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:
Point = complex


N, *XY = map(int, open(0).read().split())

P = [Point(x, y) for x, y in zip(*[iter(XY)] * 2)]

def max_distance(center):
    return max(abs(center - p) for p in P)

def g(x):
    left, right = -1000, 1000
    for _ in range(100):
        m1 = (left * 2 + right) / 3
        m2 = (left + right * 2) / 3
        if max_distance(Point(x, m1)) < max_distance(Point(x, m2)):
            right = m2
        else:
            left = m1

    return max_distance(Point(x, left))

left, right = -1000, 1000
for _ in range(100):
    m1 = (left * 2 + right) / 3
    m2 = (left + right * 2) / 3
    if g(m1) < g(m2):
        right = m2
    else:
        left = m1

print(g(left))