Problem:
Score : 600 points

Problem Statement

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}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in Python (3.4.3) (judge verdict: Accepted)

# coding: utf-8

import math

N = int(input())

xy = []
for i in range(N):
	xy.append([int(p) for p in input().split()])

def dist(a, b):
	return math.sqrt((a[0]-b[0])**2 + (a[1]-b[1])**2)

def max_dist(a):
	max_d = 0
	for b in xy:
		max_d = max(max_d, dist(a, b))
	return max_d

def g(a):
	ly = 0
	ry = 1000
	for j in range(100):
		#print("    ly = " + str(ly) + " ry = " + str(ry))
		c1 = (ly*2+ry)/3
		c2 = (ly+ry*2)/3
		if max_dist([a,c1]) > max_dist([a,c2]):
			ly = c1
		else:
			ry = c2
	return max_dist([a,ly])

lx = 0
rx = 1000
for i in range(100):
	#print("lx = " + str(lx) + " rx = " + str(rx))
	c1 = (lx*2+rx)/3
	c2 = (lx+rx*2)/3
	if g(c1) > g(c2):
		lx = c1
	else:
		rx = c2

print(g(lx))