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:
N = int(input())
XY = tuple(tuple(map(int, input().split())) for _ in range(N))

lx = 0
rx = 1000
ans = 10 ** 18
for _ in range(100):
    ly = 0
    ry = 1000
    mlx = (2 * lx + rx) / 3
    for _ in range(100):
        mry = (ly + 2 * ry) / 3
        mly = (2 * ly + ry) / 3

        Rr = max((x - mlx) ** 2 + (y - mry) ** 2 for x, y in XY)
        Rl = max((x - mlx) ** 2 + (y - mly) ** 2 for x, y in XY)
        if Rl < Rr:
            ry = mry
        else:
            ly = mly
    R_left = Rl

    ly = 0
    ry = 1000
    mrx = (lx + 2 * rx) / 3
    for _ in range(100):
        mry = (ly + 2 * ry) / 3
        mly = (2 * ly + ry) / 3

        Rr = max((x - mrx) ** 2 + (y - mry) ** 2 for x, y in XY)
        Rl = max((x - mrx) ** 2 + (y - mly) ** 2 for x, y in XY)
        if Rl < Rr:
            ry = mry
        else:
            ly = mly
    R_right = Rl

    if R_left < R_right:
        rx = mrx
    else:
        lx = mlx

print(R_right ** 0.5)