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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

def main():
    def dist_x(cx):
        b=0
        t=1000
        for _ in range(roop):
            cb=(t+2*b)/3
            ct=(2*t+b)/3
            if dist_xy(cx,cb)>dist_xy(cx,ct):
                b=cb
            else:
                t=ct
        return dist_xy(cx,b)

    def dist_xy(cx,cy):
        mx=0
        for x,y in xy:
            d=(x-cx)**2+(y-cy)**2
            if d>mx:mx=d
        return mx

    n = II()
    xy = [LI() for _ in range(n)]
    l=0
    r=1000
    roop=100
    for _ in range(roop):
        cl=(2*l+r)/3
        cr=(l+2*r)/3
        if dist_x(cl)>dist_x(cr):
            l=cl
        else:
            r=cr
    print(dist_x(l)**0.5)

main()