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:
# 2点 or 3点
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

def 外心(p1,p2,p3):
    # https://qiita.com/tatesuke/items/59133758ec25146766c3
    a,b = p1
    c,d = p2
    e,f = p3
    aa = a * a
    bb = b * b
    cc = c * c
    dd = d * d
    ee = e * e
    ff = f * f
    # 直線判定がめんどくさい!!!
    if (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f)) == 0:
        return 0, 0

    py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))

    if c == a:
        px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a))
    else:
        px = (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))

    return px, py

n = int(input())
points = [list(map(int, input().split())) for i in range(n)]

from itertools import combinations

候補 = []
# two
for p1, p2 in combinations(points, 2):
    px, py = (p1[0]+p2[0])/2, (p1[1]+p2[1])/2
    候補.append((px, py))

# three
for p1, p2, p3 in combinations(points, 3):
    候補.append(外心(p1,p2,p3))

from math import sqrt

ans = float("Inf")
for x,y in 候補:
    tmp = 0
    for px, py in points:
        tmp = max(tmp, (px-x)**2 + (py-y)**2)
    ans = min(ans, tmp)
ans = sqrt(ans)
print(ans)