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:

def want(x,y):

    ret = 0

    for i in xy:
        ret = max(ret, ((i[0]-x)**2+(i[1]-y)**2)**0.5)

    return ret


def want2(x):

    ly = miny
    ry = maxy

    while ry-ly > 10**(-7) and ry-ly > (ry / (10**6)):

        m1 = (ly*2+ry)/3
        m2 = (ly+ry*2)/3

        rm1 = want(x,m1)
        rm2 = want(x,m2)

        if rm1 > rm2:
            ly = m1
        else:
            ry = m2

    ansy = (ly+ry)/2
    return want(x,ansy)
    
    

N = int(input())

xy = []
minx = float("inf")
maxx = float("-inf")
miny = float("inf")
maxy = float("-inf")

for i in range(N):

    x,y = map(int,input().split())
    xy.append([x,y])

    minx = min(minx,x)
    miny = min(miny,y)
    maxx = max(maxx,x)
    maxy = max(maxy,y)


lx = minx
rx = maxx

while rx-lx > 10**(-7) and rx-lx > (rx / (10**6)):

    m1 = (lx*2+rx)/3
    m2 = (lx+rx*2)/3

    rm1 = want2(m1)
    rm2 = want2(m2)

    if rm1 > rm2:
        lx = m1
    else:
        rx = m2

print ((rm1+rm2)/2)