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 math
N, = map(int, input().split())
xs = []
ys = []
for _ in range(N):
    x, y = map(int, input().split())
    xs.append(x)
    ys.append(y)

def bb(a,b,c,d,e,f):
    if not (c-a)*(f-b)-(e-a)*(d-b):
        return None, None
    aa = a * a
    bb = b * b
    cc = c * c
    dd = d * d
    ee = e * e
    ff = f * f
    py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))
    px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a)) \
        if (c == a) else (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))
    return px, py


pxs = []
pys = []
for i in range(N):
    for j in range(i+1, N):
        for k in range(j+1, N):
#            print(i,j,k)
            px, py = bb(xs[i],ys[i],xs[j],ys[j],xs[k],ys[k])
            if not px:
                continue
            pxs.append(px)
            pys.append(py)
for i in range(N):
    for j in range(i+1, N):
        pxs.append((xs[i]+xs[j])/2)
        pys.append((ys[i]+ys[j])/2)

rr = 10**10
for px, py in zip(pxs,pys):
    r = 0
    for x, y in zip(xs, ys):
        r = max(r, (x-px)**2+(y-py)**2)
    rr = min(rr, r)
print(rr**0.5)