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
import math
import sys
read = sys.stdin.read
readline = sys.stdin.readline

n = int(readline())
m = map(int,read().split())
points = [(x, y) for x, y in zip(m, m)]

if n == 2:
    [(a, b), (c, d)] = points
    print(math.hypot(a - c, b - d) / 2)
    quit()


def center(a, b, c):
    M = pow(a[0], 2) - pow(b[0], 2) + pow(a[1], 2) - pow(b[1], 2)
    N = pow(a[0], 2) - pow(c[0], 2) + pow(a[1], 2) - pow(c[1], 2)
    Yab = a[1] - b[1]
    Xab = a[0] - b[0]
    Yac = a[1] - c[1]
    Xac = a[0] - c[0]
    d = Yac * Xab - Yab * Xac
    if d == 0:
        return None
    x = (M * Yac - N * Yab) / (2 * d)
    y = - (M * Xac - N * Xab) / (2 * d)
    r = math.hypot(x - a[0], y - a[1])
    return (x, y, r)


centers = []
for a, b, c in combinations(points, 3):
    cen = center(a, b, c)
    if cen is None:
        continue
    centers.append(cen)

dsq = 0
for a, b in combinations(points, 2):
    tmp = pow(a[0] - b[0], 2) + pow(a[1] - b[1], 2)
    if dsq > tmp:
        continue
    dsq = tmp
    cen = ((a[0] + b[0]) / 2, (a[1] + b[1]) / 2, math.sqrt(dsq) / 2)
centers.append(cen)

res = 1000
for cx, cy, cr in centers:
    for x, y in points:
        tr = math.hypot(x - cx, y - cy)
        if tr > cr + 10e-6:
            break
    else:
        if cr < res:
            res = cr
print(res)