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:
#abc_151_f

#utilize the characeristic of l(x,y) being convex
#Thus, 3bun search is available

n = int(input())
l = []
for i in range(n):
    x,y = [int(j) for j in input().split()]
    l.append((x,y))
    
#determine the fuction representing the longest distance ^2 from the center point to designated N points.
def loss(x,y):
    maxi = 0
    for i,j in l:
        maxi = max(maxi, (i-x)**2 + (j-y)**2)
    return maxi

def f(x):
    #return min l(x,y)
    left = 0
    right = 1000
    num = 100

    for i in range(num):
        c1 = (2*left + right)/3
        c2 = (left + 2*right)/3    
        if(loss(x,c1)<loss(x,c2)):
            right = c2
        else:
            left = c1
            
    return loss(x,left)

        
    

left = 0
right = 1000
num = 100

for i in range(num):
    c1 = (2*left + right)/3
    c2 = (left + 2*right)/3    
    if(f(c1)<f(c2)):
        right = c2
    else:
        left = c1
        
ans = f(left)**0.5
print(ans)