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

def all_points(x, y):
	return max(one_point(x, y, _x, _y) for _x, _y in points)

def one_point(x0, y0, x1, y1):
	return math.pow(x0-x1, 2) + math.pow(y0-y1, 2)

def two():
	for i in range(N):
		for j in range(i+1, N):
			yield (points[i], points[j])

def three():
	for i in range(N):
		for j in range(i+1, N):
			for k in range(j+1, N):
				yield (points[i], points[j], points[k])

def process_two():
	minimum = 1e18
	for (a, b), (c, d) in two():
		x, y = (a+c)/2, (b+d)/2
		minimum = min(minimum, all_points(x, y))
	return minimum

def process_three():
	minimum = 1e18
	for (a,b), (c,d), (e,f) in three():
		try:
			if b==d==f:
				continue
			if d==b:
				a, b, c, d, e, f = e, f, a, b, c, d
			if f==b:
				a, b, c, d, e, f = c, d, e, f, a, b
			m0x, m0y = (a+c)/2, (b+d)/2
			m0 = -(c-a)/(d-b)
			b0 = m0y - m0*m0x
			
			m1x, m1y = (a+e)/2, (b+f)/2
			m1 = -(e-a)/(f-b)
			b1 = m1y - m1*m1x

			x = (b1-b0) / (m0-m1)
			y = m0*x + b0

			minimum = min(minimum, all_points(x, y))
		except ZeroDivisionError:
			continue
	return minimum


N = int(input())
points = []
for i in range(N):
	x, y = map(int, input().split())
	points.append((x, y))


print(math.sqrt(min(process_two(), process_three())))