcenter(a,b,c,d,e,f):

    if exist_same_point(a,b,c,d,e,f) or three_points_on_a_line(a,b,c,d,e,f):
        return None,None,None

    aa = a * a
    bb = b * b
    cc = c * c
    dd = d * d
    ee = e * e
    ff = f * f

    py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))

    px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a)) \
        if (c == a) else (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))

    r = math.hypot(px - a, py - b)

    return px,py,r


def in_c(x,y,r):

    for i in range(N):

        if math.hypot(x-xy[i][0],y-xy[i][1]) > r+10**(-6):
            return False

    return True


N = int(input())

xy = []
ans = float("inf")

for i in range(N):
    x,y = map(int,input().split())
    xy.append([x,y])

for i in range(N):
    for j in range(i):

        nx = (xy[i][0] + xy[j][0]) / 2
        ny = (xy[i][1] + xy[j][1]) / 2
        nr = math.hypot(xy[i][0] - xy[j][0],xy[i][1] - xy[j][1]) / 2

        if in_c(nx,ny,nr):
            ans = min(ans,nr)

for i in range(N):
    for j in range(i):
        for k in range(j):

            nx,ny,nr = circumcenter(xy[i][0],xy[i][1],xy[j][0],xy[j][1],xy[k][0],xy[k][1])
            if nx != None and in_c(nx,ny,nr):
                ans = min(ans,nr)

print (ans)