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.readline

N=int(input())
P=[tuple(map(int,input().split())) for i in range(N)]

def calcdismax(x,y):
    MAX=0
    for px,py in P:
        MAX=max(MAX,(px-x)**2+(py-y)**2)

    return MAX
        
delta=10**(-10)

def div100(xmin,xmax,ymin,ymax):

    xh=(xmax-xmin)/100
    yh=(ymax-ymin)/100

    MIN=1<<30
    MINx=0
    MINy=0

    for i in range(101):
        xk=xmin+xh*i
        for j in range(101):
            yk=ymin+yh*j
            cd=calcdismax(xk,yk)

            #print(xk,yk,cd)

            if MIN>cd:
                MIN=cd
                MINx=xk
                MINy=yk

    #print(MINx,MINy,MIN)

    return MINx,MINy

now=500
k=500
l=500
while now>10**(-7):
    k,l=div100(k-now,k+now,l-now,l+now)
    now/=2

import math
print(math.sqrt(calcdismax(k,l)))