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())
X = []
for _ in range(N):
    x, y = map(int, input().split())
    X.append((x, y))

def circumcenter(p, q, r):
    a, b = p
    c, d = q
    e, f = r
    a, b, c, d = a-e, b-f, c-e, d-f
    g = a * d-b * c
    if p == q: return ((p[0]+r[0]) / 2, (p[1]+r[1]) / 2)
    if g == 0: return (0, 0)
    ab = a * a + b * b
    cd = c * c + d * d
    return ((d * ab - b * cd) / (2 * g) + e, (a * cd - c * ab) / (2 * g) + f)

mi = 2000000
for i, p in enumerate(X):
    for j, q in enumerate(X[i:]):
        for r in X[j+1:]:
            a, b = circumcenter(p, q, r)
            mi = min(mi, max([(x-a)**2+(y-b)**2 for x, y in X]))

print(mi ** 0.5)