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

read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
inputs = sys.stdin.buffer.readlines


#mod=10**9+7
# rstrip().decode('utf-8')
# map(int,input().split())
#import numpy as np


def main():
	n=int(input())
	x=[]
	y=[]
	for _ in range(n):
		xin,yin=map(int,input().split())
		x.append(xin)
		y.append(yin)
	
	li=[[0]*n for _ in range(n)]
	
	for i in range(n):
		for j in range(n):
			if i>j:
				li[i][j]=((x[i]+x[j])/2,(y[i]+y[j])/2,(((x[j]-x[i])**2)+(y[j]-y[i])**2)**0.5)
				li[j][i]=(-(y[j]-y[i]),(x[j]-x[i]))
	l=0
	h=1000
	
	
	for ii in range(100):
		m=(l+h)/2
		ko=[]
		for i in range(n):
			for j in range(n):
				if i>j:
					k=4*(m**2)-(li[i][j][2])**2
					if k>0:
						k=k/(4*(li[i][j][2])**2)
						k=k**0.5
						ko.append((li[i][j][0]+k*li[j][i][0],li[i][j][1]+k*li[j][i][1]))
						ko.append((li[i][j][0] - k * li[j][i][0], li[i][j][1] - k * li[j][i][1]))
		if len(ko)==0:
			l=m
			continue
		
		for point in ko:
			f=0
			for i in range(n):
				length=((point[0]-x[i])**2+(point[1]-y[i])**2)**0.5
				if length-0.0000000000001>m:
					f=1
					break
			if f==0:
				h=m
				break
		else:
			l=m
		
		
	print(l)
	
		
		
		
		
		
		
		
		
		
	
	
	
	
	
	
	
	


if __name__ == "__main__":
	main()