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 sys
input = sys.stdin.buffer.readline
from itertools import combinations
from math import hypot
n=int(input())
P=[tuple(map(int,input().split())) for _ in range(n)]
ans=1e9
for p1,p2 in combinations(P,2):
	X,Y=(p1[0]+p2[0])/2,(p1[1]+p2[1])/2
	r=0
	for x,y in P:
		t=hypot(X-x,Y-y)
		if r<t:r=t
	if ans>r:ans=r
if n>2:
	ans_=1e9
	for p1,p2,p3 in combinations(P,3):
		a=hypot(p2[0]-p3[0],p2[1]-p3[1])
		b=hypot(p3[0]-p1[0],p3[1]-p1[1])
		c=hypot(p1[0]-p2[0],p1[1]-p2[1])
		if (a+b+c)-2*max(a,b,c)<1e-8:continue
		s,t,u=(-a*a+b*b+c*c)*a*a,(a*a-b*b+c*c)*b*b,(a*a+b*b-c*c)*c*c
		X=(s*p1[0]+t*p2[0]+u*p3[0])/(s+t+u)
		Y=(s*p1[1]+t*p2[1]+u*p3[1])/(s+t+u)
		r=0
		for x,y in P:
			t=hypot(X-x,Y-y)
			if r<t:r=t
		if ans_>r:ans_=r
	# print(ans_)
	ans=min(ans,ans_)
print(ans)