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:
#!/usr/bin/env python3
from math import hypot

EPS = 10 ** -8


def f(r):
    global n, xy
    cs = []
    for i in range(n):
        for j in range(i + 1, n):
            x0, y0 = xy[i]
            x1, y1 = xy[j]
            d = hypot(x1 - x0, y1 - y0)
            if r - d / 2 < EPS:
                continue
            h = (r ** 2 - (d / 2) ** 2) ** 0.5
            c = [(x0 + x1) / 2, (y0 + y1) / 2]
            cs.append([c[0] + h * (y0 - y1) / d, c[1] + h * (x1 - x0) / d])
            cs.append([c[0] - h * (y0 - y1) / d, c[1] - h * (x1 - x0) / d])
    for cx, cy in cs:
        if all(hypot(x - cx, y - cy) - r < EPS for x, y in xy):
            return True
    return False


n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
ok = 10 ** 9
ng = 0
while abs(ok - ng) > EPS:
    m = (ok + ng) / 2
    if f(m):
        ok = m
    else:
        ng = m
print(ok)