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 maxdis(cx,cy):
    global x, y
    dmax = d = 0
    xf, yf = 0, 0
    for i in range(len(x)):
        d = max(d ,((x[i] - cx) ** 2 + (y[i] -cy) ** 2) ** 0.5)
        if dmax < d:
            dmax = d
            xf, yf =x[i], y[i]
    return xf, yf

N = int(input())
x = []; y = []
for i in range(N):
    xi, yi = map(int,input().split())
    x.append(xi);y.append(yi)

cx, cy = 500, 500
r = 500 * 1.5
i=0
while (r > 10 ** -10):
    xf, yf = maxdis(cx,cy)
    df = ((xf - cx) ** 2 + (yf - cy) ** 2) ** 0.5
    r *= 0.999
    dx = r * (xf - cx) / df
    dy = r * (yf - cy) / df
    cx += dx; cy += dy
    i += 1

    # print(i, cx, cy, df, r, xf, yf)

print(df)