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

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

def max_dist_xy(x,y):
    max_dist=0
    p=(x,y)
    for c in C:
        max_dist=max(max_dist,dist2(p,c))
    return max_dist

def max_dist_x(x):
    l=0
    r=1000
    for _ in range(80):
        m1=(2*l+r)/3
        m2=(l+2*r)/3
        d1=max_dist_xy(x,m1)
        d2=max_dist_xy(x,m2)
        if d1>d2:
            l=m1
        else:
            r=m2
    return max_dist_xy(x,l)

def solve():
    l=0
    r=1000
    for _ in range(80):
        m1=(2*l+r)/3
        m2=(l+2*r)/3
        d1=max_dist_x(m1)
        d2=max_dist_x(m2)
        if d1>d2:
            l=m1
        else:
            r=m2
    return math.sqrt(max_dist_x(l))

print(solve())