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 itertools

n = int(input())
xy = []
for i in range(n):
    xy.append(list(map(int, input().split())))

R = []
if n >= 3:
    for i, j, k in itertools.combinations(xy, 3):
        if (j[0] - i[0]) * (k[0] - i[0]) + (j[1] - i[1]) * (k[1] - i[1]) <= 0:
            r = ((j[0] - k[0]) ** 2 + (j[1] - k[1]) ** 2) ** 0.5 / 2
            R.append(r)
        elif (i[0] - j[0]) * (k[0] - j[0]) + (i[1] - j[1]) * (k[1] - j[1]) <= 0:
            r = ((i[0] - k[0]) ** 2 + (i[1] - k[1]) ** 2) ** 0.5 / 2
            R.append(r)
        elif (i[0] - k[0]) * (j[0] - k[0]) + (i[1] - k[1]) * (j[1] - k[1]) <= 0:
            r = ((i[0] - j[0]) ** 2 + (i[1] - j[1]) ** 2) ** 0.5 / 2
            R.append(r)
        else:
            x1 = j[0] - i[0]
            x2 = k[0] - i[0]
            y1 = j[1] - i[1]
            y2 = k[1] - i[1]
            cos = (x1 * x2 + y1 * y2) /(((x1 ** 2 + y1 ** 2) ** 0.5) * ((x2 ** 2 + y2 ** 2) ** 0.5))
            sin = (1 - cos ** 2) ** 0.5
            if sin != 0:
                r = (((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5) / 2 / sin
                R.append(r)
            else:
                x = [i[0], j[0], k[0]]
                y = [i[1], j[1], k[1]]
                r = ((max(x) - min(x)) ** 2 + (max(y) - min(y)) ** 2) ** 0.5
                R.append(r / 2)
else:
    r = ((xy[0][0] - xy[1][0]) ** 2 + (xy[0][1] - xy[1][1]) ** 2) ** 0.5 / 2
    R.append(r)
print(max(R))