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:
import math
from itertools import combinations

eps = 10 ** -7

def midpoint(a, b):
    return (a[0] + b[0]) / 2, (a[1] + b[1]) / 2

def distance(a, b):
    return ((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2) ** 0.5

def within(c, r, a):
    return (a[0] - c[0]) ** 2 + (a[1] - c[1]) ** 2 <= r ** 2 + eps

def tcircle(t1, t2, t3):
    x1, y1 = t1
    x2, y2 = t2
    x3, y3 = t3
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d == 0:
        return (0.0, 0.0), -1.0
    x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
    y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
    r = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
    return (x, y), r

def main():
    N = int(input())
    L = [tuple(map(int, input().split())) for _ in range(N)]
    br = float('inf')
    for p, q in combinations(L, 2):
        c, r = midpoint(p, q), distance(p, q) / 2
        if all(within(c, r, i) for i in L):
            return r
        ac, ar = (0.0, 0.0), 0.0
        for i in L:
            if within(c, r, i):
                continue
            pc, pr = tcircle(p, q, i)
            if pr == -1:
                break
            if ar < pr:
                ac, ar = pc, pr
        else:
            if ar < br and all(within(ac, ar, i) for i in L):
                br = ar
    return br

print(main())