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 = [complex(*map(int, input().split())) for _ in range(N)]
ans = 10**18

def calc(center):
    return max(abs(center - x) for x in XY)

for A in XY:
    for B in XY:
        center = (A + B) / 2
        ans = min(ans, calc(center))

        for C in XY:
            a, b, c = abs(B - C), abs(C - A), abs(A - B)

            S = 0
            T = complex(0, 0)
            for (x, y, z), u in zip([(a, b, c), (b, c, a), (c, b, a)], (A, B, C)):
                O = x**2 * (y**2 + z**2 - x**2)
                S += O
                T += O * u

            if S == 0:
                continue
            ans = min(ans, calc(T / S))

print(ans)