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:
from math import hypot

N = int(input())
pts = [tuple(map(int, input().split())) for _ in range(N)]

def getIntersectionLL(a1, b1, c1, a2, b2, c2):
    v = a1*b2 - a2*b1
    if v == 0:
        return (None, None)
    else:
        return ((b1*c2-b2*c1) / v, (-a1*c2+a2*c1) / v)
def getPerpendicularBisector(x1, y1, x2, y2):
    dx, dy = x2-x1, y2-y1
    xM, yM = (x1+x2)/2, (y1+y2)/2
    return (-dx, -dy, dx*xM+dy*yM)
def getCircumcenter(x1, y1, x2, y2, x3, y3):
    a12, b12, c12 = getPerpendicularBisector(x1, y1, x2, y2)
    a13, b13, c13 = getPerpendicularBisector(x1, y1, x3, y3)
    intLL = getIntersectionLL(a12, b12, c12, a13, b13, c13)
    return intLL

ans = float('inf')
for i in range(N):
    x1, y1 = pts[i]
    for j in range(i+1, N):
        x2, y2 = pts[j]
        xC, yC = (x1+x2)/2, (y1+y2)/2
        dist = max([hypot(x-xC, y-yC) for x, y in pts])
        ans = min(ans, dist)

for i in range(N):
    x1, y1 = pts[i]
    for j in range(i+1, N):
        x2, y2 = pts[j]
        for k in range(j+1, N):
            x3, y3 = pts[k]
            xC, yC = getCircumcenter(x1, y1, x2, y2, x3, y3)
            if xC is None: continue
            dist = max([hypot(x-xC, y-yC) for x, y in pts])
            ans = min(ans, dist)

print(ans)