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

def f(x, y):
    r = 0
    for xi, yi in XY:
        d = ((x - xi)**2 + (y - yi)**2)**0.5
        if d > r:
            r = d
    return r

def g(x):
    l, r = 0, 1000
    for _ in range(75):
        c1, c2 = (2 * l + r) / 3, (l + 2 * r) / 3
        if f(x, c1) > f(x, c2):
            l = c1
        else:
            r = c2
    return f(x, l)

l, r = 0, 1000
for _ in range(75):
    c1, c2 = (2 * l + r) / 3, (l + 2 * r) / 3
    if g(c1) > g(c2):
        l = c1
    else:
        r = c2

print(g(l))