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)]
l = 0
r = 2000
for _ in range(50):
    m = (l + r) / 2
    C = []
    for (x1, y1), (x2, y2) in combinations(XY, 2):
        d = ((x1-x2)**2+(y1-y2)**2)**0.5
        if d >= 2 * m:
            l = m
            break
        h = (m ** 2 - (d / 2) ** 2)**0.5
        hx = (y2-y1)/d*h
        hy = (x2-x1)/d*h
        x = (x1 + x2)/2
        y = (y1 + y2)/2
        C.append((x+hx,y-hy))
        C.append((x-hx,y+hy))
    else:
        if any(all(((x-x0)**2+(y-y0)**2)**0.5<=m+10**-8 for x0, y0 in XY) for x, y in C):
            r = m
        else:
            l = m
print(r)