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:
# coding: utf-8
# Your code here!
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
read = sys.stdin.read

#h,w = [int(i) for i in readline().split()]
#n,*d = [int(i) for i in read().split()]

n = int(input())
xy = [[int(i) for i in readline().split()] for _ in range(n)]

def get_max_dist_and_index(a,b):
    d = [(a-x)**2 + (b-y)**2 for x,y in xy]
    m = 0
    idx = 0
    for i,di in enumerate(d):
        if m < di:
            idx = i
            m = di
    return m,idx

x0 = y0 = 0
r = 100.0
ratio = 0.99
ans = 10000000
for _ in range(100000):
    m,i = get_max_dist_and_index(x0,y0)
    #print(m,i,x0,y0,r)
    m **= 0.5
    ans = min(ans,m)
    dx,dy = (xy[i][0]-x0),(xy[i][1]-y0)
    x0 += r*dx/m
    y0 += r*dy/m
    r *= ratio
    
    
print(ans)