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:
#!usr/bin/env python3
from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    def check(X,Y,r2,err=1e-6):
        for x,y in p:
            if (x-X)**2 + (y-Y)**2 > r2+err:
                return 0
        return 1

    n = I()
    p = LIR(n)
    ans = float("inf")
    for i in range(n):
        xi,yi = p[i]
        for j in range(i+1):
            xj,yj = p[j]
            X = (xi+xj) / 2
            Y = (yi+yj) / 2
            r2 = (xi-X)**2+(yi-Y)**2
            if ans > r2 and check(X,Y,r2):
                ans = r2
            x,y = xj-xi,yj-yi
            for k in range(j):
                xk,yk = p[k]
                a,b = xk-xi,yk-yi
                deno = 2*(a*y-b*x)
                if deno == 0:
                    continue
                X = (y*(a**2+b**2)-b*(x**2+y**2))/deno+xi
                Y = (a*(x**2+y**2)-x*(a**2+b**2))/deno+yi
                r2 = (xi-X)**2+(yi-Y)**2
                if ans > r2 and check(X,Y,r2):
                    ans = r2
    print(ans**0.5)
    return

#Solve
if __name__ == "__main__":
    solve()