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 itertools import combinations
N = int(input())
XY = [tuple(map(int, input().split())) for _ in range(N)]
def f(x_, y_):
    return max((x-x_)**2+(y-y_)**2 for x, y in XY)**.5
def g(x):
    yl = 0
    yr = 1000
    for _ in range(80):
        yl_ = (yl*2 + yr) / 3
        yr_ = (yl + yr*2) / 3
        if f(x, yl_) > f(x, yr_):
            yl = yl_
        else:
            yr = yr_
    return f(x, yl_)

xl = 0
xr = 1000
for _ in range(80):
    xl_ = (xl*2 + xr) / 3
    xr_ = (xl + xr*2) / 3
    if g(xl_) > g(xr_):
        xl = xl_
    else:
        xr = xr_
print(g(xl))