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
import itertools
N=int(input())
C=[tuple(map(int,input().split())) for _ in range(N)]
e=10**-10

def dist(p1,p2):
    return math.sqrt((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)

def dist2(p1,p2):
    return ((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)

def mid(p1,p2):
    return ((p1[0]+p2[0])/2, (p1[1]+p2[1])/2)

def angle(p1,p2):
    return math.atan2(p2[1]-p1[1], p2[0]-p1[0])

def angle2(c1,c2,r):
    d = dist(c1,c2)
    return math.acos((d/2/r))

def cross(c1,c2,r):
    if dist2(c1,c2) > (2*r)**2:
        return set()
    a = angle(c1,c2)
    t = angle2(c1,c2,r)
    return set([
        (
            c1[0]+r*math.cos(a+t),
            c1[1]+r*math.sin(a+t)
        ),
        (
            c1[0]+r*math.cos(a-t),
            c1[1]+r*math.sin(a-t)
        )
    ])

def judge(r):
    P=set()
    for c1,c2 in itertools.product(C,C):
        if c1==c2:
            continue
        P |= cross(c1,c2,r)
    for p in P:
        for c in C:
            if dist2(p,c)>(r**2+e):
                break
        else:
            return True
    return False

def solve():
    under=0
    ok=800
    while ok-under>10**-6:
        m=(ok+under)/2
        if judge(m):
            ok=m
        else:
            under=m
    return ok

print(solve())