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

def calc_max_distance(guess_x,guess_y,data):
    max_distance = 0
    for x,y in data:
        distance = math.sqrt((guess_x-x)**2 + (guess_y-y)**2)
        max_distance = max(max_distance,distance)
    
    return max_distance



EPS = pow(10,-9)

def iterate(x,data):
    left = 0.0
    right = 1000.0
    while (right-left) > EPS:
        left_mid = left + (right-left)/3
        right_mid = right - (right-left)/3
        if calc_max_distance(x,left_mid,data) > calc_max_distance(x,right_mid,data):
            left = left_mid
        else:
            right = right_mid
            
    return calc_max_distance(x,left,data)
    


def outer_iterate(data):
    left = 0.0
    right = 1000.0
    while (right-left) > EPS:
        left_mid = left + (right-left)/3
        right_mid = right - (right-left)/3
        if iterate(left_mid,data) > iterate(right_mid,data):
            left = left_mid
        else:
            right = right_mid
            
    return iterate(left,data)


    
    




n = int(input())

data = []

for _ in range(n):
    a,b = map(int,input().split())
    data.append([a,b])


#print ( n,data )
        
print (outer_iterate(data))