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

def dist(ax, ay, bx, by):
    return ((ax - bx)**2 + (ay - by)**2)**0.5

n = int(input())
XY = [tuple(int(x) for x in input().split()) for _ in range(n)]
if n == 2:
    (ax, ay), (bx, by) = XY[0], XY[1]
    print(dist(ax, ay, bx, by) / 2)
    exit()

ans = 0
for (ax, ay), (bx, by), (cx, cy) in combinations(XY, 3):
    a, b, c = sorted([dist(ax, ay, bx, by), dist(bx, by, cx, cy), dist(cx, cy, ax, ay)])
    cosC = (a**2 + b**2 - c**2) / (2 * a * b)
    if cosC < 0:
        ans = max(ans, c / 2)
    else:
        sinC = (1 - cosC**2)**0.5
        ans = max(ans, c / (2 * sinC))
print(ans)