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:
n = int(input())
xy=[list(map(int,input().split())) for i in range(n)]
import math
def calc(x1, y1, x2, y2, x3, y3):
    try:
        d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
        x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
        y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
        r2 = (x - x1) ** 2 + (y - y1) ** 2
    except:
        return 0,0,-1
    else:
        return x,y,r2
def check(cx,cy,r2):
    for tmp in xy:
        x,y=tmp
        if (x-cx)**2 + (y-cy)**2 > r2:
            return False
    return True

ans=float("inf")
eps=10**(-5)
for i in range(n):
    for j in range(i+1,n):
        x1,y1=xy[i]
        x2,y2=xy[j]
        cx=(x1+x2)/2
        cy=(y1+y2)/2

        r2=(cx-x1)**2+(cy-y1)**2
        if check(cx,cy,r2+eps):
            ans=min(ans,math.sqrt(r2))

for i in range(n):
    for j in range(i+1,n):
        for k in range(j+1,n):
            x1,y1=xy[i]
            x2,y2=xy[j]
            x3,y3=xy[k]
            cx,cy,r2=calc(x1, y1, x2, y2, x3, y3)
            if 0 < r2 and check(cx,cy,r2+eps):
                ans=min(ans,math.sqrt(r2))
print(ans)