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():
    n=II()
    xy=[LI() for _ in range(n)]
    sx=sy=1000
    bx=by=0
    for x,y in xy:
        if x<sx:sx=x
        if x>bx:bx=x
        if y<sy:sy=y
        if y>by:by=y
    x0=(sx+bx)/2
    y0=(sy+by)/2
    m=100
    roop=10000
    for _ in range(roop):
        maxd=0
        for x,y in xy:
            d=(x-x0)**2+(y-y0)**2
            if d>maxd:
                maxd=d
                vx=x-x0
                vy=y-y0
        rate=m/(vx**2+vy**2)**0.5
        x0+=vx*rate
        y0+=vy*rate
        m*=0.998
    print(maxd**0.5)

main()