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 math import hypot

MAX = 1000

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

def dist(x1, y1, x2, y2):
    return hypot(x1 - x2, y1 - y2)

def maxDist(x, y):
    res = 0
    for xx, yy in a:
        res = max(res, dist(x, y, xx, yy))
    return res

def f(x):
    left, right = 0, MAX
    for _ in range(80):
        y1 = (left * 2 + right) / 3
        y2 = (left + right * 2) / 3
        if maxDist(x, y1) > maxDist(x, y2):
            left = y1
        else:
            right = y2
    return maxDist(x, left)

left, right = 0, MAX
for _ in range(80):
    x1 = (left * 2 + right) / 3
    x2 = (left + right * 2) / 3
    if f(x1) > f(x2):
        left = x1
    else:
        right = x2
print(f(left))